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Applied Music Fundamentals: Writing, Singing, Listening
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APPLIED MUSIC FUNDAMENTALS Writing, Singing, and Listening JENA ROOT Youngstown State University New York Oxford OXFORD UNIVERSITY PRESS Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Copyright © 2014 by Oxford University Press For titles covered by Section 112 of the US Higher Education Opportunity Act, please visit www.oup.com/us/he for the latest information about pricing and alternate formats. Published by Oxford University Press 198 Madison Avenue, New York, New York 10016 http://www.oup.com Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Root, Jena. Applied music fundamentals : writing, singing, and listening / Jena Root, Youngstown State University. pages cm Includes bibliographical references and index. ISBN 978-0-19-984677-1 1. Music theory. I. Title. MT7.R784 2014 781.2—dc23 2013006146 Printing number: 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper To my parents, Robert Root and Linda Groff George, who were my first teachers. This page intentionally left blank CONTENTS Preface xv List of Informed Listening Pieces and Source Recordings xxiii CHAPTER 1 INTRODUCTION TO MUSIC NOTATION CHAPTER GOALS 1 Elements of Music 1 The Staff and the Treble Clef 2 Note Names in the Staff 2 Mapping Notes to the Staff The Treble Clef 2 3 Ledger Lines in the Treble Clef Replay 1 3 4 The Bass Clef 4 Note Names in the Bass Clef 4 Ledger Lines in the Bass Clef 5 Replay 6 Rhythm and Meter 6 Elements of Rhythm 6 Quadruple Meter and Basic Durations Metric Accents 8 The Dotted Half Note and Eighth Notes Triple Meter 10 Duple Meter 11 Meter Categories 9 11 Summary of Durations Replay 6 12 12 The Repeat Sign 13 Repeat Signs 13 Repeat Signs with Endings Replay 13 13 Notation 14 Clefs 14 Noteheads Ledger Lines 15 15 |v Stems 15 Bar Lines and Repeats 16 The Augmentation Dot 17 Beamed Eighth Notes 17 Time Signatures 18 Note-Spacing Within the Measure MEMORIZATION STRATEGIES Pitch Name Fluency 18 19 19 Singing and Hearing Exercises Duple Meter Patterns 20 Triple Meter Patterns 21 20 Quadruple Meter Patterns 21 Informed Listening: Examples for Study Duple Meter 22 Triple Meter 23 Quadruple Meter 22 24 Informed Listening: Interesting Examples 25 Informed Listening: Examples with Questions Drills to Go 28 Classroom Activities Written Exercises Composition 29 32 38 CHAPTER GOALS REVISITED CHAPTER 2 40 PITCH: THE PIANO KEYBOARD/RHYTHM: RESTS, TIES, AND SYNCOPATION CHAPTER GOALS The Keyboard 41 41 The White Keys of the Keyboard Half Steps and Whole Steps Replay 42 Accidentals 43 Sharps, Flats, and Naturals Enharmonic Notes 41 42 43 44 Why Do We Need Enharmonics? 45 Double Sharps and Double Flats 46 Diatonic and Chromatic Steps Replay Octave Designation 48 The Ottava Sign 48 Replay Contents 47 47 Octave Designation Numbers vi| 26 49 49 41 Rhythm 49 Rests 49 Ties 52 Dotted Quarter Notes and Syncopation The Anacrusis (Pickup Measure) Replay Notation 53 55 56 57 Accidentals Rests 58 Ties 59 57 Dotted Quarter Note and Single Eighth Note Notation and Metric Hierarchy 60 MEMORIZATION STRATEGIES 61 SINGING EXERCISES 61 Two-Beat Patterns 62 Three-Beat Patterns Hearing Exercises 62 66 Informed Listening: Examples for Study 68 Informed Listening: Examples with Questions Drills to Go 71 75 Classroom Activities Written Exercises Composition 75 76 87 CHAPTER GOALS REVISITED CHAPTER 3 59 89 PITCH: MAJOR KEYS 1/RHYTHM: BEAT SUBDIVISIONS CHAPTER GOALS 90 The Major Scale 90 Structure and Scale Degree Names Replay 90 92 Building Major Scales (up to Four Sharps or Flats) Replay Replay 95 98 Summary of Major Key Signatures and Scales 99 100 Sixteenth Notes 100 Dotted Eighth Notes Replay Notation 92 95 Major Key Signatures (up to Four Sharps or Flats) Rhythm 90 101 103 103 Notes, Rests, and Beaming 103 Contents |vii Beaming 104 Flagged Vocal Notation 104 MEMORIZATION STRATEGIES 105 Memorizing Scale Content 105 Mapping Scales to Solfège 105 Practice Strategies 106 Playing Scales in Tetrachord Position Keyboard and Singing Exercises 107 Sixteenth Note Combinations 108 106 Sixteenth Note Combinations with Leading Rests Hearing Exercises 112 Informed Listening: Examples for Study 114 Informed Listening: Examples with Questions Drills to Go 116 121 Classroom Activities Written Exercises Composition 121 123 134 CHAPTER GOALS REVISITED CHAPTER 4 108 136 PITCH: MAJOR KEYS 2/RHYTHM: TRIPLETS CHAPTER GOALS 137 137 More Major Scales 137 Major Scales with More Than Four Sharps or Flats Enharmonic Keys 139 Table of Key Signatures and the Circle of Fifths 141 Summary of Major Key Signatures and Scales 143 Replay 143 The Tonic Triad and Tendency Tones Replay Rhythm 145 145 Triplets 145 Replay 146 Notation 147 Writing Key Signatures Writing Triplets 147 147 MEMORIZATION STRATEGIES 149 A Visual Way to Memorize Scales 149 Shortcuts for Identifying Key Signatures 149 A Visual Way to Memorize Key Signatures 150 Flashcards 150 Practice Strategies viii| 144 Contents 151 137 Keyboard and Singing Exercises 151 Sixteenth Note Combinations and Triplet 152 Sixteenth Note Combinations and Triplet with Leading Rests Hearing Exercises 158 Informed Listening: Examples for Study 158 Informed Listening: Examples with Questions 161 Informed Listening: Tendency Tones in the Music of the Beatles Drills to Go 163 164 Classroom Activities Written Exercises Composition 164 167 177 CHAPTER GOALS REVISITED CHAPTER 5 152 179 PITCH: MINOR KEYS 1/RHYTHM: EIGHT- AND TWO-BASED SIMPLE METER CHAPTER GOALS 180 The Natural Minor Scale 181 Minor Scale Structure and Relative Keys Replay 181 185 Parallel Keys 185 Summary of Minor Key Signatures and Scales Replay La-based Minor 189 Do-based Minor 189 Replay 189 191 191 Eight-based Simple Meter 191 Two-based Simple Meter 194 Replay Notation 188 188 Minor Scales and Solfège Rhythm 180 195 196 MEMORIZATION STRATEGIES 197 Parallel and Relative Keys 197 Flashcards 198 Practice Strategies 198 Keyboard and Singing Exercises Patterns in Three-eight 199 Patterns in Three-two 200 Hearing Exercises 199 206 Informed Listening: Examples for Study Major to Relative Minor 208 Minor to Relative Major 208 208 Contents |ix Major to Parallel Minor 209 Minor to Parallel Major 209 Informed Listening: Examples with Questions Distinguishing Major and Minor Major Moving to Minor 211 Minor Moving to Major 212 Drills to Go 210 212 Classroom Activities Written Exercises Composition 213 214 227 CHAPTER GOALS REVISITED CHAPTER 6 210 229 RHYTHM: INTRODUCTION TO COMPOUND METER/PITCH: MINOR KEYS 2 CHAPTER GOALS 230 Compound Meter 230 Compound Meter vs. Triplets Counting Compound Meter 232 233 Three-four vs. Six-eight Meter Songs in Compound Meter Replay 234 235 237 The Harmonic and Melodic Minor Scales The Natural Minor Scale (Review) The Harmonic Minor Scale 237 237 238 Why Does the Harmonic Minor Scale Exist? Summary of Harmonic Minor Scales The Melodic Minor Scale Scale Degree Names in Minor Replay 240 241 Summary of Melodic Minor Scales Minor Scales in Music 238 242 244 244 245 The Tonic Triad and Tendency Tones in Minor Keys Replay Notation 245 245 MEMORIZATION STRATEGIES 247 KEYBOARD AND SINGING EXERCISES Compound Meter Patterns 247 247 Compound Meter Patterns with Leading Rests Hearing Exercises 254 Informed Listening: Examples for Study 257 Informed Listening: Examples with Questions Drills to Go 262 Classroom Activities x| Contents 245 264 258 248 230 Written Exercises Composition 267 276 CHAPTER GOALS REVISITED CHAPTER 7 279 PITCH: INTERVALS/RHYTHM: COMPOUND METER REVIEW CHAPTER GOALS 280 Interval Number and Quality Replay 280 281 Major, Minor, and Perfect Intervals Replay 281 285 Melodic and Harmonic Intervals Replay 285 285 Recognizing Major, Minor, and Perfect Intervals Building Major, Minor, and Perfect Intervals 288 Building Intervals Below a Given Note 289 Augmented and Diminished Intervals 286 288 Building Intervals Above a Given Note Replay 290 293 Summary of Interval Qualities 293 Doubly Augmented and Doubly Diminished Intervals Inversion 295 Chromatic Melody Inversion Interval Inversion 296 297 297 Enharmonic Intervals 297 Compound Intervals 298 Other Interval Patterns 299 Intervals in the Descending Major Scale Intervals in the Natural Minor Scale Replay Notation 294 295 Diatonic Melody Inversion Replay 280 299 300 301 301 MEMORIZATION STRATEGIES Interval Shapes 303 303 Letter-name Distances 303 Plain Interval Qualities 303 Identifying Intervals in a Musical Context Keyboard and Singing Exercises Hearing Exercises 305 306 310 Informed Listening: Examples for Study 312 Informed Listening: Examples with Questions 314 Contents |xi Drills to Go 316 Classroom Activities Written Exercises 316 318 Analysis and Composition 336 CHAPTER GOALS REVISITED CHAPTER 8 342 PITCH: TRIADS/RHYTHM: FOUR- AND SIXTEEN-BASED COMPOUND METER CHAPTER GOALS 343 Triad Structure and Quality Major Triads 345 Minor Triads 346 Augmented Triads 347 Diminished Triads 348 343 Summary of Triad Qualities Replay 349 Triad Inversions Replay 348 349 349 Identifying Triads in a Musical Context Replay 350 351 Sixteen- and Four-based Compound Meter Sixteen-based Compound Meter Replay 352 354 Four-based Compound Meter Replay 351 354 356 Summary of Common Meter Types Simple Meter 357 357 Compound Meter 357 MEMORIZATION STRATEGIES 359 Recognizing Triad Qualities 359 Hearing Triads in Root Position 363 Recognizing Triad Inversions by Sight and Sound Keyboard and Singing Exercises Patterns in Six-sixteen Patterns in Six-four Hearing Exercises 364 365 365 372 Informed Listening: Examples for Study 373 Informed Listening: Examples with Questions Informed Listening: Challenging Examples Drills to Go 376 Classroom Activities Written Exercises xii| Contents 377 378 374 376 364 343 Composition 390 CHAPTER GOALS REVISITED CHAPTER 9 392 (POSTLUDE) PITCH: DIATONIC TRIADS/RHYTHM: ADVANCED RHYTHMIC CONCEPTS 393 CHAPTER GOALS 393 Diatonic Triads in Major Keys 393 Diatonic Triads in Minor Keys 394 Replay Harmony 395 396 Labeling Triads in Music 396 Diatonic Triad Functions 397 Primary Triads 397 Introduction to Voice Leading Secondary Triads Replay 398 400 402 Advanced Rhythmic Concepts Irregular Meter 402 402 Subtriplets and Supertriplets Irregular Tuplets 405 Duplets and Quadruplets Hemiola 406 Replay 407 SINGING EXERCISES Hearing Exercises 403 405 409 412 Informed Listening: Examples for Rhythm Study Informed Listening: Classroom Activity Drills to Go 417 419 Written Exercises 420 CHAPTER GOALS REVISITED CODA 426 427 APPENDIX A: ALTO CLEF AND TENOR CLEF APPENDIX B: SINGING PITCH NAMES 428 430 APPENDIX C: CHROMATIC SOLFÈGE SYLLABLES APPENDIX D: MODES GLOSSARY 432 433 APPENDIX E: SEVENTH CHORDS INDEX 412 435 437 442 Contents |xiii This page intentionally left blank PREFACE TO THE STUDENT Why Does Music Move Us? Applied Music Fundamentals is an intensive course in the foundations of music. You may have purchased this book as part of a music theory course, to work on your own in preparation for college music theory, or perhaps to brush up your skills after a number of years away from musical study. When you use this book, you will not just read about music; you will do music through listening, singing, playing, and composing. Take a moment and think about one of your favorite musical pieces. It may be a song, a symphony, a jazz chart, or part of a movie or video-game soundtrack. In your mind, go to a place in the music that, no matter how many times you hear it, always stirs your emotions. It may surprise you, make you smile, or even cause you to feel deep sadness. Whatever your reaction, the music compels you to listen again and again. And again, the music astonishes you—just as if you are hearing it for the first time. Musical taste is highly personal, and these provocative moments are most certainly different for everyone. But if you are holding this book right now, there is a good chance that you have had this experience and are eager to learn more about music. Why does music have the power to evoke such visceral and emotional responses in us? I am sorry to say that you will not find the answer to that question in this book. In fact, it can never be fully answered; but it can be explored. We have a sense that music “works” because composers use musical elements such as melody, harmony, and rhythm to build tension and set up expectations. Sometimes the expectations are met; other times, they are unfulfilled, diverted, postponed, or answered in a new and beautiful way that we haven’t considered. As a starting point in your musical study, this book will teach you about the building blocks that composers use to create those expectations. Organization and Features Each chapter of this text follows the same structure. Chapter Goals are provided at the beginning of every chapter and reiterated at the end, giving you an opportunity to monitor your progress and affirm your new skill set before moving forward. After the Chapter Goals, the key concepts covered in each chapter are described in detail. Then, a number of different learning strategies are outlined to help you achieve your goal of understanding music fundamentals: • Memorization and Practice Strategies help to move you beyond traditional mnemonic devices toward a more intuitive understanding of scales, triads, and keys. Strategies include: o Tips for making flashcards o Practical suggestions for organizing the material into small bites for more efficient memorization and better retention o Visual, aural, and kinesthetic exercises designed to accommodate various learning styles |xv • Keyboard, Singing, and Hearing Exercises reinforce the crucial connection between sound and notation. Although not intended as a standalone ear-training book, Applied Music Fundamentals provides skills-based exercises in every chapter so that you will learn to apply the written concepts out loud and in real time. • Informed Listening examples challenge you to analyze repertoire by ear, without reference to printed music, in order to foster real-time musical understanding. • Drills to Go are short, portable exercises that you can do throughout the day during downtime (e.g., at the gym, walking between classes, waiting in line for lunch, etc.). Easily learned and memorized, Drills to Go help to reinforce skills and content between class meetings and study sessions. • Written Exercises stress learning through repetition with variation. For example, you are asked to write scales in treble clef, in bass clef, in letter names, and on the keyboard, and then to find a scale by unscrambling a set of given pitches, to write a composition with it, and lead the class in an improvisation over it. Although the same material is repeated and reinforced, the delivery method is varied, keeping you engaged and on task. • Classroom Activities encourage you to lead the class in group singing, guided improvisation, and gamelike drills. If you are working independently, many of the Classroom Activities may be modified for use with a tutor, study partner, or even a voice recorder. • Composition Exercises at the end of every chapter offer you the opportunity to apply your acquired musical skills and concepts in a creative and personal way. Although most of the composition assignments are traditionally constructed, a few encourage you to experiment with non-tonal composition. Most of the activities are highly adaptable, and they may be done as collaborative projects. In addition, there are special features that are called out within the text: • Interactive Online Examples (at www.oup.com/us/root) supplement the printed text, allowing for adaptation to suit a traditional classroom course, a distance-learning model, or the individual student preparing for college placement exams. Web-based examples are playback-enabled and permit you to see the music as it plays, hear individual notes or voices, or play all voices simultaneously. • Replay Sections summarize the preceding material in a few key points. • Challenge Examples venture a step beyond the foundational concept introduced in the chapter and are suitable for classes that may be able to move more quickly, for extra credit, or to engage learners for whom the basic material comes more easily. Finally, for those who desire more independent drilling, we offer a special online software program Music Theory Skill Builder that allows you to complete further exercises on key concepts at your own pace. We have created brief self-exams on all the topics in the text for you to complete; each gives you immediate feedback as to your level of mastery, offering you the ability to drill at your own pace as much as you’d like in those areas where you feel you could benefit from extra work. This software is offered at a discounted price when it is packaged with the text or can be purchased separately. See www.oup.com/us/root for more information. Mastery in Music If you have decided to pursue music as a college major, and potentially as a career, it is essential that you build mastery or fluency in the elements of music. It is sometimes difficult to know when you have achieved mastery; to understand what it should feel like, try this simple activity. xvi| Preface Name the shapes you see below: You are very likely able to name all four shapes immediately and without conscious thought. Furthermore, there is no chance that you would ever, for example, call the triangle a circle by accident. Being fluent in music means being able to identify its components (such as notes, key signatures, and intervals) quickly and accurately. Furthermore, just as with the shapes, you need to know them well enough that you are unable to make a mistake. As an old saying from the sports world advises us, “Don’t practice until you get it right. Practice until you can’t get it wrong.” This book offers many strategies to help you practice and study each musical concept until you “can’t get it wrong.” Underlying all of them is the notion that you should study the content in very small bites. For example, you might spend one thirty-minute session memorizing only three scales, writing, playing, and singing them over and over again. The next day, review those three scales and add two more. The next day, add two more, and so on. Memorization can be tedious and even frustrating. Find creative ways to add variety to your study sessions by designing your own flashcards, inventing your own mnemonic devices, or engaging in good-natured competition with a classmate. (Who can identify key signatures faster?) Above all, avoid the temptation to study what you already know. Focus instead on improving your weakest areas. For example, if you are a flute player, you will probably not need to spend much time on ledger lines above the treble staff. Instead, prioritize the bass clef and the piano keyboard. Singing One of the most basic requirements for musical study is the ability to “hear” music in your mind when no actual sound is present. There are a variety of names for this skill, including audiation, internal hearing, and musical imagination. At some point in your studies, you will need to prove that your internal hearing is accurate, and the most effective way to do this is to sing. Many of the exercises and activities in this book will require you to sing—sometimes in a group, sometimes on your own. For some students, the very idea of singing is terrifying. Rest assured that you do not have to have the voice of an opera star or a pop diva to be a successful singer in your music class. If you are new to singing, try these steps to help you become more at ease with your singing voice: 1. Sing first in a large group, where other voices will guide and bolster yours. 2. If possible, sing in a smaller group, of about ten people or fewer. 3. Sing with a trusted friend or two during one of your study sessions. 4. Sing any time you are alone. Sing in your car, sing with the radio, sing to your pet. 5. Use the rhythm exercises in this book as an opportunity to practice your singing: a. Sing each exercise on a single pitch that is comfortable in your voice. Use a neutral syllable such as “tah” or “nah.” b. As you continue to practice, try alternating between two pitches, changing at each new measure, then at each new beat, then at random points in the rhythm. c. Gradually add more pitches and try improvising your own melody over the rhythmic figures. Preface |xvii Using a Metronome It is strongly recommended that you purchase a metronome and use it faithfully during your study sessions. (There are many good metronome apps now available for smart phones and tablets.) Beginning students often misunderstand the metronome: do not use it to help yourself go faster. Instead, use it to force yourself to go more slowly. If you have trouble with a singing exercise, set your metronome to a slower tempo until you can perform it at least three times in a row with no errors. Then, increase the tempo slightly and repeat the example. If you stumble at any time, decrease the tempo again and repeat the process. Informed Listening Informed Listening examples near the end of every chapter will help you apply the musical concepts that you have just learned to actual music in a variety of styles and genres. A complete track list for these examples is given on pages xxiii–xxvii. All of the examples are available on iTunes or Spotify; you might even have some of them in your own music collection already. Many of the examples include specific timings, which will allow you to pinpoint a single interval, chord, or rhythm. Often, you will need to listen to a short passage repeatedly to hear what is being described. Remember also to go back and listen to the whole piece several times so that you can hear the larger context for the musical moment that you have just studied. Most importantly, you should use the Informed Listening passages as a starting point to help you recognize musical elements (such as meter, rhythm, intervals, etc.) in the music you hear in everyday life. Terminology In this book, we talk about musical pieces, musical works, and songs. It is worth pointing out the subtle differences in these terms. Piece and work are generic terms for any musical composition. They mean essentially the same thing, although work sometimes implies greater length and multiple sections (e.g., a four-movement symphony, a piano sonata, or a concept album). A song has lyrics and is meant to be sung. “Jingle Bells,” “Billie Jean,” and Fauré’s “Au Cimetière” are songs. All songs are pieces, but not all pieces are songs. Songs may be part of a larger work; for example, The Beatles’ Sgt. Pepper’s Lonely Hearts Club Band is a work made up of many songs. Working on Your Own It is possible that you have purchased this book in order to prepare for college placement exams or simply to improve your music skills, and that you are working on your own, without the structure of a classroom setting. This book is highly adaptable to independent study: • Musical examples that are to be sung as a class are available on the companion website at www.oup.com/us/root. These examples are interactive: you can play them, and watch the music scroll as you listen. You can click on just one staff to hear only that voice, or just one note to hear only that note. • For exercises that are to be sung in two parts, you may wish to have a friend or tutor assist you. If this is not possible, record yourself singing one part, and then sing the second part with yourself as you play back the recording. • The rhythmic patterns for each chapter are also available as interactive examples on the book’s website. If you have trouble learning them on your own, listen to each one until it is memorized. xviii| Preface Consider supplementing this book with Music Theory Skill Builder software (available separately). This program will allow you to drill as often as you like and will provide instant feedback so that you can monitor your progress toward mastery. You may access it from any computer that is connected to the internet. TO THE INSTRUCTOR Customization Applied Music Fundamentals is intended to serve a variety of learning models: a. The traditional face-to-face Music Fundamentals course, whose primary concern is the remediation of first-year music majors, but which may include nonmusic majors who are interested in better understanding the music they hear and perform in daily life. b. The distance-learning or hybrid course, where the student may be required to work independently and rely on the instructor only for occasional questions. a. The prospective music student wishing to prepare for freshman placement exams, perhaps during the spring or summer prior to enrollment. Applied Music Fundamentals proceeds at a slow but steady pace, giving the student time to absorb, practice, memorize, and apply the content of each chapter before moving forward. For example, two chapters are devoted to major scales and key signatures: in Chapter 3, students learn the structure of the scale, and the pitch content of major keys up to four sharps or flats. Extensive exercises and drills at the end of the chapter help the student memorize just these nine scales. Chapter 4 then introduces the remaining six major keys as enharmonic pairs and ties all of the keys together in the circle of fifths. Every chapter of study focuses on one pitch concept and one rhythmic concept, so that students may immediately learn to identify musical elements (such as the tonic or the meter type) in music they already know. Most chapters begin by having students sing a simple, familiar song. With the sound in mind, they learn to associate a name with that sound, and then they apply it to new situations through singing, playing, listening, improvisation, and composition. This “sound-first” approach is supported by rigorous drills in ear training, singing, and keyboard. Using the movable-do solmization system in conjunction with scale-degree numbers, students first learn the structure of the major and minor scales. Then, a few keys at a time, they learn how to map each set of pitch names onto the structure. Steady, disciplined practice in this method will help to build fluency with major and minor keys, and this will lead to a firmer grasp of intervals and triads later on. Applied Music Fundamentals is highly customizable: every chapter provides a wealth of classroom activities, singing and listening examples, and written exercises. It is unlikely that you will have time in your course to use them all; nor will all of them be suitable for every class in every semester. Feel free to choose the ones that best fit your teaching style and best accommodate the needs of your students. Or use them as a starting point for creating your own learning activities. You may also wish to adapt some of the specific learning methods to fit your own pedagogical preferences. For example: • In early rhythm and meter exercises, students are encouraged to track their place in the measure by counting beats on their fingers. If you prefer, have your students conduct instead. • Traditional counting syllables (“1 e and a, 2 e and a”) are used for simple-meter subdivisions. For compound meter and triplets, a number of methods are suggested; choose the one that works best for you and your students. Takadimi syllables may also be used. (For more information on the Takadimi system, see www.takadimi.net.) Preface |xix This book uses movable-do solfège (with do-based minor) for most singing and solmization exercises. Scale-degree numbers are used to reference general scale position, while a solfège syllable pinpoints a more exact pitch. For example: “In the ascending melodic minor scale, 6 is raised from le to la.” Or, “To go from major to parallel minor, lower scale degrees 3 (mi to me), 6 (la to le) and 7 (ti to te).” It is possible to substitute numbers throughout, but it is highly recommended that you devise a system for accommodating chromatic alterations. (For example, students may point their finger upward or downward as they sing altered scale tones.) Music Theory Skill Builder software is available to help each student practice the material at his own pace. Choose from drill sets that are ready-made for every chapter, or you can build your own practice examples and quizzes. Informed Listening There are more than eighty Informed Listening Examples in this book; they span a variety of styles, genres, and time periods. (A track list can be found on page xxiii.) All of them are available on Spotify or iTunes, and some may already be in your personal music collection. You need not use them all; nor should you compel your students to purchase every one of them. Instead, compile a listening list of pieces that will be of interest to you and your class. In the case of classical music examples, where many different recordings are available, a recommended recording is listed. The timings given in the text correspond to this particular recording. If you wish to use a different one, be sure to adjust the timings as needed. Composition It is never too early for a student to think about creating her own music. Composition exercises are suggested at the end of every chapter except the last one (see below). Some are quite short and simple (e.g., write a scale and compose a rhythm for it), while others are more sophisticated. Some projects, such as those in Chapters 7 and 8, essentially force the student to write in an atonal language. This is by design: by focusing on only a single musical element (say, intervals) the student is released from the aural preconceptions of the common-practice system, and free to experiment with the materials at hand. About Chapter 9 I have called the final chapter of this book a “Postlude,” but it could more accurately be considered a “Prelude” to further music study. It is much shorter than the others, and it includes a very brief introduction to diatonic triads and voice leading as well as some advanced rhythmic concepts. Depending on the level of your class and the pace at which it proceeds, you may or may not have time to include this chapter in your Music Fundamentals course. Since this material is often covered in later theory courses, it is possible to design a complete course around the first eight chapters only. ACKNOWLEDGMENTS My warmest thanks are due to the nearly two decades’ worth of students and colleagues who have persisted in telling me that I “really need to write a theory book.” Among all of them, I am most indebted to the late Jim Harmon (Loudoun County Public Schools) for recommending me to Norman Hirschy at Oxford University Press, to Mr. Hirschy and Jan Beatty for setting this project in motion, and to Richard Carlin for his role in bringing it to fruition. Editorial assistants Lauren Mine, Nicole LeFebvre, and Sheena Kowalski xx| Preface cheerfully answered my many questions and guided me, step-by-step, through the mysteries of the production process. I wish to thank the reviewers for their time given in careful consideration of the proposal and manuscript: Jared Anderson, Michigan Technological University Larry Arnold, the University of North Carolina at Pembroke Meredith Brammeier, California Polytechnic State University Gerald Custer, Wayne State University Laura Kelly, University of Texas at San Antonio Thomas Koch, North Carolina State University Brian Kubin, Truman State University Laura Lally, Rutgers University Daniel Luzko, Irvine Valley College Joseph T. Spaniola, University of West Florida Douglas S. Thompson, Jersey City University Anne Watson, Northeastern State University I am grateful, too, for the many friends and colleagues who read early chapter drafts and responded with practical ideas and ongoing encouragement: Frank Doyle (Northport High School), Christina Fuhrmann (Ashland University), Melissa Hoag (Oakland University), Steven G. Laitz (Eastman School of Music), Kendra Preston Leonard, Jana Millar (Baylor University), Haley B. Reale (Youngstown State University), Charlene Romano (Shenandoah University), and Dmitri Tymoczko (Princeton University). Additional guidance and support throughout the process were graciously provided by Leslie McClure and Jennifer Sterling Snodgrass (Appalachian State University). This book would not have been possible without the generosity of the Dana School of Music and Youngstown State University, who provided a sabbatical leave and release-time grants between 2011 and 2013. I would also like to thank my graduate teaching assistant, Sean Baran, for his diligent assistance in preparing the musical examples, and my colleague Steven B. Reale, who composed the counterpoint for the interval exercises in Chapter 7, and whose research on hemiola led me directly to the Phish song “First Tube,” which appears as an example in Chapter 9. Doug Smith, my husband and favorite drummer, helped to illuminate many of the Informed Listening examples through his practical insights on rhythm in rock music. Moreover, it is to him I owe my largest debt of gratitude for his unwavering patience, steadfast love and encouragement, and for the countless cups of coffee he delivered to my desk. And finally, I thank you, the reader, for your interest in this book. May a stronger understanding of music lead you to a more profound love for it. Jena Root Preface |xxi This page intentionally left blank LIST OF INFORMED LISTENING PIECES AND SOURCE RECORDINGS All recordings are available on iTunes and/or Spotify, and links are provided at www.oup .com/us/root. For classical music examples, the timings given in the text correspond to the recordings on this list. If you wish to use a different one, be sure to adjust the timings as needed. Artist/composer Title The Allman Brothers Band Album Chapter(s) Whipping Post A Decade of Hits, 1969–1979 9 The Association Along Comes Mary Cherish: The Best of the Association 9 Johann Sebastian Bach Minuet in G minor Notebook for Anna Magdalena Bach, BWV Anh. II 115 J. S. Bach, Inventions and Sinfonias, Janos Sebestyen 1,6 Minuet I and Minuet II English Suite No. 4, BWV 809 Bach: The English Suites, Vladimir Feltsman 5 Allegro (Movement III) Brandenburg Concerto No. 6, BWV 1051 Six Concertos for the Margrave of Brandenburg, The European Brandenburg Ensemble, Trevor Pinnock 6 Jesu, Joy of Man’s Desiring Cantata No. 147, BWV 147 Bach, Cantata No. 147, King’s 6 College Choir, Cambridge The Beatles Larger Work Lucy in the Sky with Diamonds Sgt. Pepper’s Lonely Hearts Club Band 1 Tomorrow Never Knows Revolver 3 I Will The Beatles (The White Album) 4,8 Do You Want to Know a Secret? Please Please Me 4 Dear Prudence The White Album 4 All My Loving With the Beatles 4 Yesterday Help! 4,8 Day Tripper Past Masters, Vol. 2 4 Oh! Darling! Abbey Road 4,6,7,8 The Long and Winding Road Let It Be 4 We Can Work It Out Past Masters, Vol. 2 4,5 While My Guitar Gently Weeps The White Album 5 Blue Jay Way Magical Mystery Tour 8 Girl Rubber Soul 9 |xxiii Artist/composer Title The Beatles BeauSoleil Larger Work Album Chapter(s) All You Need Is Love Magical Mystery Tour 9 Zarico Boogie Cajunization 1,5 Chanson Pour Tommy Cajunization 6,9 Beck The New Pollution Odelay 1,8 Ludwig van Beethoven Allegretto (Movement II) Ben Folds Five Boxing Georges Bizet “Carillon” (Movement IV) Booker T. & the MG’s One Who Really Loves You Johannes Brahms Hungarian Dance No. 5 in G Minor Symphony No. 7, Op. 92 L’Arlésienne Suite No. 1, Op. 23 Waltzes, Op. 39 Waltz No. 15 Bitteres zu sagen denkst Op. 32, No. 7 Beethoven, Complete 1,4,8 Symphonies, Overtures, and Incidental Music, Cleveland Orchestra, George Szell Ben Folds Five 1,7,8 Bizet: L’Arlésienne Suites Nos. 1 & 2; Carmen Suite, London Symphony Orchestra, Claudio Abbado 1,4,5,6 Green Onions 1,5,7 Brahms Waltzes Op. 39, Carles and Sofia Piano Duo 2,4,7 Best of Naxos 7, Budapest Symphony Orchestra 1,5,8 Brahms/Liszt: Lieder, Thomas Quasthoff 2,8 Dave Brubeck Unsquare Dance Time Further Out 9 Café Accordion Orchestra Manouche On Holiday 1,5 Chicago 25 or 6 to 4 Chicago II 1,2,5,6 Frédéric Chopin Prelude in C minor Op. 24, No. 20 Chopin: 24 Preludes; Sonata No.2, Op.35; Polonaise, Op.53; Evgeny Kissin 1,7,9 Prelude in D-flat Major Op. 24, No. 15 Chopin: 24 Preludes; Sonata No.2, Op.35; Polonaise, Op. 53; Evgeny Kissin 5,8,9 Allegretto (Movement I) Sonatina in G major, Clementi, Dussek, Kuhlau: Op. 36, No. 2 Sonatinas for Piano, Marko Nouwens 1,3,8 Allegretto (Movement II) Sonatina in G major, Clementi, Dussek, Kuhlau: Op. 36, No. 2 Sonatinas for Piano, Marko Nouwens 1,4 Muzio Clementi Creedence Clearwater Revival I Put a Spell on You Creedence Clearwater Revival 6,9 The Eagles Hotel California Hotel California 9 Earth, Wind and Fire Can’t Hide Love Greatest Hits 1,2 Duke Ellington Love You Madly The Complete Ella Fitzgerald Song Books (Ella Fitzgerald performing) 1,4 xxiv| List of Informed Listening Pieces and Source Recordings Artist/composer Title Larger Work Album Chapter(s) Gabriel Fauré Berceuse Dolly Suite, Op. 56 Faure: Four-Hand Piano 1,3,5 Music, Pierre-Alain Volondat and Patrick De Hooge Au Cimetière Op. 51, No. 2 Gabriel Fauré: Songs, Yann Beuron, Billy Eidi 2,8 Bela Fleck and the Flecktones Star of the County Down Flight of the Cosmic Hippo 1 Peter Gabriel I Have the Touch Security 4,7 Edvard Grieg Berceuse1 Daryl Hall and John Oates You Make My Dreams George Frideric Handel Hallelujah Franz Joseph Haydn Lyric Pieces, Book II, Franck Violin Sonatas/Grieg 3,4 Op. 38, No. 9 Lyric Pieces, Takako Nishizaki and Jeno Jando The Essential Daryl Hall and John Oates 1,2,5 Messiah Handel: Messiah, Apollo’s Fire and Jeanette Sorrell 3,5 Allegro (III) Cello Concerto in D Major Haydn: Cello Concertos, Yo-Yo Ma; English Chamber Orchestra; Jose Luis Garcia 5,6,8 Minuet (III) Piano Sonata in G, Hob. XVI:11 Haydn: The Piano Sonatas/ Variations/The Seven Last Words, John McCabe 5 Kyrie Mass No. 11 in D minor (Nelson) Haydn: Choral Works, Nikolaus Harnoncourt 1,3,7 The Irish Rovers Star of the County Down The Irish Rovers’ Gems 1 Michael Jackson Billie Jean Thriller 2,5 The Jimi Hendrix Experience Manic Depression Are You Experienced? 6,9 Billy Joel Don’t Ask Me Why The Essential Billy Joel 2,5 Elton John Your Song Greatest Hits 3 Scott Joplin Scott Joplin’s New Rag Scott Joplin Piano Rags, Joshua Rifkin 1,5 Alicia Keys Fallin’ Songs in A Minor 6,8 Carole King (You Make Me Feel Like a) Natural Woman Tapestry 6,7 Shelby Lynne How Can I Be Sure? Just a Little Lovin’ 1,7 Darius Milhaud Corcovado Saudades do Brasil, Op. 67 Milhaud: Piano Music, Alexander Tharaud 1,3 Mass in C minor, K. 427 Mozart: Great Mass in C Minor, Academy of St. Martin in the Fields, Sir Neville Marriner 1,8 Wolfgang Amadeus Kyrie Mozart 1 This piece was originally composed for solo piano, but the recording recommended here is an arrangement for violin and piano. It is hoped that the timbral contrast between the two instruments will help students better discern the melody from the accompaniment. List of Informed Listening Pieces and Source Recordings |xxv Artist/composer Title Larger Work Album Chapter(s) W. A. Mozart Allegro (Movement I) Eine Kleine Nachtmusik Mozart: Serenades Nos. 6 & 13, Nicholas Harnoncourt and Concentus Musicus Wien 2,5,7 Menuetto (Movement III) Symphony No. 40 in Mozart: Symphonies 40 & 41, 2,5,8,9 G minor, K. 550 Herbert von Karajan, Berlin Philharmonic Orchestra Martin Nolan Goodman’s Slip Jig Bright Silver Dark Wood 6,7 Mark O’Connor Cat in the Bag The New Nashville Cats 1,5,9 Phish First Tube Farmhouse 9 The Police Driven to Tears Zenyatta Mondatta 1,5,9 Maurice Ravel Pavane de la Belle au bois dormant Ravel: Boléro; La Valse; Rhapsodie Espagnole; Menuet antique; Ma Mère l’Oye, Cleveland Orchestra, Pierre Boulez 2,8 The Red Hot Chili Peppers The Adventures of Raindance Maggie I’m with You 5,8 Smokey Robinson and the Miracles It’s Christmas Time Our Very Best Christmas 9 Richard Rodgers and Oscar Hammerstein II My Favorite Things The Sound of Music Original Broadway Cast Recording (Mary Martin performing) 1,5 Claude-Michel Schönberg and Herbert Kretzmer At the End of the Day Les Misérables Les Misérables, Original London Cast Recording 5,6 xxvi| Ma Mere l’Oye (Mother Goose) List of Informed Listening Pieces and Source Recordings Artist/composer Title Larger Work Album Clara Schumann Allegro Moderato (Movement I) Piano Trio in G minor, Op. 17 Piano Trios: Clara Schumann, 1,5, 6 Bruch, Dvorak, Yuval Trio Scherzo (Movement II) Piano Trio in G minor, Op. 17 Piano Trios: Clara Schumann, 3 Bruch, Dvorak, Yuval Trio Andante (Movement III) Piano Trio in G minor, Op. 17 Piano Trios: Clara Schumann, 6 Bruch, Dvorak, Yuval Trio Stephen Sondheim It Would Have Been Wonderful A Little Night Music Original Broadway Cast Recording (Len Cariou and Laurence Guittard performing) 6,8 John Philip Sousa The Thunderer Hail, Sousa! University of Michigan Wind Band 1,7 Larry Unger and Ginny Snowe Gaye’s Steps Waltz Time II 1,2,5 The Ventures Walk Don’t Run The Very Best of the Ventures 5,6 Wild Asparagus Lafferty’s Contra Music: The Sound of New England 1,2,3,5 John Williams The Raiders March Indiana Jones: The Soundtracks Collection 3,8 Stevie Wonder Isn’t She Lovely? Songs in the Key of Life 9 The Young Rascals How Can I Be Sure? Groovin’ 1,5 Frank Zappa and the Mothers of Invention Zomby Woof Over-Nite Sensation 9 Raiders of the Lost Ark List of Informed Listening Pieces and Source Recordings Chapter(s) |xxvii This page intentionally left blank CHAPTER 1 Chapter Goals INTRODUCTION TO MUSIC NOTATION After you finish this chapter, you should be able to: • Name notes on the treble and bass staves, quickly and accurately. • Name notes up to three ledger lines above and below the treble and bass staves, quickly and accurately. • Understand simple duple, triple, and quadruple meters, and identify the basic meter type of music that you hear. • Accurately and fluently read rhythmic patterns containing whole notes, dotted half notes, half notes, quarter notes, and pairs of eighth notes. • Perform a simple piece of music that includes repeat signs, while understanding the structure of first and second endings. • Notate music accurately and legibly, including clefs, noteheads, ledger lines, stems, beams, augmentation dots, bar lines, meter signatures, and repeat signs. ELEMENTS OF MUSIC The purpose of this book is to teach you how to associate musical sounds with written music, also called notation. As you begin your music study, it is likely that you are more familiar with sound than with notation. Sing (or hum, or whistle) a song that you know well, or simply make up a tune. The musical sounds that you’ve just made are called pitches; some pitches are higher in your voice, while others are lower. You might also notice that you held each pitch for a definite amount of time, some longer than others. The length of time that a pitch sounds is called its duration. There are other important properties of musical sound, such as those listed below. But the two building blocks of music, and two primary concerns of this book, are pitch and duration. Properties of Musical Sound • Pitch: highness or lowness • Duration: length • Dynamic: loudness or softness • Timbre (pronounced TAM-ber): the tone color of the instrument or voice producing the pitch (e.g., trumpet, cello, guitar, voice, etc.) • Articulation: how a sound is shaped at its beginning and end, and how it connects to the sounds around it |1 THE STAFF AND THE TREBLE CLEF Note Names in the Staff Imagine you need to write down the music you just sang in the previous section. Perhaps you want to be sure you can remember it accurately, or you would like to give it to a friend to perform. Maybe you would like people to be able to perform it two hundred years from now. Whatever the reason, you need a way to communicate your music through notation. A written symbol that represents a musical sound is called a note. A note normally communicates both the pitch and the duration of a sound. The first half of this chapter will be concerned with notating pitches, and the second half with notating durations. Musical notes are arranged on a staff, a set of five parallel lines and the four spaces between them. (The plural of staff is staves.) The lines and spaces of the staff are numbered from the bottom upward. A note may occupy a line on the staff or a space on the staff. Notes are named alphabetically, and only seven letter names exist: A, B, C, D, E, F, and G. When we run out of names, we start over with A. Therefore the note directly above G is A: A B C D E F G A B C D E F G A B C etc. Mapping Notes to the Staff Throughout this book, you will learn a skill called mapping. When you map something, you assign a set of variable elements to a fixed structure, in the same way you might put pins into a map to show the distance between two places. The pins may be moved, but the map itself does not change. We can map letter names onto the staff by choosing where to put one note (for example, the note A), and arranging the rest of the letter names accordingly. 2| Introduction to Music Notation A clef is a symbol placed at the beginning of the staff to communicate the note names and their staff positions. In other words, the clef tells us how the notes are mapped onto the staff. Music uses many clefs, but this book will introduce only the two most common: the treble clef and the bass clef. (Other clefs are discussed in Appendix A.) The Treble Clef We will begin with the treble clef. When a treble clef appears at the beginning of the staff, the note G is mapped to the second line. The symbol itself developed from a stylized letter G, its middle intersecting the second line to indicate that note’s position. For this reason, the treble clef is sometimes called the G clef. The notes continue upward in alphabetical order; remember that A comes after G. The distance between two notes of the same name is called an octave. The Gs in Figure 1.1 are an octave apart. We might also say that the first G is in a lower octave and the second G is in a higher octave. EBSIT E W Figure 1.1. Notes in the treble clef, G to G. Adding notes downward from G, we continue in reverse alphabetical order. Before you proceed, memorize the names and staff positions for all of the treble staff notes shown in Figure 1.2, below. Use the Memorization Strategies included near the end of this chapter, and continue to the next section only after you have achieved fluency. EBSIT E W Figure 1.2. Notes in the treble clef, D to G. Ledger Lines in the Treble Clef Next, we will add more notes to the treble staff above the higher G. (Remember that the next note above G is another A.) At this point there are no more lines or spaces available on the staff, so a ledger line must be added to create the A and any notes above it. We must also use ledger lines to create any notes occurring below the lower D. Theoretically, an infinite number of ledger lines may be added to the staff, but for the purposes of this Introduction to Music Notation |3 book you should memorize note names and staff positions for up to three ledger lines (and the spaces between them) above and below the staff, as shown in Figure 1.3. EP L A Y R EBSIT E W Figure 1.3. Ledger lines above and below the treble staff. • A musical sound is called a pitch. • The length of time that a pitch sounds is called its duration. • A written symbol representing a pitch and/or a duration is called a note. • The staff is a set of five lines and four spaces on which musical notes are arranged. A note may occupy a line or a space on the staff. • There are seven note names: A, B, C, D, E, F, G. After G, we start again with A. • A clef is used to map pitch names to the lines and spaces of the staff. • An octave is the distance between two notes with the same name. • In the treble clef, or G clef, a G occupies the second line, and an A occupies the second space. The remaining notes are mapped in alphabetical order from bottom to top. • Ledger lines are used to write notes above and below the range of the staff. THE BASS CLEF Note Names in the Bass Clef The bass clef maps differently from the treble clef, meaning its lines and spaces represent a different arrangement of letter names. (Remember, the staff is a fixed structure; the note names assigned to it may change position.) In the bass clef, the note F maps to the fourth line. The symbol itself comes from an ornate letter F whose two horizontal lines evolved into dots surrounding the fourth line. For this reason, the bass clef is sometimes called the F clef. The pitches represented on the bass staff are lower than those on the treble staff. If the treble clef were the only clef in existence, the increasing number of ledger lines below the 4| Introduction to Music Notation staff would soon make the notes too difficult to read. The bass clef solves this problem by accommodating the lower notes. Figure 1.4 shows notes written using ledger lines below the treble staff, and the same notes written in the bass staff. When the treble and bass clefs are used together, they are called the grand staff and are connected by a brace. Instruments that play a wide range of notes, such as the piano, organ, harp, and marimba, all use the grand staff. EBSIT E W Figure 1.4. The grand staff. Between the two staves of the grand staff, there is a C on a ledger line. This note is called middle C, because it is found between the two staves, and also near the middle of the piano keyboard. (The keyboard will be discussed in the next chapter.) It may be written as a ledger line below the treble staff or as a ledger line above the bass staff. Regardless of the clef used, it is the same pitch. Memorize all of the note names and staff positions for the bass clef notes shown below in Figure 1.5. Use the Memorization Strategies included near the end of this chapter, and proceed to the next section only after you have achieved fluency. EBSIT E W Figure 1.5. Notes in the bass clef. Ledger Lines in the Bass Clef Ledger lines may be added above and below the bass staff to extend its range. Keep in mind that each note on a ledger line above the bass staff may also be written on the treble staff. For the purposes of this book, it is recommended that you memorize note names and Introduction to Music Notation |5 staff positions for up to three ledger lines (and the spaces between them) above and below the bass staff, as shown in Figure 1.6. EP L A Y R EBSIT E W Figure 1.6. Ledger lines above and below the bass staff. • Normally, higher pitches are notated in the treble clef, and lower pitches in the bass clef. • The bass clef is also called the F clef, because its symbol highlights the fourth staff line, where the note F is located. • When the treble and bass staves are used together, they are called the grand staff, and are connected by a brace. • There is one ledger line between the treble and bass staves; the note middle C occupies it. • Middle C may be written as a ledger line below the treble staff or above the bass staff. • Ledger lines may be used to extend the range of the bass staff. Pitches notated on ledger lines above the bass staff may also be written in the treble clef. RHYTHM AND METER Elements of Rhythm In the beginning of this chapter, you sang a tune made up of a series of pitches, each with its own duration. In most music, durations are organized according to an underlying pulse. Set your metronome to 88 beats per minute (bpm). The evenly spaced clicks you hear make up the pulse, and each individual click is called a beat. The number of beats per minute (eighty-eight, in this case), determines the tempo, or speed of the music. Set your metronome to a higher number, and the tempo will increase, meaning the pulse will get faster. Set it to a lower number, and the tempo will decrease, meaning the pulse will slow. The duration or value of a note is the length of time (measured in beats) that a note is to be held. The way that note durations interact with the underlying pulse is called rhythm. Quadruple Meter and Basic Durations The first four measures of the folk song “Aura Lee” are shown in Figure 1.7. Your teacher will play it several times. (If you are working on your own, listen to the example online.) Memorize the tune and sing it back several times using the letter names of the notes. 6| Introduction to Music Notation EBSIT E W Figure 1.7. Traditional, “Aura Lee,” mm. 1–4. Set your metronome to 88 bpm. Clap the pulse as you sing the song from memory several times. You should notice that: • The first six notes (C F E F G D) each last for one beat. • The seventh note (G) lasts for two beats. • The next four notes (F E D E) each last for one beat. • The final note (F) lasts for four beats. Examine the notated music in Figure 1.7 again. You should notice that: • The round part of each note, called the notehead, is sometimes filled and sometimes open. • A vertical line is attached to every notehead except for the last one. This line is called a stem. A combination of noteheads and stems is used to represent each note’s duration. “Aura Lee” uses three different durations: Name Symbol Description Duration in “Aura Lee” Quarter note 𝅘𝅥 Filled notehead Stem 1 beat Half note 𝅗𝅥 Open notehead Stem 2 beats Whole note 𝅝 Open notehead No stem 4 beats When notating a piece of music, the composer must choose which durational symbol will represent the pulse. Any symbol may be used, but the most common is the quarter note, which is made up of a filled notehead plus a stem. In “Aura Lee,” as in most music, the pulse is organized into a meter, which creates regular pulse groups called measures, or bars. Measures are separated by bar lines, which make the music easier to read and count. Measures and bar lines are visual aids that help the performer mentally organize the pulse into beat groups, and stay with the other players during ensemble pieces. Introduction to Music Notation |7 At the beginning of the music, the time signature (or meter signature) communicates information about the meter and pulse: ò The top number (4, in this case) indicates there are four beats per measure. The bottom number (4) indicates that the quarter note represents the pulse. Hence we say “Aura Lee” is in four-four meter. Four-four is one type of quadruple meter, but it is not the only one; “quadruple” is a general label for any meter that contains four beats per measure. You will learn about other quadruple meters later in the book. Metric Accents As you sing “Aura Lee,” you might notice a natural tendency to emphasize beat 1 of each measure. Beat 1 is also called the downbeat, and this natural emphasis is called a metric accent. You might also notice a slightly weaker metric accent on beat 3. Sing “Aura Lee” again. This time, half the class will sing note names, while the other half clap the pulse and count the beats aloud. (If you are working on your own, try this exercise with a friend.) The counting group should emphasize the metric accents on beats 1 and 3, with a slightly stronger accent on the downbeat. It is important in performing this music to be aware of four things simultaneously: • The meter and metric accents (1 2 3 4) • The duration (measured in beats) of each note • The letter names of the notes • The sounding pitches of the notes Having another person clap and count while you sing note names accomplishes this fairly well, but it is impossible for one person to say the counts and sing the note names at the same time. So when singing the examples in this book, you should “outsource” the counting to your fingers: count the beats of each measure by raising the appropriate number of fingers (one, two, three, four) as you sing the song on letter names. By using this fingercounting method, you will know (for example) that the G you sing in measure 2 lasts for two beats, and that it occurs on beats 3 and 4 of that measure. 8| Introduction to Music Notation The Dotted Half Note and Eighth Notes EBSIT E W Set your metronome to 100 bpm and sing “Old McDonald” on note names while fingercounting the meter. Figure 1.8. Trad., “Old McDonald.” A closing bar line is used to signal the end of a piece of music; it is made up of a normal bar line followed immediately by a thicker one. Like “Aura Lee,” “Old McDonald” is in four-four meter, but it introduces two new durations: the first is the dotted half note, found in measures 4 and 8. When an augmentation dot appears after a note, it adds half of the note’s value to itself. Since the half note lasts for two quarter notes’ worth of time, the dotted half lasts for three, because: 𝅗𝅥=2 𝅼 = half of 2 = 1 𝅗𝅥𝅼 = 2 + 1 = 3 As you sing and finger-count, notice that the dotted half note lasts for beats 1, 2, and 3, of measures 4 and 8. “Old McDonald” also contains eighth notes. An eighth note is equal to one half the length of a quarter note, so two eighth notes will occupy one beat in this meter. In other words, an eighth note is worth half of one quarter-note beat. Eighth notes are often found in pairs, where they are connected by a beam. The beam tells the performer that both notes occupy the same beat. An eighth note appearing by itself is drawn with a flag. Introduction to Music Notation |9 The word “and” is commonly used to divide the beat in half while counting, as in “ONE and TWO and THREE and FOUR and.” Sing “Old McDonald” again, with half the class singing the note names, and the other half counting the beat numbers with the “ands.” Finger-count as you sing, and notice that the “and” of each pair occurs exactly halfway between beats. Triple Meter Your teacher will play the hymn tune “Hyfrydol” (Fig. 1.9) several times. Memorize the tune and sing it back using letter names. (If you are working on your own, listen to the example online.) EBSIT 10| E W Figure 1.9. Rowland Prichard, “Hyfrydol.” “Hyfrydol” is written in three-four meter, where the top number of the time signature (3) communicates the number of beats per measure, and the bottom number (4) indicates that the quarter note represents the pulse. Three-four is one type of triple meter, but it is not the only one; “triple” is a general label for any meter that contains three beats per measure. You will learn about other triple meters later in this book. Introduction to Music Notation Set your metronome to 82 bpm, and sing the note names for “Hyfrydol” while fingercounting (1-2-3, 1-2-3, etc.). Be sure to bring out the metric accent for each measure by emphasizing each downbeat. In three-four time, a dotted half note is used to fill the entire measure. (Recall from the previous section that a dotted half note is worth three quarter-note beats.) Because there are three beats per measure, the dotted half note is the longest value that may be used in three-four. Whole notes are never used in this meter. Duple Meter Figure 1.10 is an early-American hymn tune known as “Bonner.” Your teacher will play it several times. (If you are working on your own, listen to the example online.) Learn the tune, and sing it back several times using letter names. EBSIT E W Figure 1.10. Carey Bonner, “Bonner” (Hymn tune). “Bonner” is written with the time signature two-four, where the top number (2) communicates the number of beats per measure, and the bottom number (4) signifies that the quarter note represents the pulse. Two-four is one type of duple meter, but it is not the only one. “Duple” is a general label for any meter that contains two beats per measure. You will learn about other duple meters later in this book. Set your metronome to 76 bpm, and sing “Bonner” in note names while finger-counting. As you sing and count, add a slight emphasis to the first beat of each measure (ONE-two, ONE-two, etc.), noticing the tendency of the music to fall naturally into groups of two beats. In two-four meter, the half note is the longest duration that may be used in a measure. (See mm. 6, 8, 14, and 16.) Whole notes and dotted half notes are not used in two-four. Meter Categories Meters are categorized by how the pulse divides: • In a simple meter, the pulse divides into two equal parts. • In a compound meter (introduced in Chapter 6), the pulse divides into three equal parts. • In an irregular meter (introduced in Chapter 9), the pulse division may vary. All of the meters introduced in this chapter are simple, because they all use a quarter-note pulse that divides into two eighth notes. In musical terms, we would say that: • Four-four is a simple quadruple meter. • Three-four is a simple triple meter. • Two-four is a simple duple meter. Introduction to Music Notation |11 Summary of Durations EP L A Y R Study the following chart to help you memorize the durational symbols presented in this chapter. • A pulse is made up of evenly spaced beats. • Rhythm is the interaction between note durations and the underlying pulse. • Meter is the grouping of pulses into measures or bars, which are separated by bar lines. • Most meters group into: o Two beats per measure, called duple meter o Three beats per measure, called triple meter o Four beats per measure, called quadruple meter • In a simple meter, the pulse divides into two equal parts. All of the meters introduced in this chapter are simple. • The time signature or meter signature is written at the beginning of the music to communicate the meter and the pulse. In a simple meter, the top number represents the number of beats per measure, and the bottom number represents the pulse unit. • In simple meters where the bottom number is four (such as two-four, threefour, and four-four): o The whole note lasts for four beats. o The dotted half note lasts for three beats. o The half note lasts for two beats. o The quarter note lasts for one beat. o The eighth note lasts for one-half of a beat. In this chapter, eighth notes are always beamed together in pairs. • Typically, each measure has an emphasis or metric accent on its first beat, which is also called the downbeat. • Durational symbols use a combination of stems and noteheads to indicate a note’s length in beats. • An augmentation dot placed after a note adds one-half of the note’s duration to itself. • In four-four meter, a whole note fills one measure. In three-four meter, a dotted half note fills one measure. In two-four meter, a half note fills one measure. 12| Introduction to Music Notation THE REPEAT SIGN Repeat Signs Examine “Hyfrydol” (Fig. 1.9) again, and notice that measures 9–16 are an exact repeat of measures 1–8. To save time and page space, repeated passages of music are sometimes written using repeat signs, as in Figure 1.11. The passage enclosed between the signs is to be performed twice. EBSIT E W Figure 1.11. “Hyfrydol,” written with repeat signs. Repeat Signs with Endings “Bonner” also contains repeated material, but the repeat is not exact: measures 7–8 are different from measures 15–16. In this case, repeat signs can be used with endings. “Bonner,” as written with repeats in Fig. 1.12, uses a first ending and a second ending. EP L A Y R • A passage of music enclosed within repeat signs is to be played twice. EBSIT E W Figure 1.12. “Bonner,” written with repeat signs. • If the repeated material ends differently the second time through, a first ending and second ending may be used. Introduction to Music Notation |13 NOTATION Clefs When you notate music, the first item you will draw is the clef, which should appear at the beginning of every line of music. To draw a treble clef: 1. Draw a vertical line that extends about two spaces above and below the staff. (You may wish to add a curved tail to the end of the line, but it is not required.) 2. Draw a curve from the top of the vertical line to the middle of the third space, extending outward to the right. 3. Continue the curve outward to the left, bringing it back to the vertical at the first staff line. 4. Continue the curve outward to the right, bringing it back to the vertical at the third staff line. 5. Continue the curve inward to the second staff line. Practice drawing treble clefs on the staff below. To draw a bass clef: 1. On the fourth staff line, draw a solid dot that takes up about one third of the spaces above and below. 2. Starting on the left side of the dot, draw a curve up to the fifth staff line. 3. Continue the curve downward, ending at the second staff line. 4. Draw two dots just to right of the clef, in the middle of the third and fourth spaces. 14| Introduction to Music Notation Practice drawing bass clefs on the staff below. Noteheads When a notehead occupies a space, it should take up the entire space, touching—but not passing—the lines on either side. A notehead on a line should be just large enough to fill half of each space above and below it, and the line should pass through the exact center of the note. Noteheads are oval-shaped and just slightly slanted downward and to the left. Take care not to make them too large, or to draw them as slashes. a. Correct noteheads b. Incorrect noteheads Ledger Lines Space ledger lines evenly, the same distance apart as the staff lines. Draw them so they extend just past the notehead on either side. When drawing several notes in a row using ledger lines, do not connect the ledger lines to each other; separate them for each note. Finally, do not draw extra ledger lines outside the notehead; draw them only between the notehead and the staff. a. Correct ledger lines b. Incorrect ledger lines Stems Use an upward stem for notes below the third line of the staff, and a downward stem for notes on the third line and above. Always draw an upward stem on the right side of the note, and a downward stem on the left side. Your notes should resemble a lowercase letter “p” or “d.” They should not look like a lowercase “b” or “q.” Generally, a stem is one octave long, but for any note that is beyond the first ledger line above or below the staff, extend the stem all the way to the middle line of the staff. Take Introduction to Music Notation |15 care to draw your stems straight and exactly perpendicular to the staff. Use a straight edge when drawing stems. Bar Lines and Repeats Draw bar lines using a straight edge, so that they are exactly perpendicular to the staff lines. On a single staff, extend the bar line from the bottom staff line to the top, and do not go beyond the staff. If the notated piece is complete, place a closing bar line at the end of the final measure: the first line should be normal bar-line width, and the second should be thicker. When drawing repeat signs, be sure to place the thicker bar line on the outside of the repeated passage. The dots should be drawn in the second and third spaces. A repeat sign at the beginning of a piece should come after the clef and time signature. 16| Introduction to Music Notation Bar lines on the grand staff are drawn continuously from the top line of the treble clef, through the space between the staves, to the bottom line of the bass clef. Repeat-endings are shown only on the top staff. The Augmentation Dot Always place the dot after the note, never before. If the note occupies a space, place the dot in that space. If the note occupies a line, place the dot in the space directly above the line. In both cases, draw the dot exactly in the center of the space. Beamed Eighth Notes To draw a pair of beamed eighth notes, first draw the noteheads and stems (as if you were drawing quarter notes), following the guidelines above. Connect the two stems at the very end with a straight line that is a little bit thicker than the staff lines. If you are joining two instances of the same note (for example, E to E), the beam will be perfectly horizontal. If you are connecting two differing notes, it will be a straight diagonal line between the two notes. Beams do not bend. Both stems must point in the same direction in a pair of beamed notes. If you need to beam two notes that would otherwise take opposite stems, let the note that is farthest from the middle line dictate the direction. Beams should not be drawn at a sharp slant. If the two notes are far apart on the staff, lengthen one of the stems so that you can draw the beam with only a small slant. Introduction to Music Notation |17 Time Signatures Place the time signature at the beginning of a piece of music, just after the clef. The time signature is drawn only on the first line of music. (Remember that the clef appears at the beginning of every line.) The top number should fill the top two staff spaces, and the bottom number should fill the bottom two spaces. Draw the numerals with thick dark lines so that they are legible through the staff lines. Note-Spacing Within the Measure Space notes proportionally across the measure according to their durations. (See “Summary of Durations,” above.) For example, if a measure contains eighths, quarters, and halves, then the quarter should take the space of two eighth notes, and the half note should take the space of two quarter notes. When writing music on the grand staff, always align notes that fall on the same beat vertically. Do not center notes in the measure. 18| Introduction to Music Notation MEMORIZATION STRATEGIES Pitch Name Fluency If this is your first time reading music notation, it is important to take small steps. Create a set of forty-two flashcards to help you study. On each card, draw the staff (or you can glue a scrap of staff paper to an index card), the clef, and one note. On the reverse side, write the letter name of the note. Your card should look something like this: During your study session: 1. Divide your cards into groups, as shown on the staves below. Shuffle each group separately. Memorization Strategies |19 2. Pick one clef (treble or bass) and work on each group within that clef separately. Do not move on to the next group until you can go through each stack of cards three times in a row with no mistakes. 3. Gradually combine the card groups: a. T1 + T2 b. T1 + T2 + T3 c. T1 + T2 + T3 + T4 4. Complete each stack three times with no errors before moving on to the next stack. (Be sure to shuffle the stack after each time through.) 5. Repeat the process with the other clef. 6. Gradually combine the two clefs. SINGING AND HEARING EXERCISES 1.1. Rhythmic patterns. Tempo goal: 𝅘𝅥 = 100 bpm. Practice the rhythmic patterns given below using this method: 1. Pick a time signature (two-four, three-four, or four-four) for your practice session. 2. Set your metronome to a moderately slow tempo—about 72 bpm. 3. Choose a pitch that is comfortable for your voice, and sing each rhythm in your chosen meter in the order given. Sing on a neutral syllable, such as “nah” or “tah.” 4. Repeat step 3 several times. Notice that each rhythm is two measures long and ends with a full measure’s duration (e.g., in four-four, a whole note). Use this measure as a “landing strip”; as you sustain the note, look at the next pattern and mentally prepare yourself to sing it. 5. Sing the rhythms out of order, leaping from one to the next randomly. Remember to use the landing-strip measure to choose your next rhythm, and always keep a steady pulse. 6. Gradually increase the tempo of the exercise until you have reached the tempo goal. Remember that accuracy is more important than speed. 7. Repeat the exercise with another meter. Note: in four-four meter, write out new rhythms by substituting a pair of eighth notes for any quarter note in the given patterns. 20| EBSIT E W Duple-Meter Patterns Singing and Hearing Exercises EBSIT E W Triple-Meter Patterns Quadruple-Meter Patterns 1.2. EBSIT E W Practice these four-four patterns, and then create your own by substituting a pair of eighth notes for any of the quarter notes. Write out your new rhythms and add them to your practice sessions. Hearing rhythmic patterns. Goal: ten consecutive correct answers. Choose which meter you would like to study. Your teacher or study partner will choose one of the rhythmic patterns above and will play or sing it twice. Listen carefully, finger-count, and then repeat the rhythm aloud. Choose the correct answer from the patterns notated above. Remember that four-four patterns using eighth notes are not listed; in that case, you will need to notate the pattern yourself. Singing and Hearing Exercises |21 INFORMED LISTENING: EXAMPLES FOR STUDY The examples in this section are listed according to their meter types. Listen first for the pulse, and then for metric accents. Once you are able to hear the meter, count aloud and on your fingers. The distinction between duple and quadruple meter is a subjective one; many pieces of music can be counted in either two or four. Pay special attention to the sections titled “What to Listen For,” to help you distinguish among the meter types. Refer to the List of Informed Listening Pieces and Source Recordings, in the front of this book. Direct links to the recordings appear on the companion website at www.oup.com/us/root. Timings for classical repertoire refer to the recordings on this list. Duple Meter 1.3. Johannes Brahms, Hungarian Dance No. 5 in G Minor Tempo: very fast, about 144 bpm What to listen for: • Back-and-forth “oom-pah” pattern in the bass • Upper strings play on the “ands” of each beat. (Count “ONE and TWO and . . .”) • Drastic tempo change in the middle, starting around 0’33”. The original tempo resumes at about 0’41”. 1.4. Wild Asparagus, “Lafferty’s,” from Contra Music: The Sound of New England Tempo: moderately fast, about 110 bpm What to listen for: • For the first two measures, the pulse is established by a shaker. • Beginning in measure 3, the guitar and drum alternate measures of two beats each. This technique is called call and response. • When the rest of the instruments enter, listen for the bass to play on every downbeat, supporting the metric accent. 1.5. Gabriel Faure, “Berceuse,” from Dolly Suite, Op. 56 Tempo: moderate, about 73 bpm What to listen for: • Continuous eighth notes create a back-and-forth “rocking” motion in the lowest voice. Berceuse translates as “cradle song” or “lullaby.” • After two measures, the highest voice enters with a pair of quarter notes to begin the melody. Use them to help you find the pulse. 1.6. Scott Joplin, “Scott Joplin’s New Rag” Tempo: fast, about 97 bpm What to listen for: • Back-and-forth “oom-pah” pattern in the bass • The pianist plays both the bass notes and the chords with the left hand. Listen for the bass notes on each beat and the chords on the “ands.” Count aloud: “ONE and TWO and . . .” • Compare this piece to Example 1.3 (Brahms, Hungarian Dance No. 5) 22| Informed Listening: Examples for Study 1.7. Ludwig van Beethoven, “Allegretto” (Movement II) from Symphony No. 7 Tempo: moderate, about 72 bpm What to listen for: • A strong metric accent is defined throughout by this rhythm: • In the middle section (beginning at about 2’40”), the character and melody of the music change, but the quarter-eighth-eighth rhythm remains in the bass and timpani. 1.8. Daryl Hall and John Oates, “You Make My Dreams,” from The Essential Daryl Hall and John Oates Tempo: moderate to fast, about 83 bpm What to listen for: • The song begins with guitar only; it is a bit difficult to hear the pulse until the bass drum enters at about 0’05”. • Throughout the song, the bass drum plays the pulse, and the snare drum plays the “ands” of each beat. Count aloud: “ONE and TWO and . . .” Triple Meter 1.9. Rodgers and Hammerstein, “My Favorite Things,” from The Sound of Music (performed by Mary Martin) Tempo: very fast, about 212 bpm What to listen for: • Strong metric accents on the downbeat throughout, most noticeably on words such as “rain,” “rose,” etc. • The vocal melody proceeds, for the most part, in quarter notes. Count aloud as you listen: “ONE two three ONE two three . . .” 1.10. Muzio Clementi, “Allegretto” (Movement II) from Sonatina in G Major, Op. 36, No. 2 Tempo: slow, about 68 bpm What to listen for: • The melody in the upper part of measure 1 is repeated exactly in measure 2. Each iteration is three beats long. • The same thing happens in the lower voice starting at about 0’11”. • There is a strong metric accent on beat 1, and a slightly weaker accent on beat 3 of each measure. Informed Listening: Examples for Study |23 1.11. Franz Josef Haydn, “Kyrie,” from Mass No. 11 in D Minor (“Nelson”) Tempo: moderate, about 100 bpm What to listen for: • Strong metric accents emphasized by the trumpet and timpani • When the chorus enters on the word “Kyrie” (about 0’28”), it alternates measures with the trumpet, in a call-and-response style. (Compare with Ex. 1.4, “Lafferty’s.”) 1.12. Larry Unger and Ginny Snowe, “Gaye’s Steps,” from Waltz Time II Tempo: fast, about 146 bpm What to listen for: • There is an eight-measure introduction. • The melody, beginning at about 0’10” in the upper voice of the piano, is made up of three measures of eighth notes, followed by one dotted half note: 1.13. Ben Folds Five, “Boxing,” from Ben Folds Five Tempo: moderately fast, about 104 bpm, though the performer takes liberties with the tempo What to listen for: • The piece begins with solo piano, with bass notes played on each downbeat and chords on beats 2 and 3 in an “oom-pah-pah” pattern. • The melody in the upper voice of the piano begins with this rhythm: • Very strong downbeats in the lower voice of the piano begin around 1’22”. Quadruple Meter 1.14. Booker T. & the MG’s, “One Who Really Loves You,” from Green Onions Tempo: moderately fast, about 118 bpm What to listen for: • In each measure, a much stronger accent on beat 1 than beat 3. (Compare this to the duple-meter examples, which have a strong accent every two beats.) • Throughout the piece, there is a tom-tom hit on the “and” of beat 4 in every measure, except for breaks around 1’06” and 1’38”. 24| Informed Listening: Examples for Study 1.15. Wolfgang Amadeus Mozart, “Kyrie” from Mass in C minor, K. 427 Tempo: slow, about 54 bpm What to listen for: • During the introduction, there are strong metric accents on beats 1 and 3, making the piece sound as though it might be in duple meter. • Beginning at the first chorus entrance (about 0’29”), the metric accent on beat 1 becomes much more prominent than the accent on beat 3. • In the middle section of the piece, beginning around 2’27” there is a soprano solo accompanied by the choir and orchestra. At about 3’17” listen for a calland-response section between the soprano and the chorus: the soloist sings the word “eleison” on beats 4, 1, and 2. The chorus echoes on beats 2, 3, and 4. 1.16. The Police, “Driven to Tears,” from Zenyatta Mondatta Tempo: fast, about 158 bpm What to listen for: • For the first thirty-eight seconds of the song, the bass drum plays on every beat. This technique is sometimes called four-on-the-floor, because the bass drum sits on the floor in the middle of the drum set. • The quadruple meter is established by a repeating pattern in the guitar and bass. • The feel of the song changes at the start of the chorus (about 0’39”), but the meter and tempo remain the same. The change comes from a new pattern in the bass and drums, emphasizing beats 1 and 3, instead of all four beats. The four-on-the-floor pattern returns at 0’52”. 1.17. BeauSoleil, “Zarico Boogie,” from Cajunization Tempo: moderate to fast, about 122 bpm What to listen for: • The rhythmic figure half-quarter-quarter repeats throughout the song. INFORMED LISTENING: INTERESTING EXAMPLES 1.18. Beck, “The New Pollution,” from Odelay This song starts in a fast triple meter and then changes abruptly to quadruple meter at 0′14″. 1.19a. The Young Rascals, “How Can I Be Sure,” from Groovin’ 1.19b. Shelby Lynne, “How Can I Be Sure,” from Just a Little Lovin’ Listen to both versions of this song, and compare the Young Rascals’ original in triple meter with Lynne’s cover in quadruple meter. Informed Listening: Interesting Examples |25 1.20. The Beatles, “Lucy in the Sky with Diamonds,” from Sgt. Pepper’s Lonely Hearts Club Band Like Example 1.18, this song shifts between triple meter (during the verses) and quadruple meter (during the choruses). The first meter change occurs around 0′48″. 1.21a. The Irish Rovers, “Star of the County Down,” from The Irish Rovers’ Gems 1.21b. Bela Fleck and the Flecktones, “Star of the County Down,” from Flight of the Cosmic Hippo This Irish folk tune has been recorded many times and in many styles. Compare the Irish Rovers’ very traditional version in duple meter with the Flecktones’ more modern triplemeter setting. (The meter in the Flecktones’ recording is not obvious until the bass and banjo enter at about 0′11″.) INFORMED LISTENING: EXAMPLES WITH QUESTIONS Each of the following pieces is in duple, triple, or quadruple meter. Listen to each several times, on your own or as a class. Tap the pulse, listen for the metric accents, and circle the most likely meter type. For each piece, list at least one musical reason for your answer. For example, you might say that the bass plays a note every two beats, or that the singer emphasizes certain words that align with the metric accents. 1.22. Clara Schumann, "Allegro Moderato" (Movement I) from Piano in G Minor, Op. 17 Circle one: duple triple quadruple Why? 1.23. Cafe Accordion Orchestra, “Manouche,” from On Holiday Circle one: duple triple quadruple Why? 1.24. Earth, Wind, and Fire, “Can’t Hide Love,” from Greatest Hits Circle one: duple triple quadruple Why? 1.25. Darius Milhaud “Corcovado,” from Saudades do Brasil, Op. 67 Circle one: duple triple Why? 26| Informed Listening: Examples with Questions quadruple 1.26. Mark O’Connor, “Cat in the Bag, “ from The New Nashville Cats Circle one: duple triple quadruple Why? 1.27. Georges Bizet, “Carillon” (Movement IV) from L’Arlésienne Suite No. 1, Op. 23 Circle one: duple triple quadruple Why? 1.28. John Philip Sousa, “The Thunderer” Circle one: duple triple quadruple Why? 1.29. Chicago, “25 or 6 to 4,” from Chicago II Circle one: duple triple quadruple Why? 1.30. Muzio Clementi, “Allegretto” (Movement I) from Sonatina in G Major (Op. 36, No. 2) Circle one: duple triple quadruple Why? 1.31. Ella Fitzgerald, “Love You Madly” (Duke Ellington), from The Complete Ella Fitzgerald Song Books Circle one: duple triple quadruple Why? 1.32. Frederic Chopin, Prelude in C minor, Op. 24, No. 20 Circle one: duple triple quadruple Why? 1.33. Johann Sebastian Bach, “Minuet in G Minor,” BWV Anh. II 115, from the Notebook for Anna Magdalena Bach Circle one: duple triple quadruple Why? Informed Listening: Examples with Questions |27 DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 1.34. Note names. a. Practice saying note names in order, upward and downward—that is, forward and backward in the alphabet. Practice in segments, starting on A and working your way up to a full octave: A-B-A A-B-C-B-A A-B-C-D-C-B-A A-B-C-D-E-D-C-B-A A-B-C-D-E-F-E-D-C-B-A A-B-C-D-E-F-G-F-E-D-C-B-A A-B-C-D-E-F-G-A-G-F-E-D-C-B-A b. Start the exercise on B: B-C-B B-C-D-C-B etc., up to: B-C-D-E-F-G-A-B-A-G-F-E-D-C-B c. Repeat the exercise, starting on each of the remaining note names: C, D, E, F, and G. d. Repeat the entire exercise upside down: A-G-A A-G-F-G-A A-G-F-E-F-G-A etc. 1.35. Note names with turnarounds. Starting on any note, say the letter names in ascending order, then change direction at any point and descend. Then change direction at any point and ascend again. Continue in this manner for one minute. Try to go downward more often than you go up—it’s more challenging to say the alphabet backwards. A G F E D G F F E E D C E E D D C C B B A A G 28| Drills to Go D C B etc. LE AL N ✪ GE Set your metronome to 60 bpm or slower, and speak Drill 1.34 at a steady pulse, one letter per beat. If you have trouble, decrease your starting tempo. As you become more fluent, gradually increase the tempo. How fast can you go and still maintain accuracy? CH 1.36 1.37. Listen carefully to any music that you hear as you go about your day. First, find the pulse and tap it quietly. Then find the downbeat and count the number of beats per measure. Is the music in duple, triple, or quadruple meter? Is the meter consistent throughout the piece, or does it change? Although most Western music can be counted in two, three, or four, you may occasionally encounter music with an unusual number of beats per bar, such as five, seven, or eleven. These are called irregular meters and will be discussed further in Chapter 9. Improvise rhythms over the music using the durations covered in this chapter. Create the rhythms by tapping, clapping, or singing on a neutral syllable. CLASSROOM ACTIVITIES For Exercises 1.38–1.43, designate a student to lead the class using the instructions given. Change leaders periodically. 1.38. Naming notes on the staff. For this exercise, choose a clef (treble or bass) and one of the three levels listed. Level 1: Only notes in the staff Level 2: Only ledger lines (up to three lines above and below) Level 3: All notes, up to three ledger lines above and below 1. Draw the notes on the board in ascending order. (Draw only noteheads, and do not use a meter.) Point to each note in sequential order, and the class will respond by saying its letter name. (Go upward, then downward.) 2. Repeat step 1, but this time randomize the order of the notes you choose. 3. If there are incorrect responses, point to the nearest A and “walk” the class up or down through the letter names until the correct name is reached. Then continue with the exercise. 1.39. Repeat Exercise 1.38 with these variations: 1. For the level you have chosen, write the notes on the board in descending order. 2. For the level you have chosen, write the notes on the board in random order. 1.40. Singing correct pitches and note names. 1. Choose a clef and five consecutive notes (for example, CDEFG, or ABCDE). Write the notes in ascending order on the board. (Draw only noteheads; do not use a meter.) 2. Your instructor will play the five notes on the piano in order, up and down, and the class will sing them back on letter names. Do this several times. 3. Point to the notes in random order, and the class will respond by singing the correct pitch and note name of each note. 4. If there are incorrect responses in pitch or letter name, repeat step 2, and then return to the exercise and have the class find that note again. Classroom Activities |29 2. Write the notes on the board in random order. 1.42. Guided rhythm improvisation. 1. Choose eight rhythmic patterns, all in the same meter, from Exercise 1.1. (In four-four meter, be sure to integrate the extra patterns you have composed.) 2. Write your choices on the board in two columns of four patterns each. (An example is given below.) Be sure to include the landing measure with each pattern. 3. Set your metronome at a slow tempo to establish a pulse. Choose any pitch, and lead the class in singing the rhythms in order. Use a neutral syllable such as “nah” or “tah.” 4. Repeat step 3, but this time randomize the order of your choices. Start with any rhythm, and as the class reaches the landing measure, point to the next rhythm you want them to sing. (Be sure to give them enough time to anticipate where they’re going.) 5. If there are incorrect responses, repeat that pattern until the entire class sings it correctly; then move on. Example 30| Classroom Activities LE AL N ✪ GE 1. Write the notes on the board in descending order. CH 1.41. Repeat Exercise 1.40 with these variations: LE AL N ✪ GE 1. Repeat Exercise 1.42, but this time choose a clef (treble or bass) and compose notes on the staff for the rhythms you have chosen. Use a different set of notes for each rhythm, but keep all notes in the same clef. An example is given below. CH 1.43. Rhythm improvisation with note names. 2. Write your examples on the board. Be sure to notate all measures clearly with regard to notehead size, stem length and direction, etc. 3. Where there are faster rhythms, keep the pitches adjacent. Use slower rhythms for leaps. (See example.) 4. Establish a pulse with your metronome, and lead the class in speaking the note names in rhythm. Go through your fragments in order first, and then mix them up. 5. If there are incorrect responses, repeat that pattern until the entire class sings it correctly; then move on. 1.44. Choose a piece of music that you like and know well. Play it for your class, and lead a discussion about the meter type: Is it duple, triple, or quadruple? Be prepared to support your answer by pointing out how certain instruments or voices define the metric accents. Classroom Activities |31 WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 1 online drills and quizzes at www.oup.com/us/root. 1.45. For each question: a. Label each note with the correct letter name. b. Copy the music exactly, on the empty staff below each example. (You do not need to copy the letter names onto the second staff.) 1. 32| Written Exercises 2. 3. Ç Name the notes. __ __ __ __ __ __ __ __ __ __ __ __ Ç __ T __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ Ç __ __ __ Copy the music here. Written Exercises |33 4. 34| Written Exercises EBSIT E a. Learn both parts and sing it as a class, using note names. If the class is balanced by gender, women should sing the treble part and men should sing the bass part. Otherwise, anyone may sing either part in an octave that is comfortable. If you are working on your own, listen to the example online. W 1.46. The next example is from a chorale by Johann Sebastian Bach. b. On the staves below the example, rewrite each portion (indicated by the numbers given) an octave higher or lower, as requested. Be sure to use the given clef, and observe all rules of notation. J. S. Bach, Chorale No. 10, “Aus tiefer Noth schrei’ ich zu dir” 1. Rewrite Part 1 one octave higher, treble clef. 2. Rewrite Part 1, one octave lower, bass clef. 3. Rewrite Part 2, one octave lower, bass clef. Written Exercises |35 4. Rewrite Part 2, one octave higher, treble clef. 5. Rewrite Part 3 one octave lower, treble clef. 6. Rewrite Part 3 one octave lower, bass clef. 7. Rewrite Part 4, one octave higher, bass clef. 1.47. For each question, add bar lines to create measures that contain the correct number of beats for the meter given. The first bar line of Question 1 is given. 1. 2. 3. 36| Written Exercises 1.48. Complete each measure by drawing one durational symbol. If the measure is complete as written, write the word complete under it. 1.49. Complete each measure by drawing exactly two durational symbols. (A pair of eighth notes counts as two symbols.) If the measure is complete as written, write the word complete under it. 1.50. For each question, draw the note(s) according to the instructions given; then label each with the correct letter name. Observe all rules of notation. All notes for this exercise are in the treble clef. 1. Half note on the third space (this question has been completed for you) 2. Quarter note on the first line 3. Dotted half note on the fifth line 4. Whole note on the second space 5. Quarter note on the space below the first line 6. Two beamed eighth notes, on the second line and the third space 7. Two beamed eighth notes, on the first space and the fifth line 8. Quarter note on the second ledger line above the staff 9. Half note on the space above the first ledger line above the staff 10. Whole note on the space below the second ledger line below the staff Written Exercises |37 1.51. Draw the note(s) according to the instructions given. Then label each with the correct letter name. Observe all rules of notation. All notes for this exercise are in the bass clef. 1. Quarter note on the fourth line (this question has been completed for you) 2. Half note on the third space 3. Whole note on the first line 4. Dotted half note on the space above the fifth line 5. Two beamed eighth notes, on the second space and the third line 6. Two beamed eighth notes, on the second line and the fourth line 7. Quarter note on the third ledger line above the staff 8. Half note on the space below the second ledger line below the staff 9. Whole note on the second ledger line above the staff 10. Dotted half note, one ledger line below the staff COMPOSITION 1.52. In the space below, compose eight measures of music, following these guidelines: 1. Your composition will be in three-four meter. 2. Use only rhythms (no pitches), and only the rhythmic values introduced in this chapter. 3. No two measures may be identical. 4. The piece will end with a dotted half note, given in measure 8. 5. Set your metronome to a moderate tempo and lead the class in singing your composition on a pitch that you choose. Use a neutral syllable such as “nah” or “tah.” 38| Composition LE AL N ✪ GE four meter. Measure 8 must contain a whole note. Lead the class in singing your composition on a pitch that you choose. CH 1.53. In the space below, compose a rhythm using the guidelines above, but this time use four- 1.54. If the performance is successful, try your composition as a two-part round. Divide the class in half: group 1 will start the piece on a note of your choice, and group 2 will begin one measure later on another note of your choice. Both groups will sing through the rhythm three times. 1.55. In the space below, write a two-part rhythm composition, eight measures long. Adhere to these guidelines: a. Use three-four or four-four meter. b. Be sure to space your rhythms properly, and align all beats vertically. c. Within each part, no two measures may be identical. d. In both parts, write only one duration to fill measure 8 (either a dotted half note or a whole note, depending on the meter). e. Except for the last measure, the rhythms of the two parts should contrast with each other. Divide the class in half and lead them in singing your composition. Practice each part separately before putting the two parts together. Choose any two notes (one for each part), and use a neutral syllable such as “nah” or “tah.” Composition |39 Chapter Goals Revisited Be sure that you have achieved all Chapter 1 Goals before proceeding to Chapter 2. • Name notes on the treble and bass staves, quickly and accurately. (pages 3, 4–5) • Name notes up to three ledger lines above and below the treble and bass staves, quickly and accurately. (pages 3–4, 5–6) • Understand simple duple, triple, and quadruple meters, and identify the basic meter type of music that you hear. (pages 6–8, 10–11, 22–26) • Accurately and fluently read rhythmic patterns containing whole notes, dotted half notes, half notes, quarter notes, and pairs of eighth notes. (pages 20–21) • Perform a simple piece of music that includes repeat signs, while understanding the structure of first and second endings. (page 13) • Notate music accurately and legibly, including clefs, noteheads, ledger lines, stems, beams, augmentation dots, bar lines, meter signatures, and repeat signs. (pages 14–18) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. 40| Composition CHAPTER 2 Chapter Goals PITCH: THE PIANO KEYBOARD/ RHYTHM: RESTS, TIES, AND SYNCOPATION After you finish this chapter, you should be able to: • Identify the keys of the piano by pitch names, quickly and accurately. • Find notated pitches on the piano keyboard, quickly and accurately. • Accurately sing and hear half steps and whole steps. • Play half steps and whole steps at the piano. • Understand the functions of accidental symbols, including the sharp, flat, natural, double-sharp, and double-flat. • Understand the difference between diatonic and chromatic half steps. • Understand the function of the ottava sign. • Identify any note or piano key with its letter name and octave designation number. • Accurately sing and hear rhythms that include rests, ties, dotted quarter notes, and pickup measures. • Notate music accurately and legibly, including accidental symbols, rests, ties, and single eighth notes. THE KEYBOARD The White Keys of the Keyboard You have now learned the names and staff positions for notes on the treble and bass staves. In order to understand further lessons, it is important to acquaint yourself with the piano keyboard. All musicians should become familiar with the piano, regardless of their primary instrument. Among other reasons: • Most music relies on pitch patterns. The piano makes these patterns easy to visualize because the keys are arranged in front of you horizontally. • Unlike some instruments, the keyboard allows you to play and hear multiple pitches at once. As you work through this book, it will be important to have access to an actual piano to reinforce the pitch patterns that you will learn by sight, sound, and touch. If this is not possible, there are several very good virtual pianos available on the internet, as well as piano apps for smart phones and tablets. A full piano keyboard has eighty-eight keys and spans seven and a half octaves. We will begin with only the five octaves of the keyboard that correspond to the notes that you have already learned. The pitches get lower as you move to the left, and higher as you move to the right. Examine the following keyboard, and notice that the black keys are arranged in groups of two and three. Find a white key that is immediately below a group of two black keys. This is the note C. There are five Cs on this keyboard. Middle C is found nearest the center |41 of the keyboard. The notes continue upward (to the right) and downward (to the left) from middle C. Before you proceed, memorize the letter names for the seven white keys of the piano. Use the Memorization Strategies found near the end of this chapter, and continue to the next section only after you have achieved fluency. Half Steps and Whole Steps The terms half step and whole step are used to describe incremental distances between pitches. The piano keyboard makes it very easy to see, feel, and hear these distances. If one key is immediately beside another, those pitches are a half step apart. Any two keys with one key between them are a whole step apart. It does not matter if the intervening key is black or white. EP L A 42| Y R Most of the adjacent white keys are a whole step apart, with a black key between them. The exceptions are the half steps B to C, and E to F. • The keyboard makes it easy to see, hear, and touch pitch patterns in music. • The pitch C is a white key found just below any pair of two black keys on the keyboard. The remaining pitches proceed sequentially, getting higher as you move right and lower as you move left. Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation • The C that is closest to the middle of the keyboard is called middle C. • The distance of a half step spans any two adjacent piano keys. • The distance of a whole step spans any two keys containing one key between them. It does not matter if the intervening key is black or white. ACCIDENTALS Sharps, Flats, and Naturals Using the seven pitch letters, we can name all of the white keys on the piano. To name the black keys, we do not add more letters but instead use a symbol called an accidental. There are five types of accidentals: Symbol Name Symbol What It Does Sharp ♯ Raises the pitch by one half step Flat ♭ Lowers the pitch by one half step Natural ♮ Cancels a previous accidental Double Sharp 𝄪 Raises the pitch by two half steps (one whole step) Double Flat 𝄫 Lowers the pitch by two half steps (one whole step) When a sharp appears before a note, that note is raised by a half step. When a flat appears before a note, the note is lowered by a half step. Notice that the symbol is always placed before the note on the staff, even though we say “F-sharp” or “D-flat,” and we write “F♯” and “D ♭.” Because a performer reads music from left to right, she must see the accidental first in order to play the correct pitch. Accidentals stay in effect throughout the measure: once a note is sharp or flat it stays that way, and the symbol need not be written again for the rest of the bar (Fig. 2.1.a). A natural sign is used to clear a previous accidental, usually within the same measure (Fig. 2.1b). If a note returns to its normal state in the following measure, composers will often use a courtesy natural as a reminder to the performer (Fig. 2.1c). Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |43 Figure 2.1. a. “Twinkle, Twinkle Little Star” b. “Take Me out to the Ball Game”1 EBSIT E W c. “O Little Town of Bethlehem” (Hymn tune “St. Louis”). Enharmonic Notes Every black key on the piano has both a sharp and a flat name, and each can be represented by two notes on the staff. These pairs of enharmonic notes are written differently but share the same sound (or pitch) and the same piano key. For example, G-flat and F-sharp are enharmonic notes, as are B-flat and A-sharp. All possible enharmonic pairs for the black keys of the keyboard are shown below. Because there is no black key between B and C, you might think there is no such note as B-sharp. In fact, there is a B-sharp; it is enharmonic to C. This is also true for E-sharp, which is enharmonic to F. Remember, the sharp always raises a pitch by one half step; it 1 Six-eight meter will be covered in Chapter 6. 44| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation does not matter whether the resulting note is a white key or black key. Likewise, F-flat is enharmonic to E, and C-flat is enharmonic to B. EBSIT E Students often wonder why it is necessary to have more than one name for each pitch; the answer has to do with clarity of notation. Figure 2.2a is an excerpt from a ragtime piece by Scott Joplin. Its only accidentals are D-sharp (in the treble staff) and E-flat (in the bass staff). These two enharmonic notes sound the same but must be notated differently in this piece. In the treble staff, each D-sharp proceeds to an E. If the D-sharps were instead written as E-flats, the composer would then need to add natural signs to the Es that follow and the music would look very cluttered (Fig. 2.2b). Likewise, if the E-flats in the bass staff were instead written as D-sharps, then courtesy naturals would be needed on each of the Ds. W Why Do We Need Enharmonics? Figure 2.2. Scott Joplin, “The Cascades,” mm. 4–8. a. Correct spellings for D-sharp and E-flat. b. Incorrect spellings for D-sharp and E-flat. The need for extra naturals results in cluttered notation. Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |45 Examine Figure 2.1c again. The hymn tune “St. Louis” (widely known as “O Little Town of Bethlehem”) uses the note E-sharp, which is a white-key sharp, enharmonic to F. It may seem simpler to use F instead of E-sharp, but doing so requires an extra accidental in the measure, in order to reinstate F-sharp on beat 3. Moreover, the E-sharp helps to show the “down-up” contour of the music, while the F-natural is visually deceptive, misleading the performer to think that all three notes are at the same pitch level. Double Sharps and Double Flats A double sharp raises the pitch of a note by two half steps (or one whole step). A double flat lowers the pitch of a note by two half steps (or one whole step). Double accidentals are normally enharmonic to natural (or white-key) notes. For example, C-double-sharp is enharmonic to D-natural, and B-double-flat is enharmonic to A-natural. • The double flat is notated as two flats side-by-side, just touching each other. • The double sharp is notated as an “x.” Avoid using double accidentals to express black-key notes. Technically “E-double-sharp” is enharmonic to F-sharp, and “C-double-flat” is enharmonic to B-flat. But there is rarely, if ever, a need to express a single-accidental note with a double accidental. 46| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation Diatonic and Chromatic Steps Examine the two half steps below, play both at the keyboard, and notice that they sound the same even though they are written differently. The first example, A to B-flat, is a diatonic half step, meaning it is written using two adjacent letter names (A and B). The second example, A to A-sharp, is a chromatic half step, meaning it is written using the same letter name plus an accidental. The word diatonic comes from the Greek word diatonos, which means “proceeding through tones.” When writing a diatonic half step, you should proceed to the next letter name (A to B) and then alter it, if necessary, to create a half step above the starting tone. (B becomes B-flat.) The word chromatic comes from the Greek word chromatikos, which means “colored.” A chromatic half step is simply an alteration (or a different “color”) of the same letter name. Further examples of diatonic and chromatic half steps are given below. Play each at the piano as you follow the notation. Whole steps are typically diatonic; that is, most whole steps use adjacent letter names and staff positions, regardless of the accidentals present. • A sharp sign (♯) raises the pitch of a note by one half step. • A natural sign (♮) is used to clear a previous accidental, usually within the same measure. A courtesy natural may be used in a subsequent measure after an accidental to remind the performer that the note has returned to its unaltered state. EP L A Y • Accidentals carry through the measure. R • A flat sign ( ♭) lowers the pitch of a note by one half step. • A double sharp (𝄪) raises the pitch of a note by two half steps (one whole step). Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |47 • A double flat ( 𝄫) lowers the pitch of a note by two half steps (one whole step). • In a diatonic half step, the two notes have different letter names (for example, C to D-flat). • In a chromatic half step, the two notes share the same letter name (for example, C to C-sharp). OCTAVE DESIGNATION The Ottava Sign Some instruments, such as the piano, flute, and tuba, are able to play notes that reach far outside the treble and bass staves. In order to avoid excessive ledger lines and to simplify notation for such instruments, the ottava sign may be used. Ottava, abbreviated “8va,” is the Italian word for octave. When the symbol is placed above the staff (usually the treble staff), the passage is to be played one octave higher than written. When the music is to be played one octave lower than written, the symbol is placed below the staff. In this case the designation 8va bassa (bassa = “below”), 8a bassa, or 8ab may also be used. Claude Debussy, “Brouillardes,” mm. 19–21, from Preludes, Book II. 48| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation Octave Designation Numbers Reexamine the Joplin piano excerpt in Figure 2.2. Imagine you have prepared this passage for a piano lesson. When you play it for your teacher, she responds: “You missed the C in the first measure.” This could be confusing, because that measure contains Cs in three octaves. Octave designation numbers allow us to distinguish notes of the same name that appear in different octaves. Several systems exist for octave designation, but the most common is the one used by the Acoustical Society of America. In this system, the lowest C audible by most humans is designated as C1 (“C-one”). This is also the lowest C on a full piano keyboard. Continuing upward, each note name in that octave is labeled with the number “1” until the next C, which is labeled as C2. The octave number changes at each C. For example, the “4” octave contains C4 (middle C) and the D, E, F, G, A, and B above it. The next C begins the “5” octave. The Joplin example mentioned earlier (Fig. 2.2) uses C3, C4, and C6. • The ottava sign (8va) indicates that a note or passage of notes is to be played one octave higher than written. EP L A Y • Ottava signs are used to avoid excessive ledger lines when writing notes well beyond the extremes of the treble and bass staves. R • The ottava bassa sign (8va bassa or 8ab) indicates that a note or passage of notes is to be played one octave lower than written. • An octave designation number is used to identify the exact location of a pitch. The lowest C on the piano is C1, and all of the pitches within that octave (D, E, F, G A, B) are also identified with the suffix “1.” The next C is C2, and so on. • Middle C is designated as C4. RHYTHM Rests A rest is a notated symbol that represents a definite period of silence. The chart below lists the most commonly used rests, their corresponding note values, and the length of each in a four-based meter (two-four, three-four, and four-four). Rest Name Symbol Eighth rest 𝄾 Quarter rest Duration in à, è, and ò Meter Equivalent Note One-half beat 𝅘𝅥𝅮 𝄽 One beat 𝅘𝅥 Half rest 𝄼 Two beats (Do not use in à and è) Whole rest 𝄻 Four beats or one full measure of rest in any meter 𝅗𝅥 𝅝 Divide the class in half, choose any two pitches, and sing each example of Figure 2.3 on a neutral syllable. Finger-count as you sing, and use this order: • Part 1 alone • Parts 1 and 2 together • Part 2 alone Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |49 50| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation W EBSIT E Observe all rests, and be sure to continue counting through every rest so that you reenter in the correct place. The people singing Part 2 should listen carefully to Part 1 in order to keep track of the passing beats during the rests. Figure 2.3. Rhythms with rests. As you perform each example, notice that: • The whole rest is used to fill an entire measure of any meter. (This is not the case for a whole note.) • The half rest is not used in three-four meter. Instead, two quarter rests are used (ex. b, m. 2). • There are no dotted half rests. Instead, a quarter rest and half rest are used to represent three beats in four-four meter (ex. a, m. 5). (Proper rest notation is discussed further in the “Notation” section below.) Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |51 Ties When two or more notes are connected by a tie, their durations are combined into a single sound. For example, two tied quarter notes are equal in length to a half note; three tied quarter notes are equal in length to a dotted half note. Generally, there are three cases in which a tie is necessary: 1. It is not possible to write a single duration because of an intervening bar line. 2. The sound lasts longer than the number of beats in a measure. E W 3. No single symbol exists to notate the specified duration. EBSIT Divide the class in half, and perform Figure 2.4 in the same manner as the previous examples. Figure 2.4. a. In Part 2, the last beat of measure 1 is tied to the first beat of measure 2. Because the sound “straddles” the bar line, it is impossible to write a half note on beat 3. Instead, we must use a tie. b. In Part 2, the first sound lasts for four full beats (three plus one). Because each measure of three-four meter can contain only three beats, the fourth beat of the sound must be notated as a quarter note at the beginning of measure 2, tied from the previous dotted half note. c. In Part 2, a half note is tied to an eighth note, resulting in a sound that is two and a half beats long. Since there is no single duration that represents two and a half beats, a tie is needed. 52| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation EBSIT E In the meters you have learned so far, a dotted quarter note lasts for one and a half beats. In other words, it is equal in length to a quarter tied to an eighth note. (You may also wish to think of it as three tied eighth notes.) Divide the class in half, and perform Figure 2.5 in the same manner as the previous examples. W Dotted Quarter Notes and Syncopation Figure 2.5. Dotted quarter notes. a. In Part 2, the quarter note on beat 1 is tied to the first eighth note of beat 2. In other words, the first sound happens on beat 1 and lasts through the first half of beat 2. The second sound happens on the second half (or the “and”) of beat 2. Now perform Part 3; it should sound identical to Part 2. Here, a dotted quarter note replaces the tied notes. Because the first half of beat 2 is absorbed into the dotted quarter note, the second half must be written as a single eighth note with a flag. b. In Part 2, the eighth note on the “and “ of beat 3 is tied to a quarter note on beat 4. In Part 3 (identical in sound to Part 2), a dotted quarter note replaces the two tied notes. In this example, the dotted quarter, the longest duration in the measure, occurs on the “and” of 3, drawing attention to an otherwise weak part of the measure. This disruption of the normal system of metric accents is called syncopation. Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |53 Two common syncopation techniques are the agogic accent (used in the previous example) and the dynamic accent. An agogic accent occurs when a sound on an otherwise weak part of the measure is held longer than the sounds around it. Perform Figure 2.6 in two parts: half the class will sing the rhythm on a comfortable pitch, and the other half will count eighth notes. The example contains three types of agogic accents. The affected counts are enclosed in boxes. EBSIT E W Figure 2.6. Agogic accents. EBSIT 54| Figure 2.7. Dynamic accents. E W A dynamic accent occurs when a sound on an otherwise weak part of the measure is played louder than those surrounding it. This instruction is indicated by placing the symbol > above or below a notehead. (The symbol is also used on strong beats when a composer wants to indicate even more emphasis.) Dynamic-accent syncopation is common in rock and popular styles; the performer may create a perceived syncopation in a sequence of equal durations by playing some notes louder than others. Perform Figure 2.7 using the syllable “tah,” and add extra emphasis to the accented notes. This figure is prevalent throughout Informed Listening Example 2.2 (“Billie Jean”). Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation Sing “Amazing Grace” on letter names while finger-counting. Notice that the song begins on beat 3 of the measure rather than beat 1. This is called a pickup measure or anacrusis. In order to begin the song, count: “ONE two three ONE two C F. . . .” Often, the number of pickup beats is subtracted from the last bar of the piece. In this case, the final bar contains only two beats. EBSIT E W The Anacrusis (Pickup Measure) Figure 2.8. “Amazing Grace” (Hymn Tune “New Britain”). Sing the song several more times in order to review some of the other rhythmic concepts covered in this chapter: • Quarter rests occur on beat 2 of measures 4, 8, 12, and 16. (Notice that the pickup measure is not numbered.) Observe all rests as you sing, but be sure to continue counting through the rests so that you reenter on the correct beat. • A dotted half note in measure 7 is tied to a quarter note in measure 8; the total duration of the sound is four beats (three plus one). The same is true in measures 15–16. • Dotted quarter notes occur in measures 9 and 11. As you sing and count, notice that the single eighth note following each dotted quarter occurs halfway between beats 2 and 3. The American folk tune “Wayfaring Stranger” (Fig. 2.9) begins with a pickup measure of three eighth notes (one and a half beats). Divide the class, with one half singing pitch names and the other half counting eighth notes. To begin the song, count “ONE and Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |55 E W EBSIT TWO and THREE D D A A. . . .” Notice that the final measure contains two and a half beats in order to balance the pickup measure. Figure 2.9. Trad., “Wayfaring Stranger.” Sing the song several more times in order to review some of the other rhythmic concepts covered in this chapter: • Eighth rests occur in measures 2, 4, and 6. • In measures 1, 3, 5, and 7, a half note is tied to an eighth note, resulting in a sound that is two and a half beats long. The tie is needed because no single symbol exists to represent this duration. EP L A Y R • Syncopation (via agogic accents) occurs in measures 2 and 6. The dotted quarter note that begins on the “and” of beat 2 is the longest duration in the measure. • A rest is a symbol that represents a definite length of silence. Whole rests, half rests, quarter rests, and eighth rests are covered in this chapter. Each is the same length as its corresponding note value. • A tie is used to combine two or more written durations into a single sound. Ties are normally used: o When a sound is to last longer than one measure (e.g., four beats in threefour meter) o When a sound is held over a bar line o When no single symbol exists to notate that duration (for example, a half note tied to an eighth note) • A dotted quarter note lasts one and a half beats in two-four, three-four, and four-four. It is usually accompanied by a single eighth note (or eighth rest) to complete the remaining half-beat. • Syncopation is a disturbance of the normal system of metric accents that occurs when an otherwise weak part of a measure or beat is emphasized. This may occur through an agogic accent (the note is longer than those around it) or a dynamic accent (the note is performed more loudly than those around it). • An anacrusis or pickup measure is used to start a piece of music on a beat other than beat 1. For example, “Amazing Grace” and “Auld Lang Syne” begin on beat 4, and “Wayfaring stranger” begins on the “and” of beat 3. • The final bar of music is often shortened by the length of the pickup measure. 56| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation NOTATION Accidentals Accidentals are always written before the notes they affect. To draw a sharp: the center opening of the symbol must intersect the exact line or space occupied by its corresponding note. 1. Draw the two vertical lines of the symbol exactly perpendicular to the staff lines. The second line should be slightly higher than the first. 2. Draw the horizontal segments at a slight angle to the staff lines, parallel to each other. To draw a flat: the curved opening of the flat must intersect the exact line or space occupied by its corresponding note. 1. Draw a vertical line about two staff spaces long. Its bottom half should intersect the line or space of the next note. If the flat is on a line, then the vertical should begin and end in the middle of a space. 2. Draw the curved part of the flat to the right of the line. It should look like half of a heart shape. To draw a natural: the center opening of the symbol must intersect the exact line or space occupied by its corresponding note. 1. Draw an L where the vertical leg is two spaces long, and the horizontal leg is angled slightly upward. 2. Draw an upside down L parallel to the first. To draw a double sharp: draw an x whose midpoint exactly intersects the line or space of its corresponding note. Do not draw two sharps. To draw a double flat: draw two flats, side-byside, just barely touching each other. Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |57 Rests A whole rest is drawn as a solid rectangle, about twice as wide as it is tall, in the middle of a measure. It hangs from the fourth line and takes up exactly one half of a staff space. A whole rest has two meanings: 1. It may represent four quarter-note beats of rest. 2. It may represent one whole measure of silence in any meter. A half rest is the same shape as a whole rest, but it sits on the third line. Align the half rest with the beat on which it begins, not in the middle of the two beats. A quarter rest occupies the middle two spaces of the staff, extending about halfway into the top and bottom spaces. To draw a quarter rest: 1. Starting in the middle of the fourth space, draw a slanted letter Z ending at the second line. 2. Draw a slanted letter C that intersects the second line and ends in the middle of the first space. An eighth rest occupies the middle two staff spaces. To draw an eighth rest: 1. Draw a dot that fills most of the third space. 2. Draw a number 7 whose top portion is curved downward. For the time being, do not use augmentation dots with rests; instead, use a combination of rests to represent the values that you need. 58| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation Ties A tie always connects two or more instances of the same note. Draw the tie from notehead to notehead, on the opposite side from the stem. Do not tie from stem to stem. If an altered note is tied over a bar line into the next measure, do not repeat the accidental on the tied note. But if the same note is repeated later in the subsequent measure, the accidental must be reinstated. When tying whole notes together, place the tie on the opposite side of the note from where the stem would be. Dotted Quarter Note and Single Eighth Note Recall from Chapter 1 that an augmentation dot is always placed after the note it affects. When the note occupies a space, place the dot in the same space; when the note occupies a line, place the dot in the space above that line. Draw a single eighth note with a curved flag. The flag is always drawn on the right side of the stem, regardless of stem direction. Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation |59 Notation and Metric Hierarchy The notation of beams, flags, rests, and ties should always reflect the natural metric accents in a measure. In four-four meter, half rests should only be used on beats 1–2 (the first half of the measure), or beats 3–4 (the last half of the measure). Because beat 3 receives a metric accent in 4/4, the performer needs a visual cue to see where the measure divides. Therefore, do not use a half rest in the middle of the measure, on beats 2–3. Instead, use two quarter rests. On the other hand, a half note beginning on beat 2 is acceptable. Do not use half rests in three-four meter. For two continuous beats of rest within a measure, use two quarter rests. In general, be sure that beats are visible and easily counted. A beamed pair of eighth notes should begin on a beat, not on the “and.” Do not let the pair straddle two beats. 60| Pitch: The Piano Keyboard/Rhythm: Rests, Ties, and Syncopation MEMORIZATION STRATEGIES To help you memorize the notes of the keyboard, create a set of twenty-five flashcards similar to those you made in Chapter 1. On the front of each card, draw or photocopy a picture of a two-octave piano keyboard. (You can also photograph a keyboard and crop it to two octaves.) On the keyboard, mark one key with an X. On the back, write the pitch name for that key. (For black keys, write both enharmonic spellings.) Work gradually as you study. 1. Start with only F and C. 2. Add E and B , so that you can use the white-key half steps as anchor points. 3. Add D, G, and A. 4. Add black keys with sharp names. 5. Add black keys with flat names. (Study sharps and flats separately.) SINGING EXERCISES 2.1. Rhythmic patterns. Tempo goal: 𝅘𝅥 = 100 bpm. This exercise presents typical two- and three-beat rhythmic patterns using the durations introduced in this chapter. Each pattern consists of: • A full measure of quarter notes to establish the meter and pulse • The pattern itself • A landing measure in which you should prepare to sing the following pattern Practice the patterns using this method: a. Pick a time signature (two-four or three-four) for your practice session. b. Set your metronome to a moderately slow tempo—about 72 bpm. c. Choose a comfortable pitch for your voice, and sing the rhythms in your chosen meter in the order given. Use a neutral syllable such as “nah” or “tah.” Repeat this step several times. Singing Exercises |61 d. Sing the rhythms out of order, leaping from one to the next randomly. Remember to use the landing note to choose your next rhythm, and always keep a steady pulse. e. Gradually increase the tempo of the exercise until you reach the tempo goal. f. Repeat the exercise in four-four meter (see Ex. 2.2 and 2.3). EBSIT E W Two-Beat Patterns 62| EBSIT E W Three-Beat Patterns Singing Exercises 2.2. Compose your own practice patterns in four-four using any of these methods. Be sure to begin with a measure of four quarter notes before the pattern, and end with a landing measure after the pattern. Observe all rules of notation. a. Combine any two of the two-beat patterns. b. Add a quarter note before or after one of the three-beat patterns. c. Add a pair of eighth notes before or after one of the three-beat patterns. 2.3. Compose your own practice patterns by substituting rests for one or more of the notes in the patterns above. Do the same with the four-four patterns you composed in Exercise 2.2. Practice the patterns until you become fluent. 2.4. In Exercises 2.1–2.3, tie the last beat of the pulse measure over the bar line to the first note of the pattern. Practice the patterns until you become fluent. 2.5. Rhythm exercises. Each of the examples below is in two parts, where Part 1 is a basic rhythm and Part 2 is the same rhythm with rests and/or ties added. a. Set your metronome to a slow to medium tempo, and perform Part 1 several times while finger-counting. b. Divide the class, so that one half performs Part 1 and the other performs Part 2 simultaneously. Those singing Part 2 should listen carefully to Part 1 in order to place the rests and ties accurately. c. If you are working on your own, find a friend to help you do the exercises, or record yourself singing Part 1; then play back Part 1 as you sing Part 2 over it. d. In singing the two parts together, choose any two pitches, and sing on a neutral syllable. Singing Exercises |63 e. When you are ready, gradually increase the tempo. 1. 2. 3. 4. 64| Singing Exercises 5. 6. 7. Singing Exercises |65 2.7. At the piano, choose a starting pitch that is comfortable and near the middle of your voice range. Improvise a melody comprising only whole steps and half steps, up and down. You may choose to change direction at any time, especially if you feel you’re nearing the extremes of your vocal range. Sing the name of the step as you play. A sample exercise is given below. 2.8. Repeat Exercise 2.7, but this time sing each pitch before playing it. Play the pitch only after you sing it, to check your accuracy. HEARING EXERCISES Goal for Exercises 2.9–2.15: ten consecutive correct answers. 2.9. 66| Your instructor or study partner will play one of the pitch patterns in Exercise 2.6 above. Choose the correct pattern. Hearing Exercises LE AL N ✪ CH Play and sing the next exercises at the piano until you have memorized them and can sing them all without the piano. Then, try the exercises starting on a different pitch (not D). GE 2.6. 2.10. Your instructor or study partner will play three pitches at the piano: a starting note, a step away, and then the starting note again. (For example, C - D-flat - C or G - F - G.) Identify the location of the middle pitch from among these choices: a. Half step above b. Whole step above c. Half step below d. Whole step below LE AL N CH ✪ choose from four patterns. GE 2.11. Repeat Exercise 2.10, but mix up the types of steps. The player may start on any pitch and a. Starting pitch; half step up; whole step down b. Starting pitch; whole step up; half step down c. Starting pitch; half step down; whole step up d. Starting pitch; whole step down; half step up 2.12. Your instructor or study partner will play one of the two-beat rhythmic patterns from Exercise 2.1. Choose the correct pattern. 2.13. Your instructor or study partner will play one of the three-beat rhythmic patterns from Exercise 2.1. Choose the correct pattern. one or more of the notes. LE AL N CH ✪ GE 2.15. Repeat Exercises 2.12, 2.13, and 2.14, but this time your instructor will substitute a rest for ✪ CH below. Write the correct rhythm for the blank measure. LE AL N GE 2.14. Your instructor or study partner will play a four-beat rhythmic pattern using the model 2.16. Set your metronome to a moderate tempo (about 90–100 bpm). Sing “When the Saints Go Marching In” while finger-counting. (Lyrics are given on next page.) Write the rhythm above the words given; include bar lines. (Do not write any pitches.) There will be some Hearing Exercises |67 rests between notes, but there are no ties. Use only the durations listed, all of which are used in the song. 2.17. Set your metronome to a moderate tempo (about 90–100 bpm) and sing the chorus from the song “Jingle Bells” while finger-counting. (Lyrics are given below.) Treating the first duration as a quarter note, write only the rhythm above the words given; include bar lines. Assign one duration to each syllable. The song contains no rests or ties. Use only the durations listed, all of which are used in the song. INFORMED LISTENING: EXAMPLES FOR STUDY The pieces in this section exemplify several of the rhythmic and pitch techniques introduced in this chapter. First, find the pulse and meter; then finger-count with the music as you follow each explanation. 68| Informed Listening: Examples for Study 2.18. Earth, Wind, and Fire, “Can’t Hide Love,” from Greatest Hits Meter: quadruple Tempo: moderate, about 78 bpm What to listen for: • The song begins with a heavily syncopated four-note figure in the brass against a steady beat in the drums. • The brass figure proceeds upward by whole steps (Eb - F - G - A). Find these notes on the piano and play along with the horn part. 2.19. Wild Asparagus, “Lafferty’s,” from Contra Music: The Sound of New England Meter: duple Tempo: moderately fast, about 110 bpm What to listen for: • After the call-and-response passage between the guitar and drum, the violin and flute enter with a syncopated figure tied over the bar line. The figure is present throughout most of the work. 2.20. Daryl Hall and John Oates, “You Make My Dreams,” from The Essential Daryl Hall and John Oates Meter: duple Tempo: moderate to fast, about 83 bpm What to listen for: • The pulse is difficult to detect at first; begin counting when the bass drum enters at about 0′05″. • The bass drum plays quarter notes while the guitar plays eighth notes with a strong dynamic accent on the “and” of each beat. • In the fourth measure after the bass drum enters, there is a full quarter rest on beat 2. • The voice echoes the guitar’s dynamic accents by emphasizing otherwise weak words that fall on the “ands” of beats. 2.21. Maurice Ravel, “Pavane de la Belle au bois dormant,” from Ma Mère l’Oye (Mother Goose) Meter: quadruple Tempo: very slow, about 55 bpm What to listen for: • Follow the rhythm of the solo flute, and notice the difference between the two primary rhythmic figures (labeled as A and B): Informed Listening: Examples for Study |69 Note: measures 1 and 2 contain a quarter tied to an eighth instead of a dotted quarter note. This is done so that beat 3 will be visible to the performer. 2.22. Michael Jackson, “Billie Jean,” from Thriller Meter: quadruple Tempo: fast, about 118 bpm What to listen for: • The bass plays eighth notes throughout, with dynamic accents on beat 1 and the “and” of 2 (see Fig. 2.7). These accents are highlighted by the vocal “oohs,” which enter around 0′20″. • Agogic accents occur throughout the song, but they are particularly noticeable in the chorus, on the words “not my lover”: • The syncopated “ooh” figure heard throughout most of the song is made up of a whole step and a half step (F♯ - G ♯ - A - G ♯). Play the figure in rhythm on the piano or your instrument. 2.23. Gabriel Fauré, “Au Cimetière,” Op. 51, No. 2 Meter: triple Tempo: slow, about 64 bpm What to listen for: • The piano establishes a quarter-note pulse, after which the voice enters with a pickup note on measure 2, beat 3. (Mm. 1–10 of the vocal part are notated below.) • The most prominent rhythm is a dotted quarter note followed by three eighth notes. As you listen and finger-count, notice that the first of the three eighth notes falls on the “and” of beat 2, or halfway between beats 2 and 3. The remaining two eighths are evenly divided on beat 3. • The vocal part comprises primarily half steps and whole steps (marked below). • In measure 6, the vocal part has a rest on the “and” of beat 2 and the beginning of beat 3. Notice that two eighth rests must be used here, so that beat 3 will be visible to the performer. 70| Informed Listening: Examples for Study INFORMED LISTENING: EXAMPLES WITH QUESTIONS Listen to each example, read the accompanying questions, and then listen again several times. Finger-count as you listen, and answer the accompanying questions by circling or choosing as required. Some questions ask you to distinguish between half steps and whole steps. If you have trouble, try matching the pitches on the piano as you listen. 2.24. Johannes Brahms, Waltz, Op. 39, No. 15 Meter: triple Tempo: moderate, about 102 bpm (the tempo is fluid and varies throughout) 1. Which of these rhythms is most prevalent throughout the piece? 2. True or false: this piece begins with a pickup. 3. The last two notes of the melody are a [half step / whole step] apart. If necessary, use the piano to help you. 2.25. Chicago, “25 or 6 to 4,” from Chicago II Meter: quadruple Tempo: very fast, about 148 bpm 1. At the beginning of the song, the guitar plays a set of five repeated notes, a rest, and then another set of five repeated notes. The distance between the two sets of notes is a [half step / whole step]. 2. The rest mentioned in question 1 falls on which beat? [beat 1 / beat 2 / beat 3 / beat 4] Informed Listening: Examples with Questions LE AL N CH ✪ GE 3. Notate the first four measures of the guitar part below. It begins on A and is composed entirely of half steps and whole steps. The rhythm for all measures is the same. If you have trouble, count aloud and use the piano to help you. |71 2.26. Wolfgang Amadeus Mozart, “Menuetto” from Symphony No. 40 in G Minor, K. 550 Meter: see question 1 Tempo: fast, about 145 bpm 1. The meter of this piece is most likely [duple / triple / quadruple]. 2. Which are prominently featured in the piece? (Choose one answer.) a. Rests b. Ties over bar lines c. Dotted quarter notes d. Whole steps 3. True or false: this piece begins with a pickup. 2.27. Billy Joel, “Don’t Ask Me Why,” from The Essential Billy Joel Meter: duple Tempo: moderate, about 96 bpm 1. Which describes the rhythmic relationship of the instruments and voice at the beginning of the work? a. The guitar plays the pulse, and the voice and bass drum are syncopated. b. The bass drum plays the pulse, and the guitar and voice are syncopated. c. The guitar and bass drum play the pulse, and the voice is syncopated. d. All three parts are syncopated. 2. Which of these best describes the relationship of the instruments and voice at the bridge (about 1’05”)? a. The guitar plays the pulse, and the voice and bass drum are syncopated. b. The bass drum plays the pulse, and the guitar and voice are syncopated. c. The guitar and bass drum play the pulse, and the voice is syncopated. d. All three parts are syncopated. 3. Which of these rhythmic terms best describes what happens in the chorus (found at about 0′24″, 0′54″, 2′32″), on the words “Don’t wait . . .” and “Just take . . .”? a. Metric accent b. Dynamic accent c. Agogic accent 4. The two pitches that occur on “Don’t wait” and again on “Just take” form a [whole step / half step]. 72| Informed Listening: Examples with Questions 2.28. Wolfgang Amadeus Mozart, “Allegro” (Movement I) from Eine Kleine Nachtmusik Meter: quadruple Tempo: fast, about 134 bpm 1. Which best represents the rhythm of the first four measures? 2. Which represents the rhythm of the next two measures (mm. 5–6)? 2.29. Larry Unger and Ginny Snowe, “Gaye’s Steps,” from Waltz Time II Meter: triple Tempo: fast, about 146 bpm 1. After an eight-measure introduction, a melody enters at about 0′10″ in the upper voice of the piano. This melody contains mostly [half steps / whole steps]. 2. The first four measures of the melody (beginning about 0′10″) use this rhythm: Informed Listening: Examples with Questions |73 Which of these best represents the rhythm of the next two measures? 2.30. Johannes Brahms, “Bitteres zu sagen denkst,” Op. 32, No. 7 Recommended recording: Brahms/Liszt: Lieder, Thomas Quasthoff Meter: quadruple Tempo: moderately slow, about 82 bpm 1. Which rhythm is most prevalent in the voice part? 2. Which rhythm is most prevalent in the lowest voice of the piano? 3. The last two notes sung by the vocalist (at about 1′30″) are a [half step / whole step] apart. 74| Informed Listening: Examples with Questions DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 2.31. Memorize Exercise 2.6, and sing it as you go about your day. Try starting on various pitches, taking care to stay in your vocal range. (Since you will be away from the piano, sing the first pitch on a neutral syllable instead of a letter name.) 2.32. Memorize the two- and three-beat rhythmic patterns from Exercise 2.1. As you hear music throughout the day, identify the meter of the piece of music; then choose a rhythmic pattern and repeat it continuously over the music in tempo. Choose another pattern, and do the same. As you sing, try to picture the notation of each rhythm in your mind. 2.33. Once you become fluent with Drill 2, improvise your own rhythms over the music you hear by mixing up the patterns. CLASSROOM ACTIVITIES 2.34. The songs listed here are used as examples in Chapters 1 and 2. 1. Choose one song, and write it on the board. 2. The class will sing the song on note names while finger-counting. 3. One student leader will choose three or four notes in the song and replace them with rests of the same duration, and then lead the class in performing the “new” version of the song. 4. Restore the song to its original form, and change leaders. List of songs: • “Aura Lee” • “Old McDonald” • “Hyfrydol” • “Bonner” • “Amazing Grace” 2.35. The song “Auld Lang Syne” features the rhythmic figure 𝅘𝅥• 𝅘𝅥𝅮 1. Copy the song onto the board; the class will sing it on note names while fingercounting. 2. Replace every occurrence of 𝅘𝅥• 𝅘𝅥𝅮 in the song with one of the following rhythms. 3. Perform the new version of the song, using your chosen rhythmic figure throughout. Do not change any of the pitches. Classroom Activities |75 “Auld Lang Syne” (trad.) WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 2 online drills and quizzes at www.oup.com/us/root. 2.36. For each question: a. Write the name and octave designation number in the blanks below the note. b. Match each note on the staff to its keyboard position by writing its number on the correct piano key. For black keys, write your answers in the blank above the key. Do not write the letter names on the piano keys. Because of enharmonic spellings and ledger lines, some keys will have more than one number. Middle C is marked as “C” on the keyboard, and the first two answers are given. 76| Written Exercises Written Exercises |77 2.37. For each set of questions, draw the requested clef and notate the pitches using the durations indicated. If your answer is more than three ledger lines outside the staff, use the 8va or 8va bassa symbol. The first note of each set has been completed for you. 78| Written Exercises 2.38. For each question: a. Add bar lines to fit the given meter. b. Notate the music on the staff using the notes given. Be sure to include bar lines when you write each melody on the staff. Written Exercises |79 2.39. For each set of questions, write the requested steps above and below each note. Write both notes as quarter notes, and be sure to write the upper note first. Watch for clef changes, and use the keyboard to help you. a. Write a whole step above and below each note. b. Write a diatonic half step above and below each note. c. Write a chromatic half step above and below each note. Because each set of notes occupies one measure, you will need to use natural signs for some of your answers. 2.40. Each number on the keyboard corresponds to a number on the staves below. For each question, notate the correct pitch on the staff in every possible enharmonic spelling. Some keys have three possible spellings; others have only two. If there are only two spellings, draw an X in the third measure. Do not use these answers: C-double-flat, B-double-sharp, F-double-flat, E-double-sharp. 80| Written Exercises Written Exercises |81 2.41. Rewrite each melody at the given pitch, and divide it between the treble and bass staves, so that no ledger lines are used except middle C. (All instances of middle C are given—some in treble, some in bass.) Fill in the empty spaces on each staff with the appropriate rests. Observe all rules of notation. A sample melody is given. Sample melody: “Aura Lee” (mm. 1–4) 1. “This Old Man”: Add stems and/or beams to each middle C given. 82| Written Exercises 2. “Annie Laurie”: Some measures have been completed for you. There are no middle Cs in this melody. Written Exercises |83 2.42. Provide one duration that is equal in length to the tied notes given. Write your answer at the same pitch as the given notes. 2.43. Complete each measure by writing only one rhythmic value. Notate your answer at the same pitch as the given notes in that measure. If the measure contains only rests, choose any note. If the measure is already complete, write the word complete under it. 84| Written Exercises 2.44. Complete each measure by writing exactly two rhythmic values. The durations may be the same or different. In many cases, there will be more than one correct answer. Notate your answer at the same pitch as the given notes. 2.45. Complete each measure by writing the correct combination of rests. Be sure to write the rests in the correct order and vertical position on the staff. If the measure is already complete, write the word complete under it. Written Exercises |85 86| Written Exercises LE AL N ✪ GE long to fit in a measure, so you will need to rewrite them using ties over the bar line. (For example, you might need to express a dotted half note as a quarter note at the end of one measure tied to a half note at the beginning of the next.) Two sample questions have been completed for you. CH 2.46. For each question, rewrite the given durations in the meter shown. Some durations are too COMPOSITION 2.47. For each example: a. Notate the requested pitches on the staff, taking care to include the accidentals indicated. b. Compose your own rhythm for each measure, using only the notes included for that measure. c. Write your composition on the board, and lead the class in performing it. You may use rests and ties within a measure, but do not tie any notes over a bar line. For example, if three pitches are given in a measure of four-four, you might choose from: • Two half notes • A dotted half and quarter note • Two eighth notes followed by a quarter rest and half rest Composition |87 Many other rhythmic possibilities exist. 2.48. Create your own rhythm composition using these steps: 1. Draw each of the symbols shown in the next example on an index card, and then make a second copy of the set. (You should have two half-note cards, two quarter-note cards, etc.) 2. Shuffle the cards and place them on a table in a horizontal line, in random order. 3. On a sheet of paper, rewrite the rhythm in two-four, three-four, or four-four meter, just as you did in Exercise 2.46. Add bar lines, ties, beams, and flags as necessary to show the proper beat divisions. 4. If you end up with an incomplete measure at the end, add the correct number of rests to complete it. 5. Write your composition on the board, choose a pitch, and lead the class in singing it on a neutral syllable. 88| Composition LE AL N ✪ GE to decide how many beats the pickup will be.) Add rests as necessary to complete the final measure, keeping in mind that you must compensate for the pickup measure. CH 2.49. Complete Exercise 2.48, but start your composition with a pickup measure. (You are free 2.50. Compose a two-part rhythmic composition modeled on those in Exercise 2.5: a. Your rhythm will be eight measures long. b. Use only the rhythms covered so far, and be sure to include the ones introduced in this chapter. c. Do not use any rests or ties in Part 1. d. In Part 2, duplicate the rhythm of Part 1, but add ties over the bar line and replace some notes with rests. Chapter Goals Revisited e. Write your composition on the board, and lead the class in performing it. Use the performance instructions outlined in Exercise 2.5. Be sure that you have achieved all Chapter 2 Goals before proceeding to Chapter 3. • Identify the keys of the piano by pitch names, quickly and accurately. (pages 41–42, 50, 61) • Find notated pitches on the piano keyboard, quickly and accurately. (pages 41– 42, 50, 61) • Accurately sing and hear half steps and whole steps. (pages 42–43, 66, 66–67) • Play half steps and whole steps at the piano. (pages 42–43, 66, 66–67) • Understand the functions of accidental symbols, including the sharp, flat, natural, double-sharp, and double-flat. (pages 43–44, 46) • Understand the difference between diatonic and chromatic half steps. (pages 47–48) • Understand the function of the ottava sign. (page 48) • Identify any note or piano key with its letter name and octave designation number. (page 49) • Accurately sing and hear rhythms that include rests, ties, dotted quarter notes, and pickup measures. (pages 49, 51–56, 61–65, 67–68) • Notate music accurately and legibly, including accidental symbols, rests, ties, and single eighth notes. (pages 57–60) Once you are confident you have achieved these goals with speed and accuracy, proceed to the next chapter. Composition |89 CHAPTER 3 Chapter Goals PITCH: MAJOR KEYS 1 RHYTHM: BEAT SUBDIVISIONS After you finish this chapter, you should be able to do the following, quickly and accurately, for major keys containing up to four sharps or flats: • Sing major scales with solfège, scale degree numbers, scale degree names, and letter names. • Play major scales at the keyboard. • Write major scales with or without key signatures, in treble clef, bass clef, and letter names. • Recognize major key signatures instantaneously. • Say aloud the number and names of sharps or flats in a key, in key-signature order. • Sing intervals above and below do in the major scale. • Hear intervals above and below do in the major scale. • Hear the scale degree of the first note of a song in a major key, when compared to the tonic. • In a given key, assign letter names to each solfège syllable or scale degree number. • Recognize and sing rhythms that contain sixteenth notes and dotted eighth notes. • Properly notate rhythms that contain sixteenth notes and dotted eighth notes. THE MAJOR SCALE Structure and Scale Degree Names A scale is a sequence of pitches ordered from lowest to highest or vice versa. You can derive a scale from a piece of music by taking an inventory of its notes and arranging them stepwise. EBSIT E W Figure 3.1. Trad., “Blue Bells of Scotland,” mm. 1–4. 4 &4 œ 2K Ç ZKHUH œ œ DQG RK Ç ZKHUH & œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ LV P\ Ç. JRQH" œ œ œ œ œ œ œ œ 6FDOH2U 90| KLJK ODQG ODG GLH EBSIT E W A scale is normally constructed so that all its notes fall within one octave, no matter where they appear in the music. “Hava Nashira” (Fig. 3.2) contains B-flats, Cs, Ds, and E-flats in two different octaves, but each note is represented only once in the scale. Figure 3.2. Trad. Hebrew, “Hava Nashira, Shir’Alleluia” (Round). 2 44 1 5 @ Ç 9 3 Ha Ç Ha Ha @Ç - - œ œ œ œ va - Ç na - shir 6 œ @œ 10 va shir va Ç 2 na - na - - @Ç Ç shir - - @Ç Ç 3 a, a, 11 œ œ @œ œ @ œ œ œ @œ 4 œ œ œ 8@Ç @Ç Ç shir shir Scale: œ œ @œ Ç shir 7 a, @Ç Or: "Al - le - lu - @Ç Ç ia." œ @ œ 12 @ œ œ œ œ Ç "Al - le "Al - le - - lu lu - - ia." ia." @œ œ œ œ @œ œ œ @œ Let us sing, sing "Alleluia." Most scales have a reference pitch or tonic, normally written as the highest and lowest notes of the scale. The tonic is not necessarily the first, highest, or lowest note in the actual piece of music, but it is almost always the last note. In “Bluebells of Scotland,” C is the tonic, even though the piece begins on G. In “Hava Nashira,” B-flat is the tonic, even though its highest note is E-flat. Play or sing each song, and pause before the last note. In both cases, you should feel a distinct pull toward the final pitch, as if the piece is incomplete without it. You might even feel a bit uncomfortable until you finally play that last note. It is this sense of musical completion that defines the tonic of the scale. Both of the preceding songs use the major scale. You have probably heard the major scale many times before, but listen to it again by playing Figure 3.3 at the piano. Each scale tone or degree has a name (do, re, mi, etc.) that designates its position relative to the tonic. This naming system is called solfège. Play the scale again, singing or speaking each name as you play. Figure 3.3. Major scale tones. Whole Whole do Pronounced:(doe) œ re (ray) œ mi (mee) Whole Whole œ fa (fah) œ sol (sole) Whole œ la (lah) œ Half ti (tee) œ EBSIT E & œ Half W 1 do Pitch: Major Keys 1/Rhythm: Beat Subdivisions |91 As you play and sing, notice that all of the notes in the scale are separated by whole steps except mi-fa and ti-do, which are half steps. A major scale may start on any note, but the structure of its steps is always the same. Take time to memorize the pattern: • Tonic-Whole-Whole-Half, Whole-Whole-Whole-Half or • Tonic W W H, W W W H EP L A Y R To reinforce the pattern in your memory, practice it by starting on any note of the piano. Listen carefully as you play, comparing your pitches to the sound of the major scale. If it doesn’t sound correct to you, double-check to be sure you are playing the proper pattern of steps. This book will mainly use solfège for naming degrees of the scale, but it will occasionally refer to other names as well. The notes may be assigned numbers (1, 2, 3, etc.) or a set of longer names (tonic, supertonic, etc.). Scale degree numbers normally have carets (^) above them. This is to distinguish them from the many other ways numbers are used in music (beats, measure numbers, fingerings, etc.). Study the chart below and memorize the three names for each scale degree. • A scale is a collection of the pitches used in a piece of music, condensed into one octave and arranged in stepwise order. • The tonic pitch is a musical point of stability and is very often the last note in a piece of music. The tonic is normally written as the highest and lowest notes of the scale. • The major scale consists of seven notes (plus the repeated tonic) in the stepwise pattern Tonic-Whole-Whole-Half, Whole-Whole-Whole-Half. • The tones or degrees of the major scale are identified using solfège (do, re, mi, etc.), scale degree numbers (1, 2, 3, etc.), or scale degree names (tonic, supertonic, mediant, etc.). • Half steps in the major scale occur between mi and fa (3 and 4) and ti and do (7 and 1). Building Major Scales (up to Four Sharps or Flats) The scale notated in Figure 3.3 above is a C major scale. Play and sing the scale once again, and notice three things: 1. The scale you play consists of all white keys (C-D-E-F-G-A-B-C). 2. The half step mi-fa occurs on E to F, and the half step ti-do occurs on B to C. In other words, the half steps that naturally occur between two white keys are aligned with those in the C major scale. 3. The note C is the stablest tone in the scale because it occurs on do. 92| Pitch: Major Keys 1/Rhythm: Beat Subdivisions It is these three conditions that create the C major scale: the content of the scale, the location of its half steps, and the note that is its tonic. Examine the C major scale written in letter names below. If we divide the scale in half, you will see that the result is two four-note segments separated by a whole step. These two segments are called tetrachords. Tetrachord Tetrachord W = Whole Ɛtep H = Half Ɛtep C D E F | G A B C W W H W W W H Because the two tetrachords are identical (whole-whole-half), we can use the upper tetrachord of the C major scale as the lower tetrachord of a new scale starting on G. However, if we continue to build a new upper tetrachord using only white keys, the scale does not turn out right, because the half step ends up between scale degrees 6 and 7 instead of between 7 and 1. Play the notes of the G scale below, and you will notice that it doesn’t sound quite like a major scale. To put the half step in the proper place and make the scale major, F-natural must be changed to F-sharp. Play the corrected G major scale shown below. You can repeat the process using the upper tetrachord of the G major scale to build another new scale on D. Notice that the same problem occurs. Play the new scale created in the bottom line of the chart below. Pitch: Major Keys 1/Rhythm: Beat Subdivisions |93 Once again, the scale must be corrected by adding a sharp to its seventh degree. Play the corrected D major scale shown below. Using this same process, we can generate all of the major scales that contain sharps. To fully understand the pattern, examine the chart below. Using a sheet of paper, cover everything except the top line. Reveal one line at a time to see each major scale with its new sharp shown in boldface. Remember: the newest sharp is always ti. We can also generate the flat scales through a pattern of tetrachords. To do this, start with the C major scale, and use the bottom tetrachord as the top of a new scale with a tonic of F. Play the new scale, using only white keys, and you will hear a problem: the half step that should occur between scale degrees 3 and 4 (mi and fa) instead occurs between scale degrees 4 and 5. To make the scale major, a flat must be added to the B. Play the corrected F major scale shown below. Notice that the B-flat is fa in the F major scale, and that it creates the required half step between mi and fa. Using this tetrachord pattern, we can generate all of the major scales that contain flats. To fully understand the pattern, read the chart below backwards, from right to left. Using a 94| Pitch: Major Keys 1/Rhythm: Beat Subdivisions sheet of paper, cover everything except the top line. Reveal one line at a time to see each major scale with its new flat shown in boldface. Remember: the newest flat is always fa. A major scale may contain up to seven sharps or flats. This chapter covers only those with up to four sharps or flats, because it is important that you memorize these scales thoroughly before moving on. All major scales are diatonic scales. In a diatonic scale, all seven letter names are used, and each letter name is used only once. (Recall from Chapter 2 that a diatonic half step is one that involves two different letter names. Likewise, a diatonic scale uses all seven names.) Memorize all of the major scales up to four sharps and four flats. Be able to write them out from memory in letter names, treble clef, and bass clef. EP L A Y • To generate major scales with sharps, use the upper tetrachord of one scale as the lower tetrachord of the next scale, and build upward. With each new scale, a sharp must be added to scale degree 7 to create the half step needed between ti and do. R • A tetrachord is a four-note segment of a scale. Each major scale has a lower tetrachord (do-re-mi-fa) and an upper tetrachord (sol-la-ti-do). • To generate major scales with flats, use the lower tetrachord of one scale as the upper tetrachord of the next, and build downward. With each new scale, a flat must be added to scale degree 4 to create the half step needed between mi and fa. • A major scale may contain up to seven sharps or flats, but only scales up to four sharps/flats are covered in this chapter. • All major scales are diatonic scales, which means that all seven letter names are used, and each letter is used only once. MAJOR KEY SIGNATURES (UP TO FOUR SHARPS OR FLATS) In Figure 3.4a, the folk song “Aura Lee” is written using the G major scale. (Notice that all Fs are sharp.) Rather than placing a sharp on every F in the song, it is standard practice to write the music using a key signature, as in Figure 3.4b. A sharp appears at the beginning of each line of music, on the fifth line of the treble staff, to indicate that all of the written Fs are to be played as F-sharps. Even though the sharp appears at the F5 staff position, it Pitch: Major Keys 1/Rhythm: Beat Subdivisions |95 applies to all Fs in all octaves. Because the tonic is G, we say that the piece is written in the key of G major. Figure 3.4. EBSIT E W a. “Aura Lee” written using the G major scale b. “Aura Lee” Written with the key signature of G major. Although it might not seem like a lot of work to write a sharp on every F in a piece of music, things get more complicated when a key has many sharps. In Figure 3.5, the same song is written using the E major scale. (Recall that this scale contains four sharps.) When accidentals are applied to every measure (a), the written music looks cluttered and is difficult to read quickly and smoothly. Using a key signature (b) solves the problem. a. “Aura Lee,” written using the E major scale. 96| Pitch: Major Keys 1/Rhythm: Beat Subdivisions Figure 3.5. EBSIT E W b. “Aura Lee,” written using the key signature of E major. Examine Fig. 3.2 again: “Hava Nashira” is written with the B-flat major scale, with flats applied directly to each B and E. Compare this with Figure 3.6. When the key signature is applied, there is no need to write flats throughout the music. EBSIT E W Figure 3.6. “Hava Nashira, Shir’Alleluia,” written with the key signature of B-flat major. The chart below shows all of the major key signatures up to four sharps and four flats. (Read it from the center outward.) In any key signature, the sharps or flats are always written in order (left to right) from oldest to newest. This is called key-signature order. More Pitch: Major Keys 1/Rhythm: Beat Subdivisions |97 specifically, it is sometimes called the order of sharps (F# C# G# D#) or the order of flats (B∫ E∫ A∫ D∫). One of your goals for this chapter is to recognize and identify any key signature, up to four sharps or flats, instantaneously. (You will learn the proper procedure for writing key signatures in the next chapter.) To achieve true music literacy, it is essential that you know all key signatures well enough that they are second nature. To completely memorize a key signature, you need to know three things about it: 1. The name of the tonic pitch 2. The number of sharps or flats 3. The names of the sharps/flats in key-signature order. Given any one of these items, you should be able to provide the other two. For example: Given: You Should Know: A-flat major Four flats: B∫, E∫, A∫, D∫ Four flats A-flat major: B∫, E∫, A∫, D∫ B∫, E∫, A∫, D∫ A-flat major (four flats) EP L A Y R • A key signature is placed at the beginning of each line of music to indicate which notes are to be played sharp or flat in that piece or passage. • A key signature keeps the written music uncluttered by eliminating the need to write sharps or flats throughout the music. • The sharps or flats in a key signature will always appear in order from oldest to newest. This is called key-signature order. It is also called the order of sharps (F# C# G# D#) or the order of flats (B∫ E∫ A∫ D∫). 98| Pitch: Major Keys 1/Rhythm: Beat Subdivisions SUMMARY OF MAJOR KEY SIGNATURES AND SCALES The chart below shows all major scales up to four sharps or flats. Each is written with its key signature in both the treble and the bass clefs. For each scale, the sharp/flat notes appear with dark noteheads and the natural notes with open noteheads. As you study scales, write them out in this manner to help you remember the pattern of sharps or flats for each scale. Pitch: Major Keys 1/Rhythm: Beat Subdivisions |99 RHYTHM Sixteenth Notes EBSIT E W Figure 3.7. Trad. English, “The British Grenadiers.” Set your metronome to a moderately slow tempo (about 60 bpm) and sing “The British Grenadiers” with your teacher’s guidance. Finger-count the beats as you sing the given solfège syllables. This song introduces sixteenth note and dotted eighth note durations. A sixteenth note receives one quarter of the pulse in four-based simple meters (two-four, three-four, and four-four). In other words, four sixteenth notes fill one beat, as is the case on beat 2 of measures 3, 7, 11, and 15. Sixteenth notes are commonly counted using the syllables “ONE e and a TWO e and a. . . .” Notice that the “and” falls on the half-beat, just as it does when counting eighth notes. 100| Pitch: Major Keys 1/Rhythm: Beat Subdivisions Sometimes, a combination of eighths and sixteenths will occupy a beat, as in measures 2, 6, 12, and 14. When this occurs, the entire beat is beamed together using a combination of single and double beams as necessary. The chart below shows all possible combinations of eighth and sixteenth notes within one beat. œ œ œ œ œ H D )RXUVL[WHHQWKQRWHVEHDPHG œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ H H H D D D œ œ œ 2QHHLJKWKDQG WZRVL[WHHQWKVEHDPHG œ œ œ œ 7ZRVL[WHHQWKVDQG RQHHLJKWKEHDPHG œ œ œ œ D H H D 2QHVL[WHHQWKRQHHLJKWK RQHVL[WHHQWKEHDPHG V\QFRSDWLRQ Dotted Eighth Notes “The British Grenadiers” contains dotted eighth notes in measures 9, 10, and 11. In fourbased meters, the dotted eighth is sustained for three quarters of a beat, or the equivalent of three sixteenths. Therefore a dotted eighth plus a sixteenth add up to one full beat, and they are normally beamed together. Pitch: Major Keys 1/Rhythm: Beat Subdivisions |101 The two folk songs in Figure 3.8 contain various combinations of eighths, sixteenths, and dotted eighths. Sing each several times using lyrics, solfège, and counts. The sixteenthdotted-eighth figure found near the end of “Loch Lomond” is common in traditional Scottish music and is sometimes called the “Scotch Snap.” Figure 3.8. a. Stephen Foster, “Camptown Races” (chorus). EBSIT 102| E W b. Traditional Scottish, “Loch Lomond” (chorus). Pitch: Major Keys 1/Rhythm: Beat Subdivisions R EP L A Y • Four sixteenth notes occupy the time of one quarter note. Sixteenth notes are normally counted “ONE e and a TWO e and a. . . .” • Combinations of eighth notes and sixteenth notes occurring within one beat are normally beamed together. • A dotted eighth note lasts for the duration of three sixteenth notes, or threequarters of a beat in four-based meters. The dotted eighth is often accompanied by a sixteenth note, and the two are beamed together. NOTATION Notes, Rests, and Beaming A single sixteenth note is drawn with two flags, and the sixteenth rest with two hooks. Remember that flags are always drawn on the right side of the stem, regardless of stem direction. In simple meters, dotted rests that are smaller than the beat are acceptable, so a dotted eighth rest is used to represent three sixteenth notes’ worth of silence. If rests are used within a beat, the remaining durations within that beat are beamed together. When only one duration sounds within a beat, it is flagged by itself. Sometimes rests are included within beam groups in order to further clarify the placement of the beats. This is especially helpful when the rest falls in the middle of the beat, with notes on either side. Pitch: Major Keys 1/Rhythm: Beat Subdivisions |103 Beaming When notating durations shorter than the beat, beam them together within each beat, and break the beam between beats. It might be helpful to think of each beat as a “house” containing one “family” of durations. All possible one-beat combinations of sixteenths, eighths, and dotted eighths are given in Exercise 3.1, below. Use those patterns as a guide when notating your exercises and compositions. When a sixteenth note requires a partial beam, always notate the broken beam so it faces inside the beat. Flagged Vocal Notation EBSIT E W In some older vocal music, each syllable of the lyric is notated with a separate flag, and notes falling under one syllable are beamed together. This notation style makes the music very difficult to count correctly, as it obscures the beat groupings in each measure. Most publishers have abandoned flagged notation in favor of the modern, beat-based system, but much of the older music still remains in print. Figure 3.9. Lili Boulanger, “Les lilas qui avaient fleuri” (mm. 19–24), from Clarières dans le Ciel. 104| Pitch: Major Keys 1/Rhythm: Beat Subdivisions MEMORIZATION STRATEGIES Memorizing Scale Content Scales and key signatures form the basis for virtually all further study of music. It is important that you memorize all nine scales and key signatures covered in this chapter, and that you reinforce them daily. Every day you should: 1. Write out the series of scales in tetrachords for both sharps and flats. If necessary, copy the tetrachord charts on pages 94–95. Recopy both charts several times until you can write them from memory. 2. Pick a key for the day. For that key: a. Write the scale in treble clef (no key signature). b. Write the scale in note names. c. Write the scale in bass clef (no key signature). d. Study your solfège flashcards for that key (see below). e. Write the order of sharps/order of flats in letter names for that scale. f. Play the scale on the piano while saying the note names aloud. g. Write the scale in note names. h. Study the solfège flashcards. i. Write the order of sharps/order of flats in letter names for that scale. j. Play the scale on your instrument. k. Sing the scale in note names, from memory. l. Study the solfège flashcards. Mapping Scales to Solfège In Chapter 1, you learned about the skill of mapping, where variable elements (such as notes on the staff) are assigned a meaning based on a fixed element (the clef). In the same way, solfège is a permanent structure onto which we map different note names for each key. For example, sol is always the fifth tone of the scale. If we map the notes of the B-flat major scale onto the solfège structure, then sol is F. But if instead we map the notes of D major, then sol is A. The function of a single note changes within a key because its mapping changes in relation to the solfège structure. For example, the note G: • Is do in the key of G major • Is re in the key of F major • Is mi in the key of E-flat major • Is fa in the key of D major • Is sol in the key of C major • Is la in the key of B-flat major • Is ti in the key of A-flat major To become fluent in scales, you must master both the content and the mapping of each scale. Knowing that the F major scale contains F, G, A, B∫, C, D, and E is a good start, but you must also be able to name any note’s solfège position in that key, quickly and in any order. In other words, you should be able to answer questions such as the following, quickly and accurately. Memorization Strategies |105 Questions: 1. In the key of F major, what note is la? 2. In the key of A-flat major, what note is re? 3. In the key of D major, what scale degree is F-sharp? 4. In the key of G major, what scale degree is C? Answers: 1. D 2. B-flat 3. mi 4. fa To help you study scale mapping, create a set of flashcards for each key introduced in this chapter. You should end up with nine sets, and you might find it helpful to use a different color card for each key. On the front of the card, write the key and note name (or draw it on the staff). On the back, write the solfège syllable. Study one scale at a time, integrating the flashcards with your “Key of the Day” practice. (See above.) Remember to challenge yourself: 1. Practice the cards front-to-back (see the note, and answer with solfège) and back-to-front (see the solfège, and say the note). 2. As you become fluent in each key, try combining two or more keys into one stack. PRACTICE STRATEGIES Playing Scales in Tetrachord Position As you practice the scales in the keyboard exercises below, use tetrachord position unless your teacher instructs you otherwise. Tuck both thumbs under your hands, and use your remaining fingers to play the scale. The four fingers of your left hand will play the lower tetrachord, and the four fingers of your right hand will play the upper tetrachord. Using this method, you can also hold down all of the keys for a scale simultaneously. This will allow you to see the structure of the scale and will help you memorize its notes. It is important to perform the exercises with a steady beat. Use a metronome as you practice, and start more slowly than you think you need to. Once you can perform an exercise 106| Practice Strategies consistently without any errors, gradually increase the tempo until you reach the goal indicated for the exercise. If at any point you have trouble, reduce the tempo. Accuracy is more important than speed. The G major scale in tetrachord position. When singing exercises that do not use the keyboard, you should sing in any register that is comfortable for your voice. You may use the keyboard as an occasional reference to be sure you are singing accurate pitches. If you do this, be sure to play the note after you sing it, not before. KEYBOARD AND SINGING EXERCISES 3.1. Rhythmic patterns. Tempo goal: 𝅘𝅥 = 80 bpm. Practice the rhythmic patterns given below using this method: a. Set your metronome to a moderately slow tempo—about 60 bpm. b. Choose a comfortable pitch for your voice and sing the patterns in order using the counts given. Remember to use the second measure of each pattern to prepare for the next. c. Sing the rhythms out of order, leaping from one to another randomly. Again, use the second measure to choose and prepare. d. Gradually increase the tempo of the exercise. How fast can you go and still perform accurately? Keyboard and Singing Exercises |107 EBSIT E W Sixteenth-Note Combinations EBSIT E W Sixteenth-Note Combinations with Leading Rests 3.2. Scale steps. Tempo goal: 72 bpm, one note per beat. Pick any note on the keyboard, and use it as the tonic of a major scale. Play the scale using the following pattern of steps. Listen carefully to what you are playing, and make sure it sounds like a major scale. If it doesn’t sound correct, double-check that you are playing the correct arrangement of steps. Tonic-Whole-Whole-Half, Whole-Whole-Whole-Half 3.3. Playing major scales. Tempo goal: 72 bpm, one note per beat. Practice each group of major scales, in order, at the keyboard. Play each scale several times, saying the letter names aloud and noting the new sharp or flat for each key. Practice each one until it is memorized. Flat Keys (Move down by Tetrachords) Sharp Keys (Move up by Tetrachords) 108| C major C major F major G major B∫ major D major E∫ major A major A∫ major E major Keyboard and Singing Exercises 3.4. Playing and singing major scales. Tempo goal: 𝅘𝅥 = 72 bpm. Sing each of these patterns as you play the scales in Exercise 3.3. Observe the notated rhythms, and use each rest to anticipate the next note in your mind and in your fingers. Some of the scales might not fall comfortably in your voice range. For those scales, it is OK to speak the words rather than sing them. Keyboard and Singing Exercises |109 3.5. Singing major scales without the piano. Tempo goal: 𝅘𝅥 = 100 bpm. Sing Exercise 3.4, Parts 1–4, without using the keyboard. Start on any pitch that is low and comfortable in your voice. It is important that you sing confidently, comfortably, and with accurate pitches. Remember, it is OK to check your pitch at the keyboard, as long as you play the note after you attempt to sing it. 3.6. Scale segments. Tempo Goal: 𝅘𝅥 = 80 bpm. Sing the next exercise without using the piano. It is written in C major, but you should start on any note that is low and comfortable in your voice. Use solfège and/or numbers as instructed by your teacher. Although bar lines and a time signature are absent, be sure to observe the notated rhythm and maintain a steady pulse throughout. The goal of this exercise is to develop your fluency in singing solfège/numbers in ascending and descending scale formations. You should strive for accuracy first, and speed second. 110| Keyboard and Singing Exercises 3.7. Intervals. Tempo goal: 𝅘𝅥 = 90 bpm. Using the example below, sing from do up to each scale tone. Then, sing from high do down to each scale tone. The distance between two pitches is called an interval. (Intervals will be covered in more detail in Chapter 7.) Keep a steady pulse throughout, and use each quarter rest to anticipate the next interval in your mind. Hint: If you have difficulty singing an interval, sing the corresponding scale segment before singing the troublesome interval. For example: 3.8. Intervals with letter names. Tempo goal: 𝅘𝅥 = 90 bpm. Repeat Exercise 3.7, singing letter names for each of the major keys covered in this chapter (those up to four sharps/flats). The key of B-flat major is given as an example, but be sure to practice with letter names for all keys introduced in this chapter. Keyboard and Singing Exercises |111 HEARING EXERCISES Goal for Exercises 3.9–3.11: ten consecutive correct answers. 3.9. Hearing ascending intervals. Your instructor or study partner will play an ascending major scale, and then the low do followed by a higher scale tone. Sing back the two pitches and name the scale tone using solfège. Example: 3.10. Hearing descending intervals. Your instructor or study partner will play a descending major scale, and then the high do followed by a lower scale tone. Sing back the two pitches and name the scale tone using solfège. Example: œ œ œ œ œ œ œ œ œ Your instructor plays this… œ Listen, and sing back the pitches on a neutral syllable… nah œ œ …then this. œ œ …then with solfège. nah do re Hint: If you have trouble with Exercises 3.9 and 3.10, use scale segments (Ex. 3.6) to help you measure the interval with your voice. 3.11. Hearing harmonic intervals. 112| Hearing Exercises LE AL N CH ✪ GE In Exercises 3.9 and 3.10, the intervals are to be played melodically (one note at a time). For an extra challenge, your instructor will play each interval harmonically (both notes together). Separate the two pitches in your mind, sing them melodically, and name the solfège syllables. Example: 3.12. Transcription. In the previous chapter (Ex. 2.16), you sang “When the Saints Go Marching In” and notated the rhythm. In this exercise, you will write the solfège syllables for the song. a. Copy the rhythm above the lyrics given. b. Sing the song slowly, measure by measure, and write solfège or a number below each lyric. The song begins on do, and it contains only the notes do, re, mi, fa, and sol. Take care not to guess at the notes. If you are unsure about your answer, sing the first five tones of the scale, comparing each one to the note in the song that you are trying to find. c. Sing the song in rhythm using the syllables you’ve written. d. Check your work: choose a key and play the notes at the piano. Compare this with the original song, and fix any errors you might have made. 3.13. Transcription. In the previous chapter (Ex. 2.17), you sang the chorus from “Jingle Bells” and notated the rhythm. In this exercise, you will write the solfège syllables for the song. a. Copy the rhythm above the lyrics given. b. Sing the song and hold the last pitch (tonic); then sing the first pitch of the song (“Jin-”). Compare the two pitches and find the scale degree on which the song starts. (See Ex. 3.9 if you have trouble.) Hearing Exercises |113 c. Sing the song slowly, measure by measure, and write solfège or a number below each lyric. The song contains only the notes do, re, mi, fa, and sol. Take care not to guess at the notes. If you are unsure about your answer, sing the first five tones of the scale, comparing each one to the note in the song that you are trying to find. d. Sing the song in rhythm using the syllables you’ve written. e. Check your work: choose a key and play the notes at the piano. Compare this with the original song, and fix any errors you might have made. INFORMED LISTENING: EXAMPLES FOR STUDY 3.14. Clara Schumann, “Scherzo” (Movement II) from Piano Trio in G Minor, Op. 17 Meter: triple Tempo: very fast, about 160 bpm What to listen for: • The violin melody begins with the scale tones sol-la-sol but avoids the tonic pitch. As the piece begins, listen for do sustained in the cello and the lowest voice of the piano. • The “Scotch Snap” figure (sixteenth-dotted-eighth) is prevalent throughout the melody: 114| Informed Listening: Examples for Study 3.15. Muzio Clementi, “Allegretto” (Movement I) from Sonatina in G Major, Op. 36, No. 2 Tempo: fast, about 112 bpm What to listen for: • The melody begins with an eighth-note pickup on the scale tone sol. • Sixteenth notes are used throughout the melody. There is a recurring figure of two sixteenth notes on the “and” of beat two: 3.16. Gabriel Fauré, “Berceuse,” from Dolly Suite, Op. 56 Tempo: moderate, about 73 bpm What to listen for: • The piano accompaniment uses a repeated rhythm of four sixteenths and a quarter note. The figure continues throughout most of the first section. • When the melody enters in measure 3, it begins on the scale tone sol. • In the middle section of the piece, beginning around 0’56”, the accompaniment figure changes to eighth, two sixteenths, four sixteenths: 3.17. Wild Asparagus, “Lafferty’s,” from Contra Music: The Sound of New England Tempo: moderately fast, about 110 bpm What to listen for: • The call-and-response passage between the guitar and drum at the beginning of the piece uses a variety of eighth- and sixteenth-note rhythms: Informed Listening: Examples for Study |115 3.18. Edvard Grieg, “Berceuse (Cradle Song),” from Lyric Pieces, Book II, Op. 38 Tempo: variable (the performers take liberties with the tempo) What to listen for: • In the middle section, beginning at about 0’52”, listen for this rhythm: 3.19. Frederic Chopin, Prelude in C minor, Op. 24, No. 20 Meter: quadruple Tempo: very slow, about 42 bpm What to listen for: • Every measure of the piece contains a dotted-eighth-sixteenth figure on beat 3, and quarter notes in the rest of the measure. (The exception is the final bar, which contains a whole note.) The tempo is slow enough that you can easily count sixteenth notes aloud. As you do this, listen for the note that falls on the “a” of beat 3 in each measure. INFORMED LISTENING: EXAMPLES WITH QUESTIONS Listen several times to these pieces. Find the tonic, and sing it using the syllable do. Then answer the questions given for each example. 3.20. Elton John, “Your Song,” from Greatest Hits Meter: quadruple Tempo: moderately slow, about 64 bpm 1. Sing the tonic, and then the singer’s starting pitch. What is the scale degree? (If you have trouble, see Ex. 3.9.) a. do b. mi c. fa d. sol 116| Informed Listening: Examples with Questions 2. Which of the following best represents the singer’s first rhythm? 3. Listen near the end of the chorus for the line that begins with the words “I hope. . . .” Which best represents the singer’s rhythm? (The line occurs at about 1’25” and 3′10″.) 3.21. George Frideric Handel, “Hallelujah,” from Messiah Recommended recording: Handel: Messiah, Apollo’s Fire and Jeanette Sorrell Meter: quadruple Tempo: moderately fast, about 108 bpm 1. After a three-measure introduction, the chorus enters and sings the word Hallelujah several times. Listen to the highest voice. Which of these best represents the solfège of the first two “hallelujahs”? a. |do - sol - la - sol b. |do - la - ti - la c. |do - |do - re - do Informed Listening: Examples with Questions |117 2. Which of the following best represents the rhythm of the first two “hallelujahs”? 3. Which best represents the rhythm of the third and fourth “hallelujahs”? 3.22. The Beatles, “Tomorrow Never Knows,” from Revolver Meter: quadruple Tempo: fast, about 128 bpm 1. In the introduction, the drums play for four measures before the singer enters. During this time, a pair of sixteenth notes is prominently played . . . a. . . . on the first half of beat 3 b. . . . on the “and” of beat 3 c. . . . on the first half of beat 4 d. . . . on the “and” of beat 4 2. Sing the tonic, and then the singer’s starting note. What is that note? a. do b. re c. mi d. sol 3. In the first three measures of the voice part, how many times is the tonic pitch sung? a. once b. twice c. three times d. more than three times 118| Informed Listening: Examples with Questions 3.23. Darius Milhaud, “Corcovado,” from Saudades do Brasil, Op. 67 Meter: duple Tempo: moderate, about 70 bpm 1. Which of the choices best represents the rhythm of measures 1–2 of the melody? 2. Which best represents the rhythm of measures 3–4 of the melody? 3. Which best represents the rhythm of the accompaniment? Informed Listening: Examples with Questions |119 3.24. John Williams, “The Raiders March,” from Raiders of the Lost Ark Meter: quadruple Tempo: fast, about 133 bpm 1. Sing the tonic and then the first three notes of the melody (played by trumpets and flutes). What are those notes? a. do-mi-sol b. do-re-mi c. mi-sol-la d. mi-fa-sol 2. Which of these best represents the opening rhythm of this melody? 3. The opening melody, eight measures long, is played twice. What is its highest note? (Find the pitch, sing it, and compare it to the tonic.) a. do b. mi c. fa d. la 3.25. Josef Haydn, “Kyrie,” from Mass No. 11 in D Minor (“Nelson”) Meter: triple Tempo: moderate, about 98 bpm 1. Which of these best represents the rhythm played by the trumpets? (The rhythm occurs five times, beginning in m. 2.) 120| Informed Listening: Examples with Questions 2. Which best represents the rhythm played by the strings, beginning at about 0′19″? (The rhythm is played twice.) 3. Which best represents the rhythm of the word Kyrie, on the first entrance of the chorus? (The word and the rhythm occur twice.) DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 3.26. Memorize Exercises 3.4 through 3.8, and sing them where appropriate. 3.27. As you listen to music throughout your day, hum or sing the note that you think is the tonic. Then choose any prominent note of the piece (the first note of the verse, the first note of the chorus, the highest note, etc.), compare it to the tonic, and try to identify its solfège syllable. Later, when you have access to a piano, sing the song back to yourself and check your answer. CLASSROOM ACTIVITIES Exercises 3.28–3.30 may be done at three levels: Beginner: use only the notes d r m f s Intermediate: use only the notes |t d r m f s l Advanced: use the notes |t d r m f s l t |d |r Classroom Activities |121 3.28. Point and Sing. a. Choose a level (above), and write the syllables on the board in a vertical line from lowest to highest. b. Choose a leader, who will establish a tonic and then dictate a series of syllables by pointing to them on the board. The class will respond by singing the correct pitch for each syllable. c. If the class sings an incorrect pitch (or multiple answers are given), return to do, and then “walk” the class up the scale stepwise to that scale tone. d. Change leaders periodically. 3.29. Call-and-Response Pitch Improvisation. a. Choose a level (above), and write two sets of syllables on the board, one on the left side, and one on the right. b. Choose two leaders. Leader 1 (on the left) dictates five notes to the class, beginning on do and ending on any note except do. c. Leader 2 (on the right) responds by dictating five more notes, starting on Leader 1’s last note, and ending on do. d. The class sings each note dictated by the leaders; if there are errors, the leader should return to do and then walk the class up to the problematic scale tone. e. Change leaders periodically. Leader 1: _?_ _?_ _?_ x = Any note except do _x_ _x_ _?_ _?_ _?_ _do_ Same note starts on L2’s last note, and L4 starts on L3’s last note. L4 must end on do. Leader 1: _do_ Leader 2: _?_ _?_ _?_ x = Any note except do. _x_ _?_ _?_ _?_ _?_ _x_ _?_ _?_ _do_ Same note Leader 3: _x_ _x_ Leader 4: _?_ _?_ _x_ _x_ _?_ Same note 3.31. Guided Rhythm Improvisation. Designate one student to lead the activity. 1. Choose several rhythmic patterns from Exercise 3.1 and write them on the board. 2. Set your metronome to a slow tempo to establish a pulse. Choose any pitch, and lead the class in singing the rhythms in order. Use a neutral syllable such as “nah” or “tah.” 3. Repeat step (2), but this time randomize the order of your choices. Start with any rhythm, and as the class reaches the landing measure point to the next rhythm you want them to sing. (Be sure to give them enough time to anticipate where they’re going.) 122| Classroom Activities LE AL N ✪ GE 3.30. Use four leaders (L1–L4) instead of two. L1 starts on do, L2 starts on L1’s last note, L3 CH _do_ Leader 2: 4. If there are incorrect responses, repeat the pattern until the entire class sings it correctly, and then move on. 5. Change leaders periodically. 3.32. Tonic detection. 1. Choose a recording of one of your favorite popular songs that does not have a clear ending but instead ends with a fade-out. 2. Listen to the song several times, and sing the note that you think is the tonic. 3. Play the song (or a portion of it) for your class, and lead a discussion about where you think the tonic is and why. Consider any differing opinions that might be offered by your classmates. WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 3 online drills and quizzes at www.oup.com/us/root. 3.33. Spell each of these major scales by writing letter names in the blanks above the scale degrees. Use uppercase letters. For sharps and flats, draw the correct symbol after the letter name. Question 1 has been completed for you. 1. G major: 2. A major: 3. B∫ major: 4. E major: 5. F major: 6. E∫ major: G A B C D E F# G do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 Written Exercises |123 7. C major: 8. A∫ major: 9. D major: _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 1 2 3 4 5 6 7 1 3.34. Each of the next questions represents a key signature for which only partial information is given. Fill in the remaining information. Question 1 has been completed for you. How many . . . of what (circle one)? Key name What are they? (in key-signature order) 1. A∫ major ____ 4 Sharps/ flats B∫, E∫, A∫, D∫ 2. D major ____ Sharps/flats _______________ 3. ____________ 3 flats _______________ 4. ____________ 1 sharp _______________ 5. B∫ major ____ Sharps/flats _______________ 6. E major ____ Sharps/flats _______________ 7. ____________ 3 sharps _______________ 8. C major ____ _______________ Sharps/flats 3.35. Draw a dot on each of the correct piano keys to build the requested scale. Be sure to start the scale low enough that you don’t run out of keys. Check your work by playing the scale on an actual keyboard. Question 1 has been completed for you. 124| 1. G major 2. B∫ major 3. A∫ major 4. E major 5. F major 6. A major Written Exercises 7. E∫ major 8. D major 9. C major 3.36. Name the major key and write the scale indicated by the given key signature. Use noteheads only (no stems), and fill in the noteheads for any notes in the scale that are sharp or flat. Use an open notehead for the remaining notes in the scale. Write the scale in the octave that will yield the fewest ledger lines. Question 1 has been completed for you. Written Exercises |125 3.37. Complete this chart using the information given for each question. Questions 1 and 2 have been completed for you. Name Number Solfège (question) 1. Dominant Supply the Note Name for the Given Key D: B∫: G: F: C: D: A B∫: F G: D F: C C: G E∫: A: C# F: D: B∫: E∫: G A: C# F: A D: F# B∫: D C: F: B∫: E∫: A∫: D: G: F: B∫: E: A: D: G: E∫: B∫: C: F: A: G: D: B∫: A: E∫: D: F: 8. G: B E∫: C: F: B∫: 9. D: A: F# G: C: E: 10. C: F: B∫: E∫ E∫: A∫: 11. Supertonic A: C: D: B∫: F: 12. C: C G: E∫: B∫: D: (answer) 1. Dominant 5 sol (question) 2. (answer) 2. Mediant 3 3. 6 4. mi re 5. Subdominant 6. 7. ti 1 3.38. Write the correct scale degree number (1, 2, 3, 4, 5, 6, 7) for each note in the given key. 126| Written Exercises 3.39. Write the correct solfège syllable (do, ré, mi, fa, sol, la, ti, do) for each note in the given key. ✪ CH Apply sharps or flats directly to the scales; do not use key signatures. Question #1 has been completed for you. LE AL N GE 3.40. For each question, draw the clef indicated, and then write the scale using the clue given. 1. Bass clef. Write the scale whose subdominant is E∫. 2. Treble clef. Write the scale in which 3 is C#. 3. Treble clef. Write the scale in which sol is D. 4. Bass clef. Write the scale in which the last sharp of the key signature is D#. 5. Treble clef. Write the scale in which the last flat of the key signature is A∫. Written Exercises |127 6. Bass clef. Write the scale whose leading tone is E. 7. Treble clef. Write the scale in which re is B∫. 8. Bass clef. Write the scale in which 4 is F. 9. Bass clef. Write the scale whose submediant is B. 3.41. Each question represents one quarter-note beat that is incomplete. Add the correct note value(s) to complete the beat. Be sure to observe the rules for proper beaming. Where necessary, beam your answers to the notes that are given. Questions 1 and 2 have been completed for you. 3.42. Rewrite each example so that it is beamed properly for the meter given. The first beat of Question 1 has been completed. 128| Written Exercises 3.43. Each question contains an excerpt from a song written in vocal notation. a. Rewrite each example with correct beaming. (Do not copy the words, just the notes.) All examples are in 2/4 meter. b. Identify the key of the song, on the basis of its key signature. c. Label each note with the correct solfège syllable. The first example has been started for you. 1. Wolfgang Amadeus Mozart, “Die betrogene Welt,” K. 474, mm. 4–11 Rewrite: Written Exercises |129 2. Robert Schumann, “O Ihr Herren,” from Liebesfrühling, Op. 37, mm. 1–12 Rewrite: 3. Wolfgang Amadeus Mozart, “Lied der Freiheit,” K. 506, mm. 9–17 130| Written Exercises Rewrite: LE AL N CH Note: This example requires you to add a tie. GE ✪ 4. Robert Schumann, “Intermezzo” from Liederkreis, Op. 39 Rewrite: Written Exercises |131 3.44. The examples below are well-known songs written in rhythm and solfège only. For each question, first identify the key indicated by the key signature. Then notate the song on the staff in that key. Finally, play your work at the piano and name the title of the song, if you know it. 1. Do is the lowest scale tone in this example. Notate all other tones above do. 132| Written Exercises 2. This example begins on sol. The high tonic and any notes above it are marked with a superscript (|do). The low tonic (do) is unmarked. Any notes below the low tonic are marked with a subscript (|ti). Written Exercises |133 COMPOSITION 3.45. The tonic note of a major scale is given as the first and last note of each exercise. Fill in the remaining notes of the scale, in order, and compose a rhythm that is correct for the given number of measures and the given time signature. Adhere to these four guidelines: 1. Apply sharps or flats directly to the appropriate notes; do not use key signatures. 2. Use each note of the scale only once. (Do not repeat any notes.) 3. Use only the rhythmic values seen here; do not use rests or ties. 4. Lead the class in performing your compositions. & 4 @ œ . @Ç Sample G & 4 @ œ . œ œ @ œ @ œ Possible answer 1 G & 4 @ œ . œ œ @ œ @ œ œ Possible answer 2 134| Composition œ œ @Ç Ç @Ç @Ç. 1 @Ç &4 Exercises 1–4 use ascending scales. 4 2 @Ç @œ T 3 4 & 4 Ç. Ç. 4 & 4 œ. 4 5 œ . Exercises 5-8 use descending scales. Ç 6 œ &4 44 7 œ . 4 8 @Ç Ç. 1 2 3 Ç 4 @Ç 3.46. Compose a rhythm and scale exercise using these six steps. 1. Set your metronome to a moderate tempo (about 60 bpm) and sing the following scale, one pitch per beat. (Note that the high re and the low ti are included.) Composition |135 2. Compose a new rhythm for the scale by replacing each of the quarter notes with one of these rhythms. (Each is worth one beat.) Use a variety of rhythms, but be sure to use only one scale tone per beat. 3. For example, your composition might start this way: 42 œ œ ‰ œ œ œ œ œ œ œ G LE AL N CH GE ✪ G U U P P P I I œ HWF I 4. Write your composition on staff paper in a clef and key of your (or your instructor’s) choice. 5. Set your metronome to a moderately slow tempo, and lead the class in performing your composition. Chapter Goals Revisited 6. Divide the class in half and lead them in performing your composition as a twopart round at a distance of one measure. Be sure you have achieved all Chapter 3 Goals before proceeding to Chapter 4. For major keys that contain up to four sharps or flats: • Sing major scales with solfège, scale degree numbers, scale degree names, and letter names. (pages 90–92, 109–110) • Play major scales at the keyboard. (pages 106, 108–109) • Write major scales with or without key signatures, in treble clef, bass clef, and letter names. (pages 92–95) • Recognize major key signatures instantaneously. (pages 95–99, 105) • Say aloud the number and names of sharps or flats in a key, in key-signature order. (pages 97–99, 105) • Sing intervals above and below do in the major scale. (page 111) • Hear intervals above and below do in the major scale. (pages 112–113) • Hear the scale degree of the first note of a song in a major key, when compared to the tonic. (pages 113–114) • In a given key, identify the note that correlates with a solfège syllable or scale degree number. (pages 105–106) • Recognize and sing rhythms that contain sixteenth notes and dotted eighth notes. (pages 100–103, 107–108) • Properly notate rhythms that contain sixteenth notes and dotted eighth notes. (pages 103–104) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. 136| Composition CHAPTER 4 Chapter Goals PITCH: MAJOR KEYS 2 RHYTHM: TRIPLETS After you finish this chapter, you should be able to do the following, quickly and accurately, for all major keys: • Sing major scales with solfège, scale degree numbers, scale degree names, and letter names. • Play major scales at the keyboard. • Write major scales with or without key signatures, in treble clef, bass clef, and letter names. • Recognize major key signatures instantaneously. • Correctly notate major key signatures. • In a given key, identify the note that correlates with a solfège syllable or scale degree number. • Understand the function of the tonic triad and tendency tones in the major scale. • Sing and resolve tendency tones in the major scale. • Hear and identify tendency tones with their resolution tones in the major scale. • Recognize and sing rhythms that contain triplets. • Properly notate rhythms that contain triplets. MORE MAJOR SCALES Major Scales with More Than Four Sharps or Flats In the previous chapter, you learned major scales with key signatures up to four sharps and four flats. It is very important that you thoroughly memorize those nine scales before proceeding with this chapter, in which you will learn the rest of the major scales. Recall the tetrachord pattern you learned in Chapter 3. Remember that for every major scale containing sharps, the newest sharp appears on scale degree 7 in order to create the half step needed between ti and do. We will continue the pattern, beginning with the E major scale. For every key, the newest sharp is shown in boldface. |137 C-sharp major is the last sharp key because all seven of its notes are sharp. (Notice that it is exactly one chromatic half-step higher than the C major scale, which has no sharps or flats.) Play the C-sharp major scale on the piano in tetrachord position; then hold down all of its notes at the same time. The result should look something like this: Even though all of its notes are sharp, the C-sharp major scale by necessity contains two white keys, E-sharp and B-sharp. It is incorrect to call these notes “F” and “C,” because the scale already contains an F-sharp and a C-sharp. Remember that the major scale is a diatonic scale, meaning every letter name is used, and each is used only once. Likewise, the F-sharp major scale contains an E-sharp as its seventh degree. Do not call this note “F,” because that letter is already used by the scale’s tonic, F-sharp. Recall the tetrachord pattern for flat scales that you learned in the previous chapter. Remember that each new flat is applied to scale degree 4 in order to create the half step needed between mi and fa. We will continue the pattern, beginning with the A-flat major scale. Remember to read this chart from right to left as flats are added. The newest flat in every key is shown in boldface. 138| Pitch: Major Keys 2/Rhythm: Triplets The maximum number of flats possible in a diatonic scale is seven, one for each letter name. The C-flat major scale, with seven flats, is exactly one chromatic half step lower than the C major scale, which has none. Play the C-flat major scale on the piano in tetrachord position; then hold down all of its notes at the same time. The result should look something like this: Notice that the C-flat major scale also has two white keys expressed as flats, F-flat and C-flat. Once again, it is incorrect to call these notes “E” and “B,” because every letter name must be used in a diatonic scale. Enharmonic Keys At the keyboard, play the two scales shown below. You may follow either the letter names or the notated scale. You should notice immediately that the two scales use exactly the same piano keys and sound identical, even though they are notated differently on the staff. This is because F-sharp major and G-flat major are enharmonic keys. Any key that has more than five sharps or flats has a corresponding enharmonic key. There are three pairs of enharmonic Pitch: Major Keys 2/Rhythm: Triplets |139 keys; the remaining two pairs are listed below. Play each pair of scales on the piano as you say the letter names aloud. Any two enharmonic keys have opposing accidentals (sharps vs. flats), and the total number of accidentals adds up to twelve: 140| B major C∫ major 5 sharps 7 flats = 12 F# major G∫ major 6 sharps 6 flats = 12 C# major D∫ major 7 sharps 5 flats = 12 Pitch: Major Keys 2/Rhythm: Triplets Table of Key Signatures and the Circle of Fifths Here are all major key signatures in the order of sharps and the order of flats, arranged as a table. Read the table from the center outward, and notice that the three keys on each end correspond with an enharmonic key on the other end. Imagine what the table would look like if we bent its ends downward, creating a circle where the enharmonic keys overlap at the bottom. The result is a figure called the circle of fifths, commonly used to illustrate the pattern of key signatures. The circle of fifths is so named because as you go around the circle clockwise, the tonic of each key is five notes–or a fifth–higher than the previous one. Pitch: Major Keys 2/Rhythm: Triplets |141 The Circle of Fifths 142| Pitch: Major Keys 2/Rhythm: Triplets Summary of Major Key Signatures and Scales All major key signatures and scales are shown below. For each scale, the notes that are sharp or flat are shown with dark noteheads; those notes that remain natural are shown with open noteheads. As you study, write out the scales in this manner to help you remember which notes are sharp or flat in each. • A major scale may contain up to seven sharps or flats. • Enharmonic keys sound the same but are notated differently. There are three pairs of enharmonic major keys: R EP L A Y o C-sharp and D-flat major o F-sharp and G-flat major o B and C-flat major • The pattern of keys may be illustrated on the circle of fifths. As you proceed clockwise around the circle, you will see that each key is a fifth higher than the previous one. Pitch: Major Keys 2/Rhythm: Triplets |143 THE TONIC TRIAD AND TENDENCY TONES At the piano, play and sing a C major scale; then play and sing Figure 4.1. (Use both hands if necessary.) EBSIT E W Figure 4.1. Tonic triad and tendency row. You should notice that do, mi, and sol sound stabler than the other degrees of the scale, especially when played harmonically. These three scale tones form the tonic triad. The remaining tones (re, fa, la, and ti) are called tendency tones because they are less stable and have a tendency to “pull” toward the triad tones. The movement from a tendency tone to a triad member is called resolution. We say that ti resolves to do, fa resolves to mi, etc. To hear this network of resolutions within the major scale, isolate the tonic triad by playing and singing Figure 4.2 several times. Be sure to observe the correct rhythm. This figure is called the tendency row; it is important for you to memorize it (in sound, solfège, and note names) because it will help you listen to music more carefully and discern what pitches are being played. Translating sound to notation and vice versa are essential skills for every musician. Notice that the tendency to resolve is especially strong from fa to mi and ti to do. That is because both fa and ti are a half step away from their notes of resolution, while re-do and la-sol are separated by a whole step. In the advanced tendency row, the first note of each segment is replaced by a rest, so you must leap directly to the tendency tone, then resolve it. See Exercise 4.7 for some practice tips to help you become proficient in singing both versions of the row. EBSIT 144| E W Figure 4.2. Basic and advanced tendency rows. Pitch: Major Keys 2/Rhythm: Triplets Consider for a moment the nonmusical meaning of the word tendency. If you have a tendency—for example, to lose your car keys—this means you are likely to do it but don’t necessarily do so all the time. In the same way, tendency tones in music often resolve to triad members, but not always. (Imagine how boring music would be if it always met our expectations!) • Do, mi, and sol are the stablest tones of the scale. Together, they form the tonic triad. • The remaining tones, re, fa, la, and ti, are tendency tones. Each tendency tone resolves to a member of the tonic triad. o Fa resolves to mi. EP L A Y R o Re resolves to do. o La resolves to sol. o Ti resolves to do. • Tendency tones are so named because they have the tendency, or the potential, to resolve. They do not always do so in actual music. It is the expectation of resolution—sometimes fulfilled, and sometimes not—that creates musical interest. RHYTHM Triplets With your teacher’s guidance, sing “St. Columba” several times using solfège. Notice that three notes of equal length occupy measure 6, beat 3. This figure is called a triplet, and it is notated by “squeezing” three eighth notes (instead of two) into one beat, and adding a “3” to the figure. Pitch: Major Keys 2/Rhythm: Triplets EBSIT E W Figure 4.3. “St. Columba” (Ancient Irish Melody). |145 There are many methods used to count triplets; some of the most common are listed below. Use the method preferred by your teacher. If you are working on your own, try all the methods and use the one that works best for you. EBSIT E W Figure 4.4. Counting triplets. EBSIT Figure 4.5. E W Whichever counting method you use, it is very important that you divide the beat evenly, and avoid performing a triplet as if it were a combination of eighth and sixteenth notes. Perform the melody in Figure 4.5, slowly and accurately. Each measure should sound different from the others. Y R • A triplet divides the beat into three equal parts. EP L A • Triplets are written as three beamed eighth notes with a numeral 3 written just outside the beam. • Be sure to perform triplets evenly, and do not confuse them with other figures that contain three durations in a beat (for example, two sixteenths and an eighth). 146| Pitch: Major Keys 2/Rhythm: Triplets NOTATION Writing Key Signatures Use this procedure when writing key signatures on the staff. When you write flat key signatures: 1. Start with B-flat on the third line of the treble staff, or the second line of the bass staff. 2. Proceed in a zigzag pattern up, down, up, down, until you have written the number of flats you need. 3. To practice, write the key signature for C-flat major (seven flats) several times. When you write sharp key signatures: 1. Start with F# on the fifth line of the treble clef, or the fourth line of the bass clef. 2. Proceed in a zigzag pattern down, up, down, up, until you reach A# (the fifth sharp). 3. A# must be written below D#; this will break the pattern momentarily. After A#, continue up (E#) and then down (B#). 4. To practice, write the key signature for C# major (seven sharps) several times. Writing Triplets Beam all three eighth notes of a triplet together, indicating that they occupy one beat. Place the numeral 3 on the beamed side of the figure. If there is a rest in the first or third position, use a bracket to enclose the triplet. Pitch: Major Keys 2/Rhythm: Triplets |147 This page intentionally left blank MEMORIZATION STRATEGIES A Visual Way to Memorize Scales By the time you finish this chapter you should have memorized all fifteen major scales, so that you can write them and recite them aloud quickly and accurately. You may wish to use the visual cues seen here to help you study more efficiently. To begin, write out a D major scale in letter names, and circle every note that is sharp. Then, write a D-flat major scale directly below it, and circle every note that is flat. The two scales complement each other: in the D major scale, F and C are sharp. In the D-flat major scale, all notes except F and C are flat. The same is true for any two scales that lie a chromatic half-step apart. Shortcuts for Identifying Key Signatures There are several mnemonic devices to help you memorize the order of sharps and flats, as well as shortcuts to help you identify key signatures. But ultimately, you must have scales and key signatures memorized well enough that you no longer need to stop and think about the answers. In other words, use shortcuts and mnemonics with caution (if at all), and use them only for a short time. Memorization Strategies |149 You might have noticed that the order of flats is the order of sharps in reverse. There is a nifty sentence that makes sense, both forward and backward, that will help you learn the orders: Order of sharps: Father Charles Goes Down And Ends Battle (FCGDAEB) Order of flats: Battle Ends And Down Goes Charles’ Father (BEADGCF) To identify sharp key signatures, the last sharp is the leading tone (ti) of the key. Go up a diatonic half step to find the tonic (ti-do). To identify flat key signatures, the second-to-last flat is the tonic (do), and therefore the name of the key. (You will simply need to memorize the key of F major, which contains only one flat.) A Visual Way to Memorize Key Signatures Each key signature has a unique “footprint” or shape. To identify key signatures quickly, you might find it helpful to memorize their shapes. Flashcards To create flashcards for this chapter, draw a key signature on one side of the card and write the name of the corresponding major key on the other. Include both treble and bass clefs; be sure to focus on the clef that is normally weaker for you. Group your cards by level (color coding can be very helpful), and take small steps. For example: 1. First, practice only keys up to four sharps: C, G, D, A, and E major. 2. Next, practice only the keys of B, F-sharp, and C-sharp major. 150| Memorization Strategies 3. Then practice all sharp keys. 4. Practice only keys up to four flats: C, F, B-flat, E-flat, and A-flat major. 5. Practice only the keys of D-flat, G-flat, and C-flat major. 6. Practice all flat keys. 7. Practice only keys up to four sharps/flats. 8. Practice only keys with five sharps/flats or more. 9. Practice all keys. PRACTICE STRATEGIES Review the Practice Strategies from Chapter 3, and apply them to these exercises as well. They include: • Playing scales in tetrachord position. • Using a metronome and performing the exercises with a steady pulse. (Tempo goals are given for each exercise.) • Singing confidently in a range that is comfortable for your voice. If you need to check your vocal accuracy at the keyboard, be sure to play the note after you sing it, not before. • Proceeding slowly, repeating each part of the exercise several times. Do not move on to the next exercise until you have achieved fluency. KEYBOARD AND SINGING EXERCISES Before you begin, review all Keyboard and Singing Exercises from the previous chapter. 4.1. Rhythmic patterns. Tempo goal: 𝅘𝅥 = 80 bpm. Review patterns (a) through (f), which were introduced in Chapter 3, and add pattern (g), the triplet, to your practice sessions. Remember that patterns b, c, f, and g all contain three durations, but each divides the beat slightly differently. If you are unsure whether or not you are performing the patterns correctly, listen to them on the website, or ask for your instructor’s guidance. Practice the patterns using the same method as in previous chapters: a. Set your metronome to a moderately slow tempo–about 60 bpm. b. Choose a comfortable pitch for your voice, and sing the patterns in order using the counts given. Remember to use the second measure of each pattern to prepare for the next. c. Sing the rhythms out of order, leaping from one to the next randomly. Again, use the second measure to choose and prepare. d. Gradually increase the tempo of the exercise. How fast can you go and still maintain accuracy? Keyboard and Singing Exercises |151 EBSIT E W Sixteenth-Note Combinations and Triplet EBSIT 4.2. E W Sixteenth-Note Combinations and Triplet with Leading Rests Rhythm exercises. Before you begin, review all of the rhythmic patterns in Exercise 4.1, taking extra care to perform the triplet smoothly and evenly. Each exercise in this section is in two parts, where Part 1 is a basic rhythm and Part 2 is the same rhythm with rests and/or ties added. a. Set your metronome to a slow-to-medium tempo, and perform Part 1 several times while finger-counting. b. Divide the class so that one half performs Part 1 and the other half performs Part 2 simultaneously. Those singing Part 2 should listen carefully to Part 1 in order to help accurately place the rests and ties. c. If you are working on your own, find a friend to help you do the exercises, or record yourself singing Part 1 and then play back Part 1 as you sing Part 2 over it. 152| Keyboard and Singing Exercises d. When singing the two parts together, choose any two pitches, and sing on a neutral syllable. e. Once you are ready, gradually increase the tempo. 1. 2. 3. Keyboard and Singing Exercises |153 4. 5. 6. 154| Keyboard and Singing Exercises 7. 4.3. Playing major scales. Tempo goal: 72 bpm, one note per beat. Play these major scales at the piano in order, moving clockwise around the circle of fifths. (Your hands will move up the keyboard by tetrachords.) If necessary, write out the scales first. Play each scale several times, noting the new sharp or flat for each key. Practice each one until it is memorized. 1. C major 2. G major 3. D major 4. A major 5. E major 6. B major (enharmonic to C∫ major) 7. F# major (enharmonic to G∫ major 8. C# major (enharmonic to D∫ major) 9. A∫ major 10. E∫ major 11. B∫ major 12. F major Go back to the beginning and repeat the circle: 1. C major (etc.) 4.4. Variation. Practice the scales in Exercise 4.3 in reverse order, moving counterclockwise around the circle of fifths. (Your hands will move down the keyboard by tetrachords.) 1. C major 2. F major 3. B∫ major 4. E∫ major 5. A∫ major 6. D∫ major (enharmonic to C# major) 7. G∫ major (enharmonic to F# major 8. C∫ major (enharmonic to B major) 9. E major 10. A major Keyboard and Singing Exercises |155 11. D major 12. G major Go back to the beginning and repeat the circle: 1. C major (etc.) 4.5. Playing and singing major scales. Tempo goal: 𝅘𝅥 = 100 bpm. Sing letter names as you play each scale listed in the previous example. Some of the scales might not fall comfortably in your voice range. For those scales, it is OK to speak the names rather than sing them. Use the half rest in each measure to prepare to sing the following pitch. The D-flat major scale is given as an example; substitute letter names for each key, up to seven sharps/flats. 44 œ œ » $VFHQGLQJ ' IODW Ç » & 4.6. œ œ » ( IODW œ œ » ' IODW Ç » ) œ œ » * IODW 'HVFHQGLQJ ' IODW œ œ » Ç » œ œ » $ IODW œ œ » & œ œ » % IODW % IODW œ œ » $ IODW HWF Intervals with letter names. Tempo goal: 𝅘𝅥 = 90 bpm. Review Exercise 3.8 (Interval Singing) in the previous chapter, and then repeat the exercise using letter names for each of the scales introduced in this chapter. The key of F-sharp major is given as an example; substitute letter names for each major key, up to seven sharps/ flats. Ascending 4 œ œ œ œ œ œ œ œ F - sharp G-sharp F - sharp D - sharp œ œ œ œ Descending œ œ œ œ F - sharp E- sharp F - sharp A - sharp 156| Keyboard and Singing Exercises œ œ œ œ œ œ œ œ œ œ œ F - sharp A-sharp F-sharp B F - sharp E - sharp œ œ œ œ œ œ œ œ F- sharp C-sharp F - sharp F - sharp œ œ œ œ œ œ œ œ œ œ œ F - sharp D- sharp F - sharp C- sharp F-sharp B œ œ œ œ F - sharp G - sharp œ œ œ œ F - sharp F - sharp 4.7. Tendency row with solfège and note names. Tempo goal: 𝅘𝅥 = 72 bpm. The next set of exercises will focus on the basic and advanced tendency rows (see Fig. 4.2). Recall that re, fa, la, and ti are tendency tones because they tend to resolve to the tonic triad tones do, mi, and sol. Using the chart above, practice the next exercise several times in every major key. If you are using tetrachord position, play measures 1–2 of the tendency row with your left hand, and measures 3–4 with your right hand. Some pitches in some keys may be out of your singing range. In those cases, it is OK to speak the pitch names rather than sing them. a. Choose a major key. b. Play the scale, up and down, while singing solfège. c. Play the scale, up and down, while singing letter names. d. Play the basic tendency row while singing solfège. e. Play the basic tendency row while singing letter names. f. Play the advanced tendency row while singing solfège. g. Play the advanced tendency row while singing letter names. h. Repeat the exercise in every major key. 4.8. Singing the tendency row without the piano. Sing the tendency rows in solfège without using the keyboard. Start on any pitch that is low and comfortable in your voice. It is important that you sing confidently, comfortably, and with accurate pitches. When you sing the advanced row, think the basic row. In other words, on beat 1 of each measure, imagine the note that is present in the basic row (do mi, or sol); then sing the tendency tone and resolve it. If you need to refer to the piano, do not play the tendency tone. Instead, play the resolution tone, sing the tendency tone, and resolve it. Keyboard and Singing Exercises |157 HEARING EXERCISES Goal for Exercises 4.9–4.11: ten consecutive correct answers. Before you begin, review all Hearing Exercises from the previous chapter. 4.9. Hearing the basic tendency row. Your instructor or study partner will play an ascending major scale, and then the low do followed by one segment of the basic tendency row. Sing back the pitches on a neutral syllable, and then with solfège. 4.10. Variations. a. In the beginning, the instructor will keep all questions in the same key and play the major scale only once, at the beginning of the study session. b. For a challenge, the instructor will switch keys for each question, and play a new major scale before each question to establish the key. c. For an extra challenge, after you have sung back the segment with correct solfège, the instructor will say the name of a key. Sing the segment with correct note names for that key. 4.11. Hearing the advanced tendency row. Repeat Exercises 4.9 and 4.10 using the advanced tendency row. INFORMED LISTENING: EXAMPLES FOR STUDY 4.12. Johannes Brahms, Waltz, Op. 39, No. 15 Meter: triple Tempo: moderate, about 102 bpm (the tempo is fluid and varies throughout) What to listen for: • Near the end of the work, a triplet figure occurs at about 1′05″. 158| Informed Listening: Examples for Study 4.13. Ella Fitzgerald, “Love You Madly” (Duke Ellington), from The Complete Ella Fitzgerald Song Books Meter: quadruple Tempo: fast, about 120 bpm What to listen for: • This song is performed in the key of C major. Before you listen, sing the basic and advanced tendency rows in C major; then listen to the opening of the song. • In the introduction, the piano plays the scale degrees mi-fa-mi repeatedly. • The singer enters on the tendency tone la, and it immediately resolves downward to sol. This occurs on the words “Love you,” and throughout the song at the start of every verse. 4.14. Muzio Clementi, “Allegretto” (Movement II) from Sonatina in G Major, Op. 36, No. 2 Tempo: slow, about 68 bpm What to listen for: • This piece is written in the key of C major. Before you listen, perform the basic and advanced tendency rows in C major. • During its first eight measures, the melody leaps to each tendency tone in the scale and resolves it to the nearest triad member. • The dotted-eighth-sixteenth figure occurs throughout the work, occupying nearly every beat. 4.15. The Beatles, “We Can Work It Out,” from Past Masters, Vol. 2 Tempo: fast; about 102 bpm What to listen for: • The tambourine plays sixteenth notes throughout most of the piece. • The vocal melody begins on the scale degrees do-re-do. The figure recurs at the beginning of every verse. Informed Listening: Examples for Study |159 • The Scotch Snap rhythm (sixteenth-dotted-eighth) occurs on the first two words of the title (“We can . . .”) every time it is sung. 4.16. Ludwig van Beethoven, “Allegretto” (Movement II) from Symphony No. 7 Meter: duple Tempo: moderate; about 76 bpm What to listen for: • As we observed in Chapter 1, this piece is dominated by the rhythm quartereighth-eighth, but other rhythms move gradually in and out of the overall musical texture. • At about 0′57″ the rhythm the middle voice. This figure recurs throughout the work. is heard in • At about 1′56″ the lower voices begin playing triplets in the accompaniment. They may be difficult to hear because of the prominence of the melody in the winds, so listen carefully to the lowest voices while counting triplets aloud: • The triplets move to the accompanying middle voice beginning at about 2′41″. The original rhythm (quarter plus two eighths) continues in the lowest voices. As you listen, count aloud, alternating the two rhythms: • At about 3′04″ a new melody enters in the clarinet. The melody begins on the tendency tone fa and proceeds down the scale. Its rhythm includes a combination of dotted quarters, eighths, and triplets. As you listen, sing the melody in solfège, and then in counts. • At about 4′00″ the accompaniment changes to sixteenth notes, but a triplet figure remains in the melody. As you listen, count aloud, alternating sixteenths with triplets: 160| Informed Listening: Examples for Study INFORMED LISTENING: EXAMPLES WITH QUESTIONS 4.17. Edvard Grieg, “Berceuse (Cradle Song),” from Lyric Pieces, Book II, Op. 38 Meter: duple Tempo: fast, about 132 bpm 1. Listen to the opening of the piece several times, and sing the tonic. What are the first four melody pitches? a. do-sol-do-la b. do-sol-la-sol c. do-sol-ti-sol d. do-sol-do-sol 2. Which of the following best represents the rhythm of the opening melody? Informed Listening: Examples with Questions LE AL N CH ✪ GE 3. Which best represents the rhythm of the accompaniment? |161 4.18. Georges Bizet, “Carillon” (Movement IV), from L’Arlésienne Suite No. 1, Op. 23 Meter: triple Tempo: fast, about 132 bpm 1. A repeated three-note figure begins the piece and is heard most of the way throughout. The three notes that make up this figure are: a. do-la-ti b. mi-do-re c. re-ti-do d. sol-do-mi 2. After a four-measure introduction played by the horns, the strings enter with a melody that features a triplet on which beat? a. Beat 1 b. Beat 2 c. Beat 3 3. The strings’ melody (see question 2) begins on what note? a. sol b. |do c. mi d. la 1. The tonic is sustained prominently throughout the introduction. Sing it, and then listen carefully to the opening vocal line. This line is made up of what four scale tones? a. fa-mi-re-do b. sol-mi-re-do c. sol-fa-re-do d. sol-fa-mi-re 2. In the last line of the first verse (ca. 0’40”), what scale tones occur when the words of the title are sung? a. mi-re b. mi-do c. re-do d. fa-mi 3. In this same place, which of these best represents the rhythm? 162| Informed Listening: Examples with Questions LE AL N CH ✪ GE 4.19. Peter Gabriel, “I Have the Touch,” from Security INFORMED LISTENING: TENDENCY TONES IN THE MUSIC OF THE BEATLES Each of these Beatles songs begins with a tendency tone followed by its resolution tone. Unless otherwise noted, the pair of notes happens at the very first vocal entrance. Listen to each song at least twice: once to find the tonic, and again to compare the tonic to the opening tendency tone. Circle the correct answer from among the choices given. 4.20. “I Will,” from The Beatles (White Album) The vocal part begins with: a. re-do b. fa-mi c. la-sol d. ti-do 4.21. “Do You Want to Know a Secret?” from Please Please Me After a short introduction featuring voice and guitar, the word Listen is sung on which pitches? a. re-do b. fa-mi c. la-sol d. ti-do 4.22. “Dear Prudence,” from The Beatles (White Album) 1. The vocal part begins with: a. re-do b. fa-mi c. la-sol d. ti-do 2. Throughout most of the song, the guitar repeats what two pitches? a. sol-mi b. mi-do c. sol-do d. re-do 4.23. “All My Loving,” from With the Beatles 1. The vocal part begins with which three pitches? a. re-do-ti b. la-sol-fa c. sol-fa-mi d. fa-mi-re 2. Throughout most of the song, the guitar plays: a. eighth notes b. triplets c. sixteenth notes 4.24. “Yesterday,” from Help! 1. The vocal part begins with: a. re-do b. fa-mi c. la-sol d. ti-do 2. At the end of the song, the singer hums the last line, which does not end on do. On what scale tone does the voice part end? a. re b. mi c. fa d. sol 4.25. “Day Tripper,” from Past Masters, Vol. 2 The vocal part begins with which four scale tones? a. re-do-ti-la b. fa-mi-re-do c. la-sol-fa-mi d. do-ti-la-sol Informed Listening: Tendency Tones in the Music of the Beatles |163 4.26. “Oh! Darling,” from Abbey Road Which pair of scale tones is sung on the word darling? a. re-do b. fa-mi c. la-sol d. ti-do 4.2. “The Long and Winding Road,” from Let It Be The vocal part begins with: a. re-do b. fa-mi c. la-sol d. ti-do DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 4.28. Choose a key for the day, taking care to focus on the keys covered in this chapter: a. Sing the major scale first in solfège, and then in note names for that key. b. Sing the interval pattern (Ex. 4.6) in solfège, and then in note names for that key. c. Sing the basic and advanced tendency rows in solfège, and then in note names for that key. 4.29. Starting on a note in the middle of your voice range, sing the major scale in solfége, up and down, changing direction at any time you choose. For example, start on do, ascend for a few pitches, then descend for a few, then ascend again, etc. Your improvisation might look something like this: G U P U G W O V O W G U P I œ œ œ œ œ œ œ V O V I V I P HWF LE AL N ✪ GE 4.30. Choose a key for the day and repeat Exercise 4.29, substituting note names for that key. CH œ œ œ œ œ œ œ œ œ œ œ œ œ œ 4.31. Sing the basic and advanced tendency rows (Ex. 4.8) in solfège from memory. Then, improvise patterns by leaping through the segments of the rows in random order. CLASSROOM ACTIVITIES 4.33. Guided improvisation: tendency row 1. Write the solfège for the tendency row on the board as illustrated below. 2. Sing through the row in order from bottom to top. 3. A class leader dictates segments from the row by pointing to them in random order. (For example: mi-fa-mi, do-ti-do, etc.) The class responds by singing the correct segment. 164| Classroom Activities LE AL N CH ✪ GE 4.32. Choose a key for the day and repeat Exercise 4.31, substituting note names for that key. 4. If there are incorrect responses, return to do and “walk” the class up or down the scale to the troublesome segment; then proceed with the exercise. 5. Change leaders periodically. 6. Repeat the exercise using the advanced tendency row. (Erase the first syllable of each segment.) | d-t-d s-l-s m-f-m d-r-d 4.34. Variation: note names Repeat Exercise 4.33, but instead of using solfège syllables choose a clef and key signature and write the tendency row using notes on the staff. (An example is given below in the key of D-flat major.) The leader points to the notes, and the class responds with solfège syllables. Change leaders periodically; every leader chooses a new key. ✪ CH 1. Write the solfège for the tendency row on the board, as in Exercise 4.26. LE AL N GE 4.35. Repeat Exercise 4.33 with these changes: 2. The leader chooses a major key (for example, B major). 3. As the leader points to each tendency row segment, the class must respond with the proper letter names for that key. 4. For example, in the key of B major, the leader points to do-ti–do. The class responds by singing: “B–A sharp–B.” 5. Change leaders periodically. Each leader chooses a new key. 4.36. Clave scales This activity is based on the clave1 rhythm, a repeated figure that is the basis for much Afro-Cuban music. Choose one leader to perform the Call, while the rest of the class speaks the Response. All class members, including the leader, perform the clave continuously throughout the activity. Be creative with the activity: a. The leader may go through the keys in the order of flats/order of sharps, or pick keys in a random order. b. Arrange the class in a circle, with the role of leader shifting to the next person for each key. 1 Pronounced “CLAH-vay.” This exercise is written in two-two meter, which is introduced in Chapter 5. Because the clave rhythm is so prevalent throughout popular music, the instructor might wish to teach the pattern by rote. Classroom Activities |165 c. As a study/review method, two people may perform the activity, alternating the roles of Call and Response. 166| Classroom Activities WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 4 online drills and quizzes at www.oup.com/us/root. 4.37. Spell each of the major scales by writing letter names in the blanks above the given scale degrees. Use uppercase letters. Be sure to draw sharp/flat symbols after the letter name. Question 1 has been completed for you. 1. B∫ major: B∫ C D E∫ F G A B∫ do re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do 2. G∫ major: _____ 3. E major: Written Exercises |167 4. C# major: _____ _____ _____ _____ _____ _____ _____ _____ re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do _____ _____ _____ _____ _____ _____ _____ _____ do re mi fa sol la ti do do 5. D∫ major: _____ 6. B major: 7. A∫ major: _____ do 8. C∫ major: _____ do 9. F# major: _____ do 10. E∫ major: _____ 11. D major: 4.38. For each question, draw the clef and key signature indicated. Name the major key represented by the key signature; then write the scale on the staff. Use noteheads only (no stems), and fill in the noteheads for any notes in the scale that are sharp or flat. Use an open notehead for the remaining notes in the scale. Write the scale in the octave that will yield the fewest ledger lines. Question 1 has been completed for you. 1. Treble clef, 3 flats Key of E∫ 2. Treble clef, 6 sharps 3. Treble clef, 5 flats 168| Written Exercises Key of ______ Key of ______ 4. Bass clef, 7 flats Key of ______ 5. Treble clef, 6 flats Key of ______ 6. Bass clef, 2 flats Key of ______ 7. Bass clef, 3 flats Key of ______ 8. Treble clef, 5 sharps Key of ______ 9. Bass clef, 4 flats Key of ______ 10. Bass clef, 1 sharp Key of ______ 11. Treble clef, 7 sharps Key of ______ Written Exercises |169 4.39. Draw a dot on each of the correct piano keys to build the requested scale. Be sure to start your scale low enough that you don’t run out of keys. Check your work by playing the scale on an actual keyboard. Question 1 has been completed for you. 1. G major 2. D∫ major 3. F# major 4. C∫ major 5. B major 6. C# major 7. G∫ major 8. B∫ major 9. E major 10. F major 11. E∫ major 170| Written Exercises 4.40. Identify the major key for each key signature given, then label each note with the correct solfège syllable for that key. Question 1 has been completed for you. Written Exercises |171 4.41. Notate the pitch that corresponds to the solfège syllable in the key given. Use half notes for all of your answers, taking care to use the proper stem direction for each note. Write your answers in any octave that is convenient. (Avoid ledger lines.) Please note: there are no key signatures given, so you must apply the sharp or flat directly to the note if needed. Question 1 has been completed for you. 4.42. Notate the pitch that corresponds to the scale-degree number in the key given. Use half notes for all of your answers, taking care to use the proper stem direction for each note. Write your answers in any octave that is convenient. (Avoid ledger lines.) Please note: there are no key signatures given, so you must apply the sharp or flat directly to the note if needed. Question 1 has been completed for you. 4.43. For each question, a note and solfège syllable are given. Provide the name of the key. Question 1 has been completed for you. 172| Written Exercises 4.44. For each question, a note and scale-degree number are given. Provide the name of the key. Question 1 has been completed for you. 4.45. For each question, the notes of a major scale are given in random order. Put the scale in the correct order by writing the correct solfège syllable or scale-degree number under each note name. Hint: Count the number of sharps or flats in each scale; that will tell you the tonic. Then label the notes accordingly. Question 1 has been completed for you. 1. D F E C A B∫ G la do ti sol mi la re OR: 6 1 7 5 3 4 2 3. E# C# B# A# F# G# D# ___ ___ ___ ___ ___ ___ ___ F# A# C# B E D# G# ___ ___ ___ ___ ___ ___ ___ D∫ C∫ E∫ B∫ F G∫ A∫ ___ ___ ___ ___ ___ ___ ___ E∫ D∫ C∫ F∫ G∫ A∫ B∫ ___ ___ ___ ___ ___ ___ ___ 5. 7. 9. 2. 4. 6. 8. 10. C# E# D# G# B A# F# ___ ___ ___ ___ ___ ___ ___ F C A∫ E∫ G B∫ D ___ ___ ___ ___ ___ ___ ___ E D C# A B F# G ___ ___ ___ ___ ___ ___ ___ C# B F# G# D A E ___ ___ ___ ___ ___ ___ ___ G∫ C D∫ F E∫ A∫ B∫ ___ ___ ___ ___ ___ ___ ___ 4.46. Rewrite each example with correct beams and bar lines to fit the given meter. Question 1 has been completed for you. 1. Written Exercises |173 2. 3. 4.47. Each example is beamed incorrectly. Rebeam the notes correctly to fit the given meter. Do not change any of the given note durations. The first measure of question 1 has been completed for you. 1. 2. 3. 4. 174| Written Exercises 4.48. Each question contains an excerpt from a song written in vocal notation. Rewrite the example with correct beaming for the given meter. You do not need to rewrite the lyrics. The first example has been started for you. 1. Lili Boulanger, “Elle était descendue” from Clarières dans le Ciel, mm. 13–18 Written Exercises |175 2. Wolfgang Amadeus Mozart, “Ariette,” K. 307, mm. 11–22 3. Johannes Brahms, “Liebe und Frühling II” from Six Songs, Op. 3, No. 3, mm. 33–36 176| Written Exercises COMPOSITION 4.49. Compose an eight-measure melody in four-four meter, using these guidelines. Refer to the template and sample composition given below. a. Use only the above rhythmic figures, and do not use rests or ties. b. Your composition will begin and end on do. c. Use only stepwise motion, but move in any direction you choose. In other words, your composition may go up and down the scale, changing direction at any time. d. Measure 8 will contain only do, with a whole-note duration. e. Measure 4 will contain only sol, in the rhythm given. (Use the sol five notes above the starting do.) f. The first note of measure 5 will be the high do. g. The last note of measure 7 will be re or ti (in order to lead stepwise into do). h. The last note of measure 3 will be fa or la (in order to lead stepwise into sol). i. The highest note in your piece will occur somewhere in measure 6 or 7, and it may only happen once. j. The lowest note in your piece may occur anywhere but may only happen once. Use the blank template given to compose your melody in solfège. Then write the melody on staff paper in a clef and key of your instructor’s choice. Perform your composition at the piano or on your instrument, or lead the class in singing it. Composition |177 Here is a sample composition written first in solfège, and then in bass clef, B major. 4.50. Compose a two-part rhythm exercise modeled on those in Exercise 4.2. a. Your composition will be eight measures long. b. Use a variety of rhythmic figures, but those covered in Chapters 3 and 4 should predominate. Be sure to use at least one triplet. c. Do not use any rests or ties in Part 1. d. In Part 2, duplicate the rhythm of Part 1, but add ties across the bar line or the beat. Choose several beats in your exercise and replace the first duration of the beat with a rest. (For example: sixteenth note, dotted eighth note becomes sixteenth rest, dotted eighth note.) e. Set your metronome to a moderate tempo and lead the class in singing your composition, following the performance instructions in Exercise 4.2. 4.51. Recompose the basic tendency row (shown below) according to the following guidelines: a. Replace beats 1 and 2 of each measure with one of the rhythmic figures shown below. Beat 3 of each measure should remain a quarter note. b. Use each figure at least once, but do not use the same figure twice in one measure. c. Write your composition on staff paper in a clef and key of your instructor’s choice. d. Lead the class in performing your composition first using counts, and then with solfège. (Do not perform with note names, as the multisyllabic names will confuse the rhythms.) Use only these rhythms: 178| Composition Chapter Goals Revisited A sample composition is given in solfège and in D-flat major. Be sure that you have achieved all Chapter 4 Goals before proceeding to Chapter 5. • Sing major scales with solfège, scale degree numbers, scale degree names, and letter names. (pages 151, 156) • Play major scales at the keyboard. (pages 151, 155–156) • Write major scales with or without key signatures, in treble clef, bass clef, and letter names. (pages 137–143) • Recognize major key signatures instantaneously. (pages 141–143, 149–151) • Correctly notate major key signatures. (page 147) • In a given key, identify the note that correlates with a solfège syllable or scale degree number. (page 143) • Understand the function of the tonic triad and tendency tones in the major scale. (pages 144–145) • Sing and resolve tendency tones in the major scale. (page 157) • Hear and recognize tendency tones with their resolution tones in the major scale. (page 158) • Recognize and sing rhythms that contain triplets. (pages 145–146, 151–155) • Properly notate rhythms that contain triplets. (page 147) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. Composition |179 CHAPTER 5 Chapter Goals PITCH: MINOR KEYS 1/ RHYTHM: EIGHT- AND TWO-BASED SIMPLE METER After you finish this chapter, you should be able to do the following, quickly and accurately, for all minor keys: • Sing natural minor scales with solfège and letter names. • Play natural minor scales at the keyboard. • Write natural minor scales with or without key signatures, in treble clef, bass clef, and letter names. • Name the major and minor keys represented by any key signature. • Recognize, by sound, whether a piece of music is in a major or minor key. • Understand the connection between relative keys, and recognize it in music you hear. • Understand the connection between parallel keys, and recognize it in music you hear. • For any major key, name the relative minor and parallel minor. • For any minor key, name the relative major and parallel major. • In a given key, map letter names to each solfège syllable or scale degree number. • Sing and hear intervals above and below do in the natural minor scale. • Perform basic rhythms in eight-based and two-based simple meters. • Properly notate basic rhythms in eight-based and two-based simple meters. 180| THE NATURAL MINOR SCALE EBSIT E As you work through this chapter, it is especially important to have a piano nearby. If an actual piano is not available, use an online piano or smart-phone app. With your teacher’s guidance, sing “Hatikvah” (Fig. 5.1) several times using counts or letter names. W Minor Scale Structure and Relative Keys Figure 5.1. “Hatikvah” (Israeli National Anthem). Examine the notated music: the key signature contains one sharp, and all of the notes of the G major scale are present (G-A-B-C-D-E-F#). But as you sing, you may notice that the song does not sound or “feel” as though it is in the key of G major. And in fact it is not, because the tonic pitch is E, not G. A closer look at the music bears this out: • The piece beings and ends on E. • E is the highest note. • Four of its five phrases end on E. • E is emphasized by octave leaps in measures 9 and 11. “Hatikvah” is written using the minor scale, and since E is clearly the tonic, we say that the song is in the key of E minor. Several types of minor scales exist, but the one covered in this chapter is commonly called the natural minor (or pure minor) scale. At the piano, play the two scales shown in Figure 5.2. The natural minor scale can be derived by rotating the major scale to begin on its sixth scale degree while keeping all of the Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter |181 same pitches. In this case, G major is reordered to begin on its sixth degree, E. Shifting the scale’s tonic changes the order of half steps and whole steps, resulting in a different sound and character.1 EBSIT E W Figure 5.2. G major and E minor are relative keys. G major and E minor are called relative keys because they share all of the same pitches, as well as a key signature of one sharp: Key signature (one sharp) for the relative keys of G major and E minor. In musical terminology, we say that: • E minor is the relative minor of G major. and • G major is the relative major of E minor. Next, we will derive the relative minor scale of A-flat major. To do this, we will write out an A-flat major scale, then reorder it to begin on its sixth degree, F. The result is an F minor scale. EBSIT E W Figure 5.3. A-flat major and F minor are relative keys. 1 You may have heard it said that major keys sound “happy” or “bright,” while minor keys sound “sad,” somber,” or “ominous.” These generalizations are not always accurate (many somber pieces happen to be written in major keys), but they might be helpful in distinguishing the two scale types by sound. 182| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter A-flat major and F minor are relative keys because they share all of the same pitches, and they share a key signature of four flats: Key signature (four flats) for the relative keys of A-flat major and F minor. In musical terminology, we say that: • F minor is the relative minor of A-flat major. and • A-flat major is the relative major of F minor. Every major key has a relative minor key that shares the same key signature. Notice that the tonic of a minor key is always the sixth scale degree of its relative major. Just as with major keys, there are three pairs of enharmonic minor keys, found on the outside of the chart. • A-flat minor is enharmonic to G-sharp minor. • E-flat minor is enharmonic to D-sharp minor. • B-flat minor is enharmonic to A-sharp minor. Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter |183 It is also possible to map all major and relative minor keys onto the circle of fifths. In this example, the major keys are shown outside the circle, and their relative minor keys inside. To find the relative minor key from a major scale, reorder the major scale so that it begins on scale degree 6. In other words, go down a half step, and then a whole step from the majorkey tonic (1–7–6). For example: • Given: A major. Find the relative minor key. • Find 6 by counting down the A major scale. 1̂–7̂–6̂ = A-G#-F# • F# minor is the relative minor key of A major. • You can also count A (half step)—G# (whole step)—F#. 184| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter To find the relative major key from a minor scale, imagine that the minor-key tonic is 6 in a major scale. Then count upward to the major tonic. In other words, go up a whole step, and then a half step from the minor-key tonic (6–7–1). For example: • Given: G minor. Find the relative major key. • Imagine that G is scale degree 6 in a major scale. What is the scale? Count upward: 6̂–7̂–1̂ = G–A–B-flat. • B-flat major is the relative major key of G minor. EP L A Y • Relative keys share the same key signature and pitch content but start on different tonics. R • You can also count G (whole step) > A (half step) > B-flat. • To find the relative minor of a major key, reorder the major scale so that it begins on 6̂. In other words, go down a half step, and then a whole step from the major-key tonic (1̂–7̂–6̂). • To find the relative major of a minor key, treat the minor-key tonic as scale degree 6̂ and count upward to the major tonic (6̂–7̂–1̂). • Examples of relative keys include: o E-flat major and C minor (C is scale degree 6̂ in E-flat major) o D major and B minor (B is scale degree 6̂ in D major) o A major and F-sharp minor (F-sharp is scale degree 6 in A major) Parallel Keys Let us revisit the A-flat major and F minor scales from Figure 5.3. We already know that the F minor scale can be constructed by starting the A-flat major scale on 6. Now compare the F minor scale with an F major scale. Play the three scales in Figure 5.4, in order. Parallel keys Amajor scale: A B C D E F F minor scale: F G A B C D E F F major scale: F G A C D F B E G A EBSIT E Relative keys W Figure 5.4. Parallel and relative keys for F minor. The scales of F major and F minor are parallel because they both begin on the same tonic (F). Notice that there are pitch differences between the parallel F scales: in the F minor scale, the third, sixth, and seventh degrees are each a half step lower than in the F major scale (A/A-flat, D/D-flat, and E/E-flat). Parallel keys share the same tonic but differ in pitch content. To derive the parallel minor from a major scale, begin on the same tonic (in this case F), but add three flats to the key signature. The three flats that you add will always be in key-signature order and will lower the third, sixth, and seventh degrees. For clarification, examine the circle of fifths, and notice that the key signature for F major contains one flat, while the key signature for F minor contains four flats. Three flats are added. As a further example, we will return to the G major and E minor scales, rewritten below in Figure 5.5. Recall that we found the E minor scale by starting on the sixth degree of G major. But when E minor is written next to its parallel key, E major, we see that once again Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter |185 the minor scale has a lowered third, sixth, and seventh in comparison to its parallel major (in this case, G-sharp to G, C-sharp to C, and D-sharp to D). EBSIT E W Figure 5.5. Parallel and relative keys for E minor. Relative keys Parallel keys Gmajor scale: G A B C D E E minor scale: E F G A B C D E E major scale: E F G A B C D E F G In comparing F major and F minor, we discovered that the parallel minor scale is found by adding three flats to the key signature of a major scale. In the case of Figure 5.5, we begin with a sharp key, E major. In order to lower scale degrees 3, 6, and 7, we must subtract three sharps from the key signature. (E major contains four sharps; E minor contains one sharp.) Subtracting a sharp is equivalent to adding a flat. You can also use the circle of fifths: to find the key signature for a parallel minor key, start at the major key and move three places counterclockwise on the circle. For example: 1. Given: B-flat major. Find the parallel minor key. • The parallel minor is B-flat minor (same tonic), • Start at B-flat major (two flats) and move three places counterclockwise (add three flats). You will find that the key signature for B-flat minor has five flats. 2. Given: D major. Find the parallel minor key. • The parallel minor is D minor (same tonic). • Start at D major (two sharps) and move three places counterclockwise. The key signature for D minor has one flat. • In this case, we must subtract two sharps and add one flat (the equivalent of adding three flats). Because the maximum number of flats in a key signature is seven, it is not always possible to add three flats. For these keys, you must use the enharmonic parallel minor. For example: 1. Given: D-flat major. Find the parallel minor key. • Start at D-flat major (five flats) and move three places counterclockwise on the circle of fifths. • There is no key of D-flat minor. (Its key signature would have eight flats.) • The parallel minor key is C-sharp minor (four sharps). 2. Given: G-flat major. Find the parallel minor key. • Start at G-flat major (six flats) and move three places counterclockwise on the circle of fifths. • There is no key of G-flat minor. (Its key signature would have nine flats.) • The parallel minor key is F-sharp minor (three sharps). 3. Given: C-flat major. Find the parallel minor key. • Start at C-flat major (seven flats) and move three places counterclockwise on the circle of fifths. • There is no key signature for C-flat minor. (It would have ten flats.) • The parallel minor key is B minor (two sharps). 186| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter To find the parallel major key signature from a minor key, simply use the major key signature for the same tonic. For example: 1. Given: G minor. Find the parallel major key. • The parallel major is G major (same tonic). • You already know that G major has one sharp. Some minor keys have no parallel major equivalent. For those keys, you must use the enharmonic parallel major. For example: 1. Given: G-sharp minor. Find the parallel major key. • There is no key signature for G-sharp major. (It would require eight sharps.) • The parallel major is A-flat major (four flats). 2. Given: D-sharp minor. Find the parallel major key. • There is no key signature for D-sharp major. (It would require nine sharps.) • The parallel major is E-flat major (three flats). 3. Given: A-sharp minor. Find the parallel major key. • There is no key signature for A-sharp major. (It would require ten sharps.) • The parallel major is B-flat major (two flats). The Moldau, by the Czech composer Bedrı̆ch Smetana, is based on the same folk tune as “Hatikvah.” Throughout the work, the tune occurs in the key of E minor (Fig. 5.6a), but near the end it reappears in the parallel key of E major (Fig. 5.6b). Play and sing both examples and compare the sound of the parallel keys. Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter EBSIT E W Figure 5.6. Bedrı̆ch Smetana, The Moldau. |187 Summary of Minor Key Signatures and Scales EP L A Y R All major key signatures and scales are shown below. For each scale, the notes that are sharp or flat are shown with dark note heads; those notes that remain natural are shown with open note heads. As you study, write out the scales in this manner to help you remember which notes are sharp or flat in each. • Parallel keys share the same tonic, but they have different note content and key signatures. • Every minor key has a lowered third, sixth, and seventh degree compared to its parallel major. 188| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter • Examples of parallel keys include: o C major and C minor o F major and F minor o B-flat major and B-flat minor • To find the parallel minor of a major key, move three places counterclockwise on the circle of fifths. This will add three flats to the key signature (or subtract three sharps, or some combination thereof). The three added flats are applied to scale degrees 3, 6, and 7. • To find the parallel major of a minor key, simply use the major key signature for the same letter name. (For D minor the parallel major is D major. You already know that D major has two sharps.) MINOR SCALES AND SOLFÈGE There are two methods commonly used for mapping solfège syllables to minor scales: the la-based minor system and the do-based minor system. La-based Minor The la-based minor system maps la to the tonic of the minor scale, highlighting the shared pitch content between a minor scale and its relative major. Remember that la is scale degree 6, so (for example) in E minor G is still called do. In the la-based system, the minor scale is spelled la-ti-do-re-mi-fa-sol-la. Sing the E minor scale up and down, then sing “Hatikvah” using la-based minor syllables. Do-based Minor In this book, we will use the do-based minor system to name the degrees of the minor scale. In this system, do is mapped to the tonic of the minor scale, highlighting the connection between a major scale and its parallel minor. Remember that parallel keys have the same tonic, but differing pitch content: scale degrees 3, 6, and 7 are lowered by one half step in the parallel minor. Modified solfège syllable names are used to reflect these alterations: • When mi (3) is lowered by a half step, it becomes me (pronounced “may”). • When la (6) is lowered by a half step, it becomes le (pronounced “lay”). • When ti (7) is lowered by a half step it becomes te (pronounced “tay”). Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter |189 In the do-based system, the minor scale is spelled do-re-me-fa-sol-le-te-do. Sing the E minor scale up and down, and then sing “Hatikvah” using do-based minor syllables. To help you learn the solfège for the minor scale, sing the following warm-up exercise several times; then sing “Hey Ho, Nobody Home” using solfège syllables. Only a few syllables are given in the song; you must fill in the remaining ones as you sing. Always remember to call scale degrees 3 and 7 me and te, respectively. (Because you are learning the song, ignore the repeat signs; they are used only when the song is sung as a round.) EBSIT 190| E W Figure 5.7. Trad., “Hey Ho, Nobody Home.” Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter Once you have learned to sing the song in solfège, divide the class into three groups and sing it as a three-part round, using the words. (Entrances are indicated every two measures.) Sing the music between the repeat signs three times; at the end of the third time, each part will in turn proceed to measure 7 and finish the piece. If the class is large enough to divide into six groups, this round may also be sung in six parts, with a group entering every measure. EP L A Y • The do-based minor system maps do to the tonic of the scale. It is useful for understanding the link between a minor key and its parallel major. R • The la-based minor system maps the syllable la to the tonic of the minor scale. It is useful for understanding the link between a minor key and its relative major. • In the do-based natural minor scale, the lowered 3 is called me (“may”), the lowered 6 is called le (“lay”), and the lowered 7 is called te (“tay”). RHYTHM Eight-based Simple Meter So far, we have discussed only meters with a denominator (bottom number) of four, in which the quarter note represents the pulse: Although four-based meters are by far the most common in music, other note values may be used to represent the pulse as well. These three meters all use the eighth note as the pulse: You may have encountered other eight-based meters such as six-eight or twelve-eight; those will be covered in the next chapter. For now, let us consider only the meters shown above. Reexamine the music for “Hey Ho, Nobody Home” (Fig. 5.7). The song is typically written in four-four meter, but it may also be written in four-eight meter, where the eighth note represents the pulse instead of the quarter note. Sing the song again (or listen to it online) while reading Figure 5.8 and finger-counting the eighth-note pulse shown in the bottom staff. Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter |191 EBSIT E W Figure 5.8. “Hey Ho, Nobody Home,” written in four-eight meter. Comparing the two versions of the song, you should notice several things: 1. Both versions are to be performed at exactly the same tempo. Writing the music in four-eight does not make it go faster than in four-four. In both versions, the designated tempo is 100 bpm: 2. To convert the song from four-four to four-eight meter, every note and rest is reduced by half its value. In other words, every quarter note becomes an eighth 192| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter note, every half note becomes a quarter note, every dotted half note becomes a dotted quarter note, etc. 3. Each eighth note is flagged individually. Normally, eighth notes are not beamed together in four-eight meter, because each one represents an entire beat. This notation convention is not consistent, so you may encounter music that does use beamed eighth notes in four-eight meter. Examine the first four bars of “The Star-Spangled Banner” (Fig. 5.9), written first in three-four meter (a), and then again in three-eight meter (b). Once again, the tempo of the music stays the same even though the note values have been reduced by half. The dotted eighth-sixteenth figure from (a) becomes a dotted sixteenth followed by a thirty-second note when rewritten in (b). A thirty-second note is one-half the length of a sixteenth note; it is written with three beams (or three flags if it occurs alone). Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter EBSIT E W Figure 5.9. “The Star-Spangled Banner” in three-four and three-eight. |193 In Figure 5.10, “Oh Susannah” is notated in two-four meter, and then in two-eight. Notice that the pairs of sixteenth notes become pairs of thirty-second notes in the two-eight version. EBSIT E W Figure 5.10. “Oh Susannah” in two-four and two-eight. Two-based Simple Meter EBSIT E W The following meters use the half note to represent the pulse. Figure 5.11 shows a short melody written in two-four meter, and then rewritten in twotwo. Notice that in order to convert a four-based meter to a two-based meter, it is necessary to double all of the note values. (The quarter note becomes a half note, the eighth note becomes a quarter note, etc.) Figure 5.11. Two-four vs. two-two meter. 194| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter Remember that changing the meter of a piece of music does not change its tempo. In the example above, the quarter note equals 88 bpm in two-four, and the half note equals 88 bpm in two-two. Thus, the examples sound identical even though they are written differently. Two-based meters have a visual disadvantage: compare the two versions of “Hey Ho, Nobody Home” in Figure 5.12. Version (a) in four-four is easier to read because each beat divides into two eighth notes, which can be beamed together. Version (b), in two-two, uses a half-note pulse, so the pulse division is the quarter note. Because quarter notes cannot be beamed, there is no way to visually group every pair of quarter notes into one beat. EBSIT E W Figure 5.12. “Hey Ho, Nobody home” in four-four and four-two. Likewise, the dotted quarter and eighth in “The Star-Spangled Banner” (Fig. 5.13) cannot be beamed together to indicate that they occupy beat 3. When working with music in two-based meters, you might find it helpful to bracket each beat, as shown below. EP L A Y R • In eight-based meters, the eighth note is used to represent the pulse. EBSIT E W Figure 5.13. “The Star-Spangled Banner” in three-four and three-two. • Eight-based simple meters include two-eight, three-eight, and four-eight. • In two-based meters, the half note is used to represent the pulse. • Two-based simple meters include two-two, three-two, and four-two. Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter |195 NOTATION Beaming conventions in eight-based meters tend to be inconsistent across various pieces of music. For example, in three-eight meter you may see each eighth-note beat flagged individually, as in “The Star-Spangled Banner” (Fig. 5.9), above. In other cases, the composer may choose to beam the eighth notes together. In the Bach piece shown below, entire measures of three-eight are beamed together. Whichever notation you use, always be sure to beam together notes within each beat wherever possible. J. S. Bach, Invention No. 4 in D minor, BWV 775. 196| Pitch: Minor Keys 1/Rhythm: Eight- and Two-based Simple Meter MEMORIZATION STRATEGIES Parallel and Relative Keys Sometimes students confuse the meanings of “relative” and “parallel” when studying the relationships between major and minor keys. A simple mnemonic device may help to clarify the terms. For parallel keys: think of double letters: The word “parallel” has two L’s in the middle, and parallel keys share the same letter name for their tonics (for example, A major and A minor). For relative keys: think of the word “la” in the middle of the word “reLAtive.” To find a relative minor key from its major, find 6 (or la) in the major key, and that will be the tonic of the relative minor. If you are visually oriented, picture the relative keys in a vertical line, with the major key “living” above its relative minor. In other words, to go from major to minor go downward. To go from minor to major, go upward. Conversely, visualize parallel keys as “living” side by side, with the minor key to the left of its parallel major. Positioning the keys in this way, you can create a network of major and minor key relationships. (See Ex. 5.37.) Memorization Strategies |197 Flashcards To create flashcards for this chapter, draw a key signature on one side of the card and write the name of the corresponding minor key on the other. Include both treble and bass clefs, and be sure to focus on the clef that is normally weaker for you. Group your cards by level (color coding can be very helpful), and take small steps. For example: 1. First, practice only keys up to four sharps: A, E, B, F-sharp, and C-sharp minor. 2. Next, practice only the keys of G-sharp, D-sharp, and A-sharp minor. 3. Then practice all sharp keys. 4. Practice only keys up to four flats: A, D, G, C, and F minor. 5. Practice only the keys of B-flat, E-flat, and A-flat minor. 6. Practice all flat keys. 7. Practice only keys up to four sharps/flats. 8. Practice only keys with five sharps/flats or more. 9. Practice all keys. PRACTICE STRATEGIES Review the Practice Strategies from Chapters 3–4, and apply them to the following exercises as well. They include: • Playing scales in tetrachord position. • Using a metronome to perform the exercises with a steady pulse. (Tempo goals are given for each exercise.) • Singing confidently in a range that is comfortable for your voice. If you need to check your vocal accuracy at the keyboard, be sure to play the note after you sing it, not before. • Proceeding slowly, repeating each part of the exercise several times. Do not move on to the next exercise until you have achieved fluency. 198| Practice Strategies KEYBOARD AND SINGING EXERCISES 5.1. Rhythmic patterns. Tempo goal: 80 bpm. Practice the rhythmic patterns given below using this method: a. Set your metronome to a moderately slow tempo–about 60 bpm. Pay close attention to the pulse unit! b. Choose a comfortable pitch for your voice, and sing the patterns in order using the counts given. Remember to use the second measure of each pattern to prepare for the next. c. Sing the rhythms out of order, leaping from one to the next randomly. Again, use the second measure to choose and prepare. d. Gradually increase the tempo of the exercise. Remember that accuracy is more important than speed. The rhythmic patterns for this chapter are the same as for Chapter 4, but they have been rewritten in three-eight and three-two meter. The patterns will sound identical to the ones you learned before, so you should focus on mapping the sounds you already know to the durations in the new time signatures. EBSIT E W Patterns in Three-eight Keyboard and Singing Exercises |199 EBSIT E W Patterns in Three-two 5.2. Variation. Write out each of the patterns above, but replace the first duration of beat 3 with the equivalent rest. Add the new patterns to your practice sessions. 5.3. Rhythm exercises. Each of the following exercises is in two parts, where Part 1 is a basic rhythm and Part 2 is the same rhythm with rests and/or ties added. a. Set your metronome to a slow-to-medium tempo, and perform Part 1 several times while finger-counting. b. Divide the class, so that one half performs Part 1 and the other performs Part 2 simultaneously. Those singing Part 2 should listen carefully to Part 1 in order to help accurately place the rests and ties. c. If you are working on your own, find a friend to help you do the exercises, or record yourself singing Part 1, and then play back Part 1 as you sing Part 2 over it. d. When singing the two parts together, choose any two pitches, and sing on a neutral syllable. e. Once you are ready, gradually increase the tempo. 1. 200| Keyboard and Singing Exercises 2. 3. 4. Keyboard and Singing Exercises |201 5. 6. 7. 202| Keyboard and Singing Exercises 5.4. Playing natural minor scales. Tempo goal: 72 bpm, one note per beat. Play these minor scales at the piano in order, moving clockwise around the circle of fifths. (Your hands will move up the keyboard by tetrachords.) If necessary, write out the scales first. Play each scale several times, noting the new sharp or flat for each key. Practice each one until it is memorized. 1. A minor 2. E minor 3. B minor 4. F# minor 5. C# minor 6. G# minor (enharmonic to A∫ minor) 7. D# minor (enharmonic to E∫ minor) 8. A# minor (enharmonic to B∫ minor) 9. F minor 10. C minor 11. G minor 12. D minor Go back to the beginning and repeat the circle: 1. A minor (etc.) 5.5. Variation. Practice the scales in Exercise 5.4 in reverse order, moving counterclockwise around the circle of fifths. (Your hands will move down the keyboard by tetrachords.) 5.6. Playing and singing natural minor scales. Tempo goal: 𝅘𝅥 = 120 bpm. Sing each of the patterns in the next example as you play the scales in Exercise 5.4. Observe the notated rhythms, and use each rest to anticipate the next note in your mind and in your fingers. Some of the scales might not fall comfortably in your voice range. For those scales, it is OK to speak the words rather than sing them. Keyboard and Singing Exercises |203 5.7. Singing minor scales without the piano. Tempo goal: 𝅘𝅥 = 120 bpm. Sing the scales above in solfège without using the keyboard. Start on any pitch that is low and comfortable in your voice. It is important that you sing confidently, comfortably, and with accurate pitches. Remember, it is OK to check your pitch at the keyboard, as long as you play the note after you attempt to sing it. 5.8. Scale segments. Tempo goal: 𝅘𝅥 = 70 bpm. Sing the next exercise without using the piano. It is written in B minor, but you should start on any note that is low and comfortable in your voice. Use solfège and/or numbers as instructed by your teacher. Although bar lines and a time signature are absent, be sure to observe the notated rhythm and maintain a steady pulse throughout. The goal of this exercise is to develop your fluency in singing solfège/numbers in ascending and descending scale formations. You should strive for accuracy first, and speed second. 204| Keyboard and Singing Exercises 5.9. Intervals in the natural minor scale. Tempo goal: 𝅘𝅥 = 90 bpm. Using the example below, sing from do up to each scale tone. Then, sing from the high do down to each scale tone. Keep a steady pulse throughout, and use each quarter rest to anticipate the next interval in your mind. Hint: if you have difficulty singing an interval, sing the corresponding scale segment before singing the troublesome interval. For example: Keyboard and Singing Exercises |205 5.10. Intervals with letter names. Tempo goal: 𝅘𝅥 = 90 bpm. Sing Exercise 5.9 using letter names for all of the natural minor scales covered in this chapter. The key of D minor is given as an example, but be sure to practice with letter names for all keys introduced in this chapter. & b 43 œ œ Œ ' ( &b œ œ Œ ' & œ ' Œ œ œ Œ œ œ $VFHQGLQJ ' œ Œ ) ' ' œ œ Œ œ œœŒ ' ' 'HVFHQGLQJ ' * Œ œ œ & % IODW $ œ œ Œ ' $ œ ' œœŒ %IODW HWF 5.11. Inside-out scales. Tempo goal: 𝅘𝅥 = 90 bpm. Sing the major and natural minor scales “outward” from the tonic, as shown in the examples below. Begin on any comfortable pitch in the middle of your voice range. HEARING EXERCISES Goal for Exercises 5.12–5.15: ten consecutive correct answers. 5.12. Hearing scales. Your instructor or study partner will play either a major or a natural minor scale. Name the scale type. 5.13. Hearing ascending intervals. Your instructor or study partner will play an ascending natural minor scale, and then the low do followed by a higher scale tone. Sing back the two pitches and name the scale tone using solfège. 206| Hearing Exercises Example: 5.14. Hearing descending intervals. Your instructor or study partner will play a descending natural minor scale, and then high do followed by a lower scale tone. Sing back the two pitches and name the scale tone using solfège. Example: œ œ œ œ œ œ œ œ œ œ Your instructor plays this… Listen, and sing back the pitches on a neutral syllable… œ nah œ …then this. œ œ …then with solfège. nah do le Hint: if you have trouble with Exercises 5.13 and 5.14, sing scale segments (Ex. 5.8) to help you measure the interval with your voice. Hearing Exercises LE AL N ✪ GE In Exercises 5.13 and 5.14, the intervals are to be played melodically. For an extra challenge, your instructor will play each interval harmonically. You will then need to separate the pitches in your mind, sing the two notes melodically, and name the solfège syllables. Example: CH 5.15. Hearing harmonic intervals. |207 INFORMED LISTENING: EXAMPLES FOR STUDY Major to Relative Minor The next set of examples begins in a major key and move to the relative minor. Listen to each several times as you read the accompanying description. To hear the relationship between the two keys, sing the original tonic, and then sing down three scale tones (1-7-6 or tonicwhole-half) to hear the tonic of the relative minor key. If you have trouble, play the pitches on the piano or your instrument. 5.16. Georges Bizet, “Carillon” (Movement IV) from L’Arlésienne Suite No. 1, Op. 23 What to listen for: • This piece begins in the key of E major and moves to the relative minor key of C-sharp minor. • The key change happens at about 1′25″, and the new tonic is clearly heard at about 1′33″. The music stays in C-sharp minor only briefly before moving to another key (G-sharp minor) at about 1′53″. • The piece returns to C-sharp minor at about 3’00”, and to the original key of E major at about 3′22″. 5.17. Johann Sebastian Bach, “Minuet I” and “Minuet II” from English Suite No. 4 in F major, BWV 809 What to listen for: • The performer will play Minuet I and Minuet II, and then repeat Minuet I. • Minuet I is in F major; Minuet II begins at about 1′21″ and is in the relative minor key of D minor. • Minuet I returns in the original key of F major at about 2′46″. Minor to Relative Major The next examples begin in a minor key and move to the relative major. Listen to each several times as you read the accompanying description. To hear the relationship between the two keys, sing the original tonic; then sing upward by three scale degrees (do-re-me or tonic-whole-half) to hear the tonic of the relative major key. If you have trouble, play the pitches on the piano or your instrument. 5.18. Chicago, “25 or 6 to 4,” from Chicago II What to listen for: • The piece begins in the key of A minor. • The song moves to the relative major key, C major, at the beginning of the chorus, at about 0′55″. • The move to C major is very brief, and the song returns to A minor at about 1′05″. The song continues to alternate between A minor (verse) and C major (chorus). 208| Informed Listening: Examples for Study 5.19. Clara Schumann, “Allegro moderato” from Piano Trio in G Minor, Op. 17 What to listen for: • The piece begins in G minor. • The relative major key, B-flat major, appears at about 3′23″. Major to Parallel Minor These examples begin in a major key and move to the parallel minor. Listen to each several times as you read the accompanying description. To hear the relationship between the major and parallel minor, first sing the tonic of the original key, and then sing the first three degrees of the major scale (do-re-mi). When the music changes to parallel minor, sing the same tonic, and then the first three degrees of the minor scale (do-re-me). If you have trouble, play the pitches on the piano or your instrument. 5.20. Franz Josef Haydn, “Allegro” (Movement III) from Cello Concerto in D Major What to listen for: • From D minor, the piece moves to the relative key of F major at 2′35″ and then returns to D minor at 3′16″. LE AL N CH ✪ GE • The piece begins in D major and moves to the parallel key of D minor at about 2′17″. Notice that the recurring major melody is now heard in minor. • The original key of D major returns at 3′34″. 5.21. The Young Rascals, “How Can I Be Sure?” from Groovin’ What to listen for: • The piece begins in D major. The tonic is played in quarter notes on the strings, but it is not established in the voice until the word constantly, on the pitches mi-re-do (F#-E-D). • When the verse begins, on the words “Whenever I . . .” the song moves to the parallel key of D minor. • The original key of D major returns at about 0′38″, on the words “How do I know?” After that, the song continues to alternate between the parallel keys of D major and D minor. Minor to Parallel Major The following three examples begin in a minor key and move to the parallel major. Listen to each several times as you read the accompanying description. To hear the relationship between the keys, first sing the tonic of the original key; then sing the first three tones of the minor scale (do-re-me). When the music changes to parallel major, sing the same tonic, and then the first three tones of the major scale (do-re-mi). If you have trouble, play the pitches on the piano or your instrument. 5.22. Wolfgang Amadeus Mozart, “Menuetto” from Symphony No. 40 in G Minor, K. 550 What to listen for: • The piece begins in the key of G minor and moves to the parallel key of G major at about 1′45″. Informed Listening: Examples for Study |209 • The middle section stays in the key of G major for the most part, but it contains a few brief visits to the key of D major (about 2′03″ and 2′25″). • The original key of G minor returns suddenly at 3′32″. 5.23. The Beatles, “While My Guitar Gently Weeps,” from The Beatles (“The White Album”) What to listen for: • The piece begins in A minor, and the tonic is prominently repeated throughout the introduction. • At the beginning of the verse, the voice repeats the scale degrees do-re-me. • The song moves to the parallel major key, A major, during the bridge, beginning at about 0′51″. • The original key of A minor returns at 1′24″. LE AL N CH GE ✪ • The bridge, in A major, occurs again at 2′31″, after which the original key returns at 3′04″. • Listen to the bass line at the beginning of the song, and sing it as the recording plays. Then compare it with the opening bass line of “25 or 6 to 4,” above. How are they similar? INFORMED LISTENING: EXAMPLES WITH QUESTIONS Distinguishing Major and Minor Listen to each example and decide whether it is in a major or minor key. Circle the correct answer from the choices in brackets. If you have trouble with these examples, sing the scale segments do-re-mi (do–whole step–whole step) and do-re-me (do–whole step–half step) as you listen. Decide which segment fits better with the music. 210| 5.24. Michael Jackson, “Billie Jean” [major / minor] 5.25. Wild Asparagus, “Lafferty’s” [major / minor] 5.26. Mark O’Connor, “Cat in the Bag” [major / minor] 5.27. Rodgers and Hammerstein, “My Favorite Things” [major / minor] 5.28. Booker T. and the MG’s, “One Who Really Loves You” [major / minor] 5.29. Handel, “Hallelujah,” from Messiah [major / minor] 5.30. BeauSoleil, “Zarico Boogie” [major / minor] 5.31. Larry Unger and Ginny Snowe, “Gaye’s Steps” [major / minor] 5.32. Billy Joel, “Don’t Ask Me Why” [major / minor] Informed Listening: Examples with Questions 5.33. The Police, “Driven to Tears” [major / minor] 5.34. Mozart, “Eine Kleine Nachtmusik” [major / minor] 5.35. Cafe Accordion, “MaNouche” [major / minor] 5.36. Gabriel Fauré, “Berceuse,” from Dolly Suite [major / minor] 5.37. Hall and Oates, “You Make My Dreams” [major / minor] Major Moving to Minor All of the next examples start in a major key and move to a minor key at some point. Listen to each several times and decide whether the piece goes to the relative minor or the parallel minor. Circle the correct answer from the choices given in brackets; then write the name of the correct key in the blank. If you have trouble, sing the original tonic, and then sing the tonic after the change to minor. If the two tonics are the same, the keys are parallel. If the minor tonic is below the major tonic, the keys are relative. If you continue to have trouble, use the piano to help you find the pitches. 5.38. The Beatles, “We Can Work It Out,” from Past Masters, Vol. 2. The change from major to minor happens at the bridge, at about 0′35″. The song returns to the original key at about 1′03″. This song moves from major to [relative / parallel] minor. It begins in D major and moves to the key of _____ minor. 5.39. Edvard Grieg, “Berceuse (Cradle Song),” from Lyric Pieces, Book II, Op. 38 The change from major to minor happens at about 0′51″. The music stays in the new key very briefly, for about ten seconds, before moving to another key. The original key returns at about 1′46″. This piece moves from major to [relative / parallel] minor. It begins in G major and moves to the key of _____ minor. 5.40. Frederic Chopin, Prelude in D-flat Major (“Raindrop”), Op. 24, No. 15 Note: this prelude is nicknamed “Raindrop” because of a repeating pitch that is present throughout almost the entire work. As you listen to find the tonic of the first section, keep in mind that this repeated pitch is sol, not do. Listen instead to the melody and bass to help you find the tonic. If you still have trouble, play the tonic, D-flat, at the piano. The piece moves from major to minor at about 1′31″, and it stays in the new minor key for about forty seconds before moving to another key. The original major key returns at about 4′25″. This piece moves from major to [relative / parallel] minor. It begins in D-flat major and moves to the key of _____ minor. 5.41. Scott Joplin, “Scott Joplin’s New Rag” The piece moves from major to minor at about 0′44″, and returns to the original major key at about 1′22″. This piece moves from major to [relative / parallel] minor. It begins in C major and moves to the key of _____ minor. Informed Listening: Examples with Questions |211 5.42. Franz Josef Haydn, “Minuet” (Movement III) from Piano Sonata in G, Hob. XVI: 11 This piece moves between major and minor several times; the first move to minor happens at about 0′43″. The pieces moves from major to [relative / parallel] minor. It begins in G major and moves to the key of _____ minor. Minor Moving to Major All of the examples in this section begin in a minor key and at some point move to a major key. Listen several times to each example and decide whether the piece goes to the relative major or the parallel major. Circle the correct answer from the choices given in brackets, and then write the name of the correct key in the blank. Remember to sing the tonics of the two keys to help you find their relationship. If you continue to have trouble, use the piano to help you find the pitches. 5.43. Claude-Michel Schönberg/Herbert Kretzmer, “At the End of the Day,” from Les Misérables After an introduction that goes through several keys, the minor-key section begins at about 0′35″ when the singers enter. The piece moves to major at about 1′12″, and it returns to the original key at about 1′31″. This piece moves from minor to [relative / parallel] major. It begins in F minor and moves to _____ major. 5.44. The Red Hot Chili Peppers, “The Adventures of Rain Dance Maggie,” from I’m with You The song begins in a minor key and moves to major during the chorus, at about 1′05″. After that, each verse is in minor and each chorus is in major. This song moves from minor to [relative / parallel] major. It begins in E minor and moves to _____ major. 5.45. Johannes Brahms, Hungarian Dance No. 5 in G Minor Recommended recording: Best of Naxos 7, Budapest Symphony Orchestra The piece moves to major at about 1′02″, returning to the original key at about 1′37″. This piece moves from minor to [relative / parallel] major. It begins in G minor and moves to _____ major. 5.46. The Ventures, “Walk Don’t Run,” from The Very Best of the Ventures This piece moves between major and minor several times; the first move to major happens at about 0′17″. The piece moves from minor to [relative / parallel] major. It begins in A minor and moves to _____ major. DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 5.47. Memorize Singing Exercises 5.7 through 5.11, and sing them where appropriate. 212| Drills to Go 5.48. Starting on a note in the middle of your voice range, sing the natural minor scale in solfège, up and down, changing direction at any time you choose. Start on do, ascend for a few scale tones, then descend for a few, then ascend again, etc. Your improvisation might look something like this: œ œ œ œ œ œ œ œ G U PH I PH U PH I œ œ œ œ œ œ V OH V I PH œ œ œ œ œ œ œ U G WH G U G WH OH HWF 5.49. As you listen to music throughout your day, hum or sing the pitch that you think is the tonic. Then decide whether the piece is in a major or minor key. To help you do this, sing the scale segments do-re-mi (do–whole step–whole step) and do-re-me (do–whole step–half step) as you listen. Decide which segment fits better with the music. CLASSROOM ACTIVITIES Exercises 5.50 and 5.51 are performed using the natural minor scale and may be done at three levels: Beginner: use only the notes d r me f s Intermediate: use only the notes |te d r m f s le Advanced: use the notes |te d r me f s le te d |r 5.50. Point and sing. a. Choose a level (above), and write the syllables on the board in a vertical line from lowest to highest. b. Designate a class leader, who establishes a tonic and then dictates a series of syllables by pointing to them on the board. The class responds by singing the correct pitch for each syllable. c. If the class sings an incorrect pitch (or multiple answers are given), the leader will return to do and then “walk” the class up the scale stepwise to that scale tone. d. Change leaders periodically. 5.51. Call and response/pitch improvisation. a. Choose a level (above), and write two sets of syllables on the board, one on the left side and one on the right. b. Choose two leaders. Leader 1 (on the left) dictates five notes to the class, beginning on do and ending on any note except do. c. Leader 2 (on the right) responds by dictating five more notes, starting on Leader 1’s last note, and ending on do. d. Change leaders periodically. Leader 1: _do_ _?_ Leader 2: _?_ x = Any note except do. _?_ _x_ _x_ _?_ _?_ _?_ _do_ Same note Classroom Activities |213 5.52. Variation. Repeat Exercises 5.50 and 5.51, but this time reorder the pitches so that do is in the middle (see Exercise 5.11, Inside-out scales): | f-|s-|le-|te-do-re-me-f-s-le 5.53. Guided rhythm improvisation. 1. Choose a meter (three-eight or three-two) and write the rhythm patterns from Exercise 5.1 on the board. 2. Set your metronome at a slow tempo to establish a pulse. Choose any pitch, and lead the class in singing the rhythms in order. Use a neutral syllable such as “nah” or “tah.” 3. Repeat step (2), but this time randomize the order of your choices. Start with any rhythm, and as the class reaches the landing measure point to the next rhythm you want them to sing. (Be sure to give them enough time to anticipate where they’re going.) 4. If there are incorrect responses, repeat that pattern until the entire class sings it correctly, and then move on. 5. Change leaders about every sixty seconds. 5.54. Clave scales. Repeat the “Clave scales” activity introduced in the previous chapter (Exercise 4.36), but this time use minor key signatures and natural minor scales instead of major. WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 5 online drills and quizzes at www.oup.com/us/root. 5.55. For each question, draw the clef and key signature indicated; then name the major and minor keys represented by that key signature. 214| Written Exercises 5.56. For each question, write the name of parallel (P) and relative (R) minor keys in the blanks as indicated. (Write the relative minor below, and the parallel minor to the left.) The first question has been completed for you. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Written Exercises |215 5.57. For each question, write the name of the parallel (P) and relative (R) major keys in the blanks as indicated. (Write the relative major above, and the parallel major to the right.) For some questions, you will need to answer with enharmonic keys. The first question has been completed for you. 216| 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Written Exercises LE AL N ✪ GE you will have a network of all major and minor keys that you may use for reference. CH 5.58. Fill in each chart with the parallel and relative keys as indicated. When you are finished, 1. 2. Written Exercises |217 3. 5.59. Spell each of these natural minor scales by writing letter names in the blanks above the scale degrees. Use uppercase letters. For sharps and flats, draw the correct symbol after the letter name. Question 1 has been completed for you. 1. B minor: B C# D E F# G A B∫ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ re me fa sol le te do 2. D# minor _____ 3. A minor 4. C minor 5. G# minor _____ 6. E∫ minor 7. C# minor _____ do 8. A# minor _____ do 218| Written Exercises 9. F minor 10. B∫ minor 11. D minor 12. F# minor 13. E minor 14. G minor 15. A∫ minor _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do _____ _____ _____ _____ _____ _____ _____ _____ do re me fa sol le te do 5.60. For each question, draw a dot on the correct piano keys to build the requested natural minor scale. Be sure to start your scale low enough that you don’t run out of keys. Check your work by playing the scale on an actual keyboard. Question 1 has been completed for you. 1. E minor 2. B minor 3. G minor 4. C-sharp minor 5. B-flat minor 6. A-flat minor Written Exercises |219 7. F-sharp minor 8. D minor 9. F minor 10. E-flat minor 5.61. For each question, write the natural minor scale that begins on the given tonic. Do not use a key signature, but apply the sharps or flats directly to each note where necessary. The first question has been completed for you. 220| Written Exercises 5.62. For each question, write the minor scale indicated by the given key signature. Use any octave that is convenient. (Avoid ledger lines.) CH ✪ completed for you. Major scale that is relative to G minor: B∫ C D E∫ F G A B∫ Natural minor scale that is relative to G-flat major: ___ ___ ___ ___ ___ ___ ___ ___ Major scale that is parallel to F-sharp minor: ___ ___ ___ ___ ___ ___ ___ ___ Natural minor scale that is parallel to C-sharp major: ___ ___ ___ ___ ___ ___ ___ ___ Major scale that is relative to B-flat minor: ___ ___ ___ ___ ___ ___ ___ ___ Natural minor scale that is relative to A-flat major: ___ ___ ___ ___ ___ ___ ___ ___ Major scale that is parallel to B minor: ___ ___ ___ ___ ___ ___ ___ ___ Natural minor scale that is parallel to D major: ___ ___ ___ ___ ___ ___ ___ ___ Major scale that is relative to D minor: ___ ___ ___ ___ ___ ___ ___ ___ Written Exercises GE 5.63. For each question, spell the requested scale in letter names. The first question has been LE AL N |221 5.64. A well-known song is written below in rhythm and solfège only. For each question, rewrite the song using the instructions given. Play your work at the piano and name the title of the song, if you know it. 1. Rewrite the example in this clef and key. (Identify the key.) 2. Rewrite the example in this clef and key. (Identify the key.) 222| Written Exercises 3. Rewrite the example in treble clef, B-flat minor. (Write the key signature at the beginning of each line of music.) 4. Rewrite the example in bass clef, E minor. (Write the key signature at the beginning of each line of music.) 5.65. Complete each measure by writing only one rhythmic value. If the measure is already complete, write the word “COMPLETE” under it. The first measure of each example has been completed for you. 1. Written Exercises |223 2. 3. 4. 5.66. For each song: 1. Label each note with the correct solfège syllables. 2. Rewrite the song in the meter(s) indicated. Remember that you will either double or halve each note value, depending on the new meter. Do not change the number of durations in each measure. 1. “America” 224| Written Exercises Written Exercises |225 2. “Joy to the World” 3. “Wayfaring Stranger” 226| Written Exercises COMPOSITION 5.67. Choose any song in a major key from Chapters 1 through 4. a. Rewrite the song in the parallel minor key by changing its key signature. b. Rewrite the song in the relative minor key by maintaining the original key signature and changing the tonic. c. Lead the class in singing the original version and one of the minor versions in solfège. As you sing, remember that mi is lowered to me, la is lowered to le, and ti is lowered to te. Suggested Songs: “Old McDonald” (Chapter 1) “Hyfrydol” (Chapter 1) “Bonner” (Chapter 1) “Amazing Grace” (Chapter 2) “When the Saints Go Marching In” (Chapter 2) “Jingle Bells” (Chapter 2) “Auld Lang Syne” (Chapter 2) “Annie Laurie” (Chapter 2) “Blue Bells of Scotland” (Chapter 3) “Hava Nashira” (Chapter 3) “The British Grenadiers” (Chapter 3) “Loch Lomond” (Chapter 3) “Oh Susannah” (Chapter 3) “Deck the Halls” (Chapter 3) “St. Columba” (Chapter 4) Composition |227 5.68. Choose any minor-key song from this chapter or the next one. a. Rewrite the song in the parallel major key, by changing the key signature. b. Rewrite the song in the relative major key, by keeping the key signature and changing the tonic. c. Lead the class in singing the original version and one of the major versions in solfège. Suggested Songs “Wayfaring Stranger” (Chapter 5) “Hatikvah” (Chapter 5) “Hey Ho, Nobody Home” (Chapter 5) “Greensleeves” (Chapter 6) “When Johnny Comes Marching Home” (Chapter 6) 5.69. For each example, write the requested minor scale on the staff, ascending and descending. Compose your own rhythm for each scale using these guidelines: a. Apply sharps or flats directly to the appropriate notes; do not use key signatures. b. Use each note of the scale only once in each direction; do not repeat any notes in succession. The last note of each exercise is given. c. Fill the empty measures of the given meter using any of the patterns found in Exercise 5.1. Substitute notes for rests wherever you wish. d. Avoid using ties. e. Lead the class in performing your compositions. & 22 6DPSOH)PLQRU w 2 bœ bœ œ bœ bœ Œ œ œ bœ œ. bœ bœ & 2 œœ J J J œ 3RVVLEOHDQVZHU j bœ œ bœ bœ œ Œ bœ bœ œ bœ 2 & 2 œ. œ bœ J J bœ œ 3RVVLEOHDQVZHU 228| Composition w w 3 &8 (IODWPLQRU 4 &8 %PLQRU & 32 *VKDUSPLQRU ? 42 'VKDUSPLQRU ? 28 &PLQRU ? 22 Chapter Goals Revisited $PLQRU bœ. Ç #w. #w w œ w Be sure that you have achieved all Chapter 5 Goals before proceeding to Chapter 6. • Sing natural minor scales with solfège and letter names. (pages 189–191, 198, 203–205) • Play natural minor scales at the keyboard. (pages 198, 203–205) • Write natural minor scales with or without key signatures, in treble clef, bass clef, and letter names. (pages 181–189) • Name the major and minor keys represented by any key signature. (pages 184, 188, 198) • Recognize, by sound, whether a piece of music is in a major or minor key. (page 206) • Understand the connection between relative keys, and recognize it in music you hear. (pages 181–185, 208–209) • Understand the connection between parallel keys, and recognize it in music you hear. (pages 185–187, 209–210) • For any major key, name the relative minor and parallel minor. (pages 197–198) • For any minor key, name the relative major and parallel major. (pages 197–198) • In a given key, map letter names to each solfège syllable or scale degree number. (pages 189–191) • Sing and hear intervals above and below do in the natural minor scale. (pages 205–206) • Perform basic rhythms in eight-based and two-based simple meters. (pages 191–195, 199–202) • Properly notate basic rhythms in eight-based and two-based simple meters. (page196) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. Composition |229 CHAPTER 6 RHYTHM: INTRODUCTION TO COMPOUND METER/ PITCH: MINOR KEYS 2 Chapter Goals After you finish this chapter, you should be able to do the following, quickly and accurately: • Understand the difference between simple and compound meters. • Perform, recognize, and notate basic rhythms in six-eight, nine-eight, and twelveeight meter. • Distinguish between simple and compound meters in music you hear. • Sing harmonic and melodic minor scales with solfège and letter names for all keys. • Play harmonic and melodic minor scales for all keys at the piano. • Write harmonic and melodic minor scales for all keys in treble clef, bass clef, and letter names. • Distinguish major, natural minor, harmonic minor, and melodic minor scales by sound. • Sing and resolve tendency tones in the minor scale. • Hear and identify tendency tones with their resolution tones in the minor scale. COMPOUND METER So far, you have learned about simple meters, where each beat divides into two equal parts. In a compound meter, each beat divides into three equal parts. EBSIT E W Figure 6.1. Pulse division in simple and compound meter. 42 œœ œ œœ œ 6LPSOHPHWHU 3XOVH 3XOVH'LYLVLRQ 68 œœ . œ œ œœ . œ œ &RPSRXQGPHWHU In compound meter the pulse is always represented by a dotted note, because three equal durations add up to a dotted duration: 230| This chapter will introduce the compound meters six-eight, nine-eight, and twelve-eight. In all of them, the bottom number (8) represents the beat division. Because three eighth notes occupy every beat, the pulse is represented by a dotted quarter note. In some modern music, compound meter is notated as a numeral over a dotted note, in order to more clearly communicate the pulse value. Although this notation is not widespread, it might be helpful to think of compound meter in this way. Meter Type Time Signature Pulse/Pulse Division Think of It This Way Compound duple Compound triple Compound quadruple Every measure of six-eight meter contains two dotted-quarter-note beats, and each beat divides into three eighth notes. Six-eight is a compound duple meter: • Duple because there are two beats per measure • Compound because each beat divides into three equal parts EBSIT E W Figure 6.2. Six-eight meter. In nine-eight meter, every measure contains three dotted-quarter-note beats, and each beat divides into three eighth notes. Nine-eight is a compound triple meter: • Triple because there are three beats per measure • Compound because each beat divides into three equal parts Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 EBSIT E W Figure 6.3. Nine-eight meter. |231 In twelve-eight meter, every measure contains four dotted-quarter-note beats, and each beat divides into three eighth notes. Twelve-eight is a compound quadruple meter: • Quadruple because there are four beats per measure • Compound because each beat divides into three equal parts EBSIT E W Figure 6.4. Twelve-eight meter. Compound Meter vs. Triplets The three-part beat in compound meter is very similar to a triplet in simple meter. Both figures divide the beat into three equal parts. The difference is that a triplet in simple meter is an exception to the usual division of the beat into two parts. In compound meter, a three-part beat is the rule, while two- and four-part divisions are exceptional.1 As an example, suppose you are writing a piece in quadruple meter. Most of the time, you divide the beat into two or four parts (using eighth and sixteenth notes, respectively), and only occasionally use a triplet. You would likely use four-four meter for your composition. If, on the other hand, your quadruple-meter piece uses mostly three-part divisions of the beat, then you should use twelve-eight meter. EBSIT E W Figure 6.5. Four-four vs. twelve-eight. 1 These exceptions are called duplets and quadruplets; they are discussed briefly in Chapter 9. 232| Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 Counting Compound Meter Using numbers to count every beat division in compound meter can be very awkward, especially in nine-eight and twelve-eight, where the unwieldy “seven” and “eleven” are involved. Instead, assign numbers only to the dotted-quarter-note pulses: count two beats in six-eight, three beats in nine-eight, and four beats in twelve-eight. When counting subdivisions, you may wish to use the same syllables that you use to count triplets in simple meter. a. 2 8 œ œ la œ lee œ TWO œ la œ lee œ THREE œ la œ lee œ FOUR œ la lee 2 8 œ œ ta œ ta œ TWO œ ta œ ta œ THREE œ ta œ ta œ FOUR œ ta œ ta 2 8 œ œ œ œ œ œ œ œ œ a œ FOUR œ and œ 2 8 œ œ 2 œ 3 œ TWO œ 2 œ 3 œ THREE œ 2 œ 3 œ FOUR œ 2 œ 2 8 œ œ œ œ œ œ œ œ œ œ œ œ ONE b. ONE c. ONE and a TWO and a THREE and (Do not confuse with the figure rdg in simple meter.) d. ONE e. TA ka da TA ka da TA ka da TA ka œ a 3 da Of the methods shown above, (e) probably works best for fast music, while (d) is the most advantageous for counting subdivisions: 12 8 œ œœœœœ œ œœœœœ 21( 7:2 HWF Count using the system recommended by your teacher; if you are studying on your own, use the one that works best for you. Ultimately, you will benefit most by simply memorizing the typical rhythmic patterns found in compound meter. (These are listed in Exercise 6.1, below.) Learn each pattern by sound so that you can perform it on sight, instantly, and without the need to stop and count it out every time. Learning rhythms this way is similar to what happens when you first learn to read words. For example, the first time you saw the word cat, you probably put it together by sounding out the letters c-a-t. But now you Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 |233 no longer need to recreate that process: once you comprehend the word as a single unit, you instantly understand its sound and meaning every time you see it. Three-four vs. Six-eight Meter It is possible to write a measure of six eighth notes in both six-eight and three-four time, but there is a crucial difference between these two meters. To better understand the distinction, consider this group of six eighth notes: • In three-four meter (simple triple), the eighth notes are grouped in pairs. The result is three sets of two eighth notes each, or three quarter-note beats. • In six-eight meter (compound duple), the eighth notes are packaged in groups of three. The result is two sets of three eighth notes each, or two dotted-quarter note beats. Perform each example in Figure 6.6, singing the melody and clapping or finger-counting the pulse. Use the counts shown, and be sure to emphasize the accented notes. Notice that the rhythm itself doesn’t change, but there is a strong difference in “feel” created by the different pulses. Notice also that the beaming reflects the groupings for each meter. EBSIT 234| E W Figure 6.6. Three-four vs. six-eight. Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 Songs in Compound Meter Divide the class in half and perform the songs in this section. Use a metronome to set the tempo indicated for the dotted quarter note. • Both groups: sing the song using the lyrics given. • Group 1: finger-count the dotted-quarter note beats. • Group 2: clap the eighth notes quietly, emphasizing the first of each group of three. • If you are working on your own: listen to the songs online, or record yourself clapping the pulse; then sing along with the recording. Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 EBSIT E W Figure 6.7. Trad., “When Johnny Comes Marching Home.” |235 EBSIT E W Figure 6.8. Stephen Foster, “Beautiful Dreamer.” EBSIT 236| E W Figure 6.9. Frederic Chopin, Nocturne in E-flat Major, Op. 9, No. 2. Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 EP L A Y • The most frequently used compound meters are six-eight, nine-eight, and twelve-eight. In these meters, the dotted quarter note represents the pulse. Each dotted quarter divides into three eighth notes. R • In a compound meter, the pulse unit is always a dotted note, and the pulse divides into three parts. • Six-eight is a compound duple meter. Each measure contains two dottedquarter-note beats and six eighth-note divisions. • Nine-eight is a compound triple meter. Each measure contains three dottedquarter-note beats and nine eighth-note divisions. • Twelve-eight is a compound quadruple meter. Each measure contains four dotted- quarter-note beats and twelve eighth-note divisions. THE HARMONIC AND MELODIC MINOR SCALES The Natural Minor Scale (Review) First, we will review what we learned about minor scales in the previous chapter. Relative keys share the same pitch content and the same key signature but have different tonics. To find the relative minor key from a major scale, start on the sixth degree of the major scale. The relative keys F major and D minor are shown in Figure 6.10. EBSIT E W Figure 6.10. Relative keys of F major and D minor. Parallel keys share the same tonic but have different note content and key signatures. To find the parallel minor key from a major scale, lower scale degrees 3, 6, and 7 by a half step. This effectively adds three flats to the key signature. (Remember, subtracting sharps is equivalent to adding flats.) The parallel keys F major and F minor are shown in Figure 6.11. Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 EBSIT E W Figure 6.11. Parallel keys of F major and F minor. |237 The minor scales you have learned so far are called natural (or pure) minor because they use only the notes prescribed by the key signature. There are two other forms of the minor scale commonly used in tonal music: the harmonic minor and melodic minor scales. The Harmonic Minor Scale The harmonic minor scale results when the seventh degree of the natural minor scale is raised by one chromatic half step. Recall that in a chromatic half step, both notes have the same letter name. In this case, C-natural is raised to C-sharp. Compare the two scales shown in Figure 6.12. EBSIT E W Figure 6.12. D minor scale, natural and harmonic forms. Why Does the Harmonic Minor Scale Exist? Return to Figure 6.11 and compare the parallel scales of F major and F natural minor. Because the natural minor scale contains a whole step between scale degrees 7 and 1, it lacks the half-step tendency created by the leading tone (E natural) present in the F major scale. In the harmonic minor scale, the leading tone is borrowed from the parallel major scale in order to achieve the ti-do resolution normally found in major keys. As tonal music evolved through the centuries, composers traditionally added the leading tone to minor- 238| Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 key pieces to strengthen the resolution to the tonic. Consider this famous example from J. S. Bach’s Toccata and Fugue in D Minor: EBSIT E W Figure 6.13. J. S. Bach, Toccata and Fugue in D Minor, BWV 565, m. 1 (two versions). As you listen to the example, notice the strong pull from C-sharp to D. If Bach had left the Cs natural, the resolution would sound much less satisfying. Compare the actual version (a) to the fictional natural minor version (b) and decide which you prefer. Sing “When Johnny Comes Marching Home” (Fig. 6.7, above), and then repeat the song with this alternate ending: EBSIT E W Figure 6.14. In the second version, the penultimate pitch is changed from E-flat to E natural. The result is a half step between ti and do (E and F), creating a stronger resolution into the last note. The E natural comes from the harmonic minor scale. “Johnny” is a typical folk song that has been passed down through generations by repeated singing and hearing rather than by written notation. For this reason, both versions (the one with te and the one with ti) have survived. Sing both endings again, and decide which one you prefer. Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 |239 Summary of Harmonic Minor Scales Harmonic minor scales for all keys are shown below. As you study the scales, keep in mind: 1. The raised seventh scale degree always appears as an accidental; it is never added to the key signature. 2. The raised seventh scale degree may appear as a natural, a sharp, or a double sharp. In order to notate the leading tone correctly, it is important to keep the key signature in mind. 240| Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 The Melodic Minor Scale Go to the piano and play a B harmonic minor scale, as illustrated in the example below. Remember that the harmonic minor scale exists in order to create a strong half-step tendency between scale degrees 7 and 1. But raising the seventh degree (in this case, A to A-sharp) creates a gap of one and a half steps between the notes G and A-sharp. Play only the upper four notes of the scale, in order. You will hear the gap very plainly, and it might sound awkward to you because it creates a disjunct melodic line. The solution to this problem is the melodic minor scale. The melodic minor scale keeps the raised seventh degree found in harmonic minor, but it also raises the sixth degree of the scale. In other words, the melodic minor scale borrows la and ti from the parallel major. Typically, the raised degrees are used only when the melodic line of a piece ascends to the tonic (sol-la-ti-do), so practically speaking the melodic minor scale exists only in ascending form. When it descends, the melodic minor scale is identical to natural minor. Figure 6.15 contains all three forms of the minor scale. Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 EBSIT E W Figure 6.15. |241 E W EBSIT Figure 6.16 contains an excerpt from a chorale by J. S. Bach. Here, the ascending and descending forms of the melodic minor scale are used in close proximity in an actual piece of music. The descending form (do-te-le-sol) is used in the bass voice of measures 1–2. The ascending form (sol-la-ti-do) is used in the alto part of measure 2. Figure 6.16. J. S. Bach, Chorale No. 16, “Es woll’ uns Gott genadig sein.” Summary of Melodic Minor Scales Ascending melodic minor scales for all keys are shown below. As you study the scales, keep in mind: 1. The raised sixth and seventh degrees (la and ti) always appear as accidentals; they are never added to the key signature. 2. The raised degrees may appear as naturals, sharps, double sharps, or a combination of these. (See, for example, D minor and G-sharp minor.) In order to notate the pitches correctly, you must know the key signature. 242| Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 |243 Scale Degree Names in Minor The formal names used for the scale degrees in major (tonic, supertonic, etc.) also apply to the minor scale, but scale degree 7 is called the leading tone only if it is raised, as in harmonic and melodic minor. The seventh degree of the natural minor scale is called the subtonic, in order to call attention to the fact that it does not resolve to the tonic by a half step (and therefore does not “lead.”) The raised sixth degree (used in melodic minor) does not take a special name; it is simply called the “raised submediant.” Minor Scales in Music You will encounter a lot of music that does not strictly adhere to one form of the minor scale. Generally, composers do not sit down to write and decide, for example, “Today I am going to compose a piece in harmonic minor.” You should of course memorize all three forms of each minor scale. But once you have done that, and you begin to study actual music, it is more helpful to think of a single minor scale with variable sixth and seventh degrees. The folk song “Greensleeves” draws on all three forms of the minor scale: • Measures 1–4 use a combination of natural and harmonic minor: o Le appears in measure 1 and ti in measures 3–4. Notice that the two pitches are not used in succession, so that the gap between them is avoided. EBSIT E W o Te-do (natural minor) appears in measure 2. • Measure 7 uses la and ti from the melodic minor scale in order to create: o A half-step resolution between scale degrees 7 to 1. o A smooth melody between scale degrees 6 and 7. The same figure occurs in measures 15–16. Figure 6.17. Trad., “Greensleeves” (mm. 1–8). 244| Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 Like “When Johnny Comes Marching Home,” “Greensleeves” is a traditional folk song that has been passed down in many versions for generations. You may have heard other versions of the song that use different inflections of scale degrees 6 and 7. Find several different recordings of the song, and see if you can detect variations in the melody. • The natural minor scale uses only the notes included in the key signature. EP L A Y • The melodic minor scale raises 6̂ and 7̂ by a half step, changing le to la, and te to ti as the scale ascends. The descending form is identical to the natural minor scale. R • The harmonic minor scale raises 7̂ by a half step, changing te to ti. • Most music in minor keys uses a combination of the three scale forms. Composers draw on the different inflections of 6̂ and 7̂ as needed. THE TONIC TRIAD AND TENDENCY TONES IN MINOR KEYS Recall that in major keys do mi, and sol are members of the tonic triad, while re, fa, la, and ti are tendency tones. Each tendency tone resolves to a member of the tonic triad. Recall that in minor keys, scale degree 3 is called me, so the minor tonic triad is made up of do, me, and sol. The tendency tones are derived from the harmonic minor scale, so the resolutions from le to sol and ti to do are both half steps (Fig. 6.18a). In the advanced tendency row (Fig. 6.18b), the first note of each segment is replaced by a rest, so you must leap directly to the tendency tone and then resolve it. See Exercise 6.9 for some practice tips to help you become proficient in singing both versions of the row. EBSIT E W Figure 6.18. The tendency row in minor keys. • In minor keys, the tonic triad is made up of the degrees do, me, and sol. • Tendency tones and their resolutions in the minor scale are: R EP L A Y o re to do (whole step) o fa to me (whole step) o le to sol (half step) o ti to do (half step) NOTATION When writing music in six-eight, nine-eight, and twelve-eight, beam each dotted-quarternote beat together, and do not beam between the beats. You might find it helpful to think of each dotted quarter as a separate “house” occupied by a “family” of smaller notes, such as eighths, dotted eighths, and sixteenths. Rests occurring in the middle of the beat are Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 |245 normally included in the beam groups. The quarter note, of course, cannot be beamed to any duration. Use a dotted quarter rest to represent one beat of silence, and a dotted half rest to represent two beats of silence. Remember that twelve-eight is a quadruple meter, where beats 1 and 3 are emphasized. Just as in four-four, do not “straddle” beats 2 and 3 with a rest. A dotted whole note is used to fill one measure of twelve-eight. In nine-eight, use a dotted half note tied to a dotted quarter, since there is no single duration that represents nine eighth notes. Remember that a whole rest represents one full measure of silence in any meter. 246| Rhythm: Introduction to Compound Meter/Pitch: Minor Keys 2 MEMORIZATION STRATEGIES Review the minor key signature flashcards that you created in the previous chapter. More than ever, it is important to be fluent in minor key signatures. When you raise a scale degree, you must use the appropriate accidental, which means that you need to know whether the affected scale tone starts as a flat, natural, or sharp. If you tend to confuse melodic and harmonic minor, try these memory aids: 1. Remember that the melodic minor scale raises 6 and 7 in order to create a smoother melody. 2. Both harmonic and melodic minor scales contain the raised seventh degree, ti. The melodic minor also has a raised sixth, la. The word “melodic” contains the sound “la” in the middle. KEYBOARD AND SINGING EXERCISES 6.1. Rhythmic patterns. Tempo goal: 𝅘𝅥 = 52 bpm. When you practice these patterns, begin by setting your metronome to the eighth-note pulse division. As you increase your speed, use your metronome to set the dotted-quarter-note pulse. Compose your own rhythms by substituting a pair of sixteenth notes for any eighth note in the patterns below. Add these new patterns to your practice sessions. Compound Meter Patterns Keyboard and Singing Exercises |247 Compound Meter Patterns with Leading Rests 6.2. Rhythm exercises. a. Each of these exercises is in two parts, where Part 1 is a basic rhythm and Part 2 is the same rhythm with rests and/or ties added. b. Set your metronome to a slow-to-medium tempo, and perform Part 1 several times while finger-counting. c. Divide the class, so that one half performs Part 1 and the other performs Part 2 simultaneously. Those singing Part 2 should listen carefully to Part 1 in order to help accurately place the rests and ties. d. If you are working on your own, find a friend to help you do the exercises, or record yourself singing Part 1; then play back Part 1 as you sing Part 2 over it. e. When singing the two parts together, choose any two pitches, and sing on a neutral syllable. f. Once you are ready, gradually increase the tempo. Remember that accuracy is more important than speed. 1. 248| Keyboard and Singing Exercises 2. 3. 4. Keyboard and Singing Exercises |249 5. 6. 7. 250| Keyboard and Singing Exercises 6.3. Playing minor scales. Tempo goal: 72 bpm, one note per beat. Practice these minor scales, in ascending circle-of-fifths order, at the keyboard. (Your hands will move up the keyboard by tetrachords.) For each scale, play the natural, harmonic, and melodic forms, ascending and descending. Practice each one until it is memorized. 1. A minor (natural, harmonic, and melodic) 2. E minor (natural, harmonic, and melodic) 3. B minor (etc.) 4. F# minor 5. C# minor 6. G# minor (enharmonic to A∫ minor) 7. D# minor (enharmonic to E∫ minor) 8. A# minor (enharmonic to B∫ minor) 9. F minor 10. C minor 11. G minor 12. D minor Go back to the beginning and repeat the circle: 1. A minor (etc.) 6.4. Variation. Practice the scales in Exercise 6.3 in reverse order, moving counterclockwise around the circle of fifths. (Your hands will move down the keyboard by tetrachords.) 6.5. Playing and singing harmonic and melodic minor scales. As you play the scales in Exercise 6.3, sing each in solfège, and then letter names. Observe the notated rhythms, and use each rest to anticipate the next note in your mind and in your fingers. Some of the scales might not fall comfortably in your voice range. For those scales it is OK to speak the names rather than sing them. Keyboard and Singing Exercises |251 6.6. Singing scales without the piano. Sing both parts of Exercise 6.5 without using the keyboard. Start on any pitch that is low and comfortable in your voice. It is important that you sing confidently, comfortably, and with accurate pitches. Remember, it is OK to check your pitch at the keyboard, as long as you play the note after you attempt to sing it. 6.7. Intervals. Tempo goal: 𝅘𝅥 = 90 bpm. Using the examples below, sing from do up to each tone in the harmonic and melodic minor scales. Then, sing from the high do down to each scale tone. Keep a steady pulse throughout, and use each quarter rest to anticipate the next interval in your mind. Perform the exercise using solfège, and then letter names for each minor key. (The key of D minor is given as an example.) 252| Keyboard and Singing Exercises 6.8. Minor tendency row with solfège and note names. Tempo goal: 𝅘𝅥 = 72 bpm. Using the previous example, practice the following exercise several times in every minor key. If you are using tetrachord position, play measures 1–2 of the row with your left hand, and measures 3–4 with your right hand. Some pitches in some keys may be out of your singing range. In those cases, it is OK to speak the pitch names rather than sing them. a. Choose a minor key. b. Play the harmonic minor scale, up and down, while singing solfège. c. Play the harmonic minor scale, up and down, while singing letter names. d. Play the basic tendency row while singing solfège. e. Play the basic tendency row while singing letter names. f. Play the advanced tendency row while singing solfège. g. Play the advanced tendency row while singing letter names. h. Repeat the exercise in every minor key. Keyboard and Singing Exercises |253 6.9. Singing the tendency row without the piano. Tempo goal: 72 bpm. Repeat Exercise 6.8 without using the keyboard. Start on any pitch that is low and comfortable in your voice. It is important that you sing confidently, comfortably, and with accurate pitches. When you sing the advanced row, think the basic row. In other words, on beat 1 of every measure, imagine the note that is present in the basic row (do me, or sol), and then sing the tendency tone and resolve it. If you need to refer to the piano, do not play the tendency tone. Instead, play the resolution tone, sing the tendency tone, and resolve it. HEARING EXERCISES Goal for Exercises 6.10–6.13: ten consecutive correct answers. 6.10. Hearing scales. Your instructor or study partner will play one of these scales, ascending only. Identify the scale type, and sing it back using solfège. • Major • Natural minor • Harmonic minor • Melodic minor 6.11. Hearing tendency tones in minor. Your instructor or study partner will play a harmonic minor scale up and down, and then the low do followed by one segment of the basic tendency row. Sing back the pitches on a neutral syllable, and then with solfège. 254| Hearing Exercises 6.12. Variations: a. In the beginning, the instructor will keep all questions in the same key, and play the harmonic minor scale only once, at the beginning of the study session. b. For a challenge, the instructor will switch keys for each question, and play a new harmonic minor scale before each question to establish the key. c. For an extra challenge, after you have sung back the segment with correct solfège, the instructor will say the name of a key. Sing the segment with correct note names for that key. 6.13. Hearing the advanced tendency row. Repeat Exercises 6.11 and 6.12 using the advanced tendency row. 6.14. Rhythm transcription. Sing “Silent Night” using the solfège or lyrics given below. Write the correct rhythm of the song, including bar lines, in the space above the solfège. Choose your rhythmic figures from those given; each is equal to one dotted quarter note, so you will need to use two rhythms per measure of six-eight. The last measure, a dotted half note on the word peace, is given. Choose from these rhythms. (Not all of the given rhythms are used in the song.) a. Write the rhythm of the melody: Hearing Exercises |255 b. Write the song on the staff below, in a clef and key chosen by your instructor. c. As a class, perform the song with solfège. 6.15. Rhythm and solfège transcription. The lyrics to the song “Row, Row, Row Your Boat” are given below. a. Write the rhythm of the song above the lyrics. It contains only these durations, and no rests nor ties (the song uses all of the durations listed): • Eighth notes • Quarter notes • Dotted quarter notes • Dotted half notes b. Write the correct solfège under the lyrics. The song: • Is in a major key • Begins and ends on do • Uses only stepwise motion plus leaps between tonic triad members (do, mi, and sol) c. Write the song on the staff below, in a clef and key chosen by your instructor. d. As a class, perform the song with solfège, first together and then as a round. 256| Hearing Exercises INFORMED LISTENING: EXAMPLES FOR STUDY 6.16. Georges Bizet, “Carillon” (Movement IV) from L’Arlésienne Suite No. 1, Op. 23 Like many of the listening examples in this book, “Carillon” is in ABA or ternary form, meaning there is an opening section (A), a contrasting middle section (B), and a return of the (A) section. The (A) section is in three-four, highlighted by a repeating quarter-note figure (mi-do-re) in the horn. As you listen to it, focus on the meter by counting aloud, alternating measures of quarter notes and eighth notes. The (B) section, beginning at 1′25″, is in six-eight meter. As you listen to it, count dotted quarter notes, and then divide to eighth notes. Alternate measures, counting in this way: The (A) section returns at 3′21″. 6.17. J. S. Bach, Chorale: “Jesus bleibet meine Freude” (“Jesu, Joy of Man’s Desiring”), from Cantata No. 147: Herz und Mund und Tat und Leben, BWV 147 This piece is written in nine-eight (compound triple) meter. Count along with the orchestra as you listen to the introduction: The choir enters at 0′22″ and sings longer note values. The piece proceeds as a call-and-response between the choir and orchestra. As you listen, count dotted quarter notes during the choir entrances (ONE-TWO-THREE) and eighth notes during the orchestral entrances (ONE-2-3 TWO-2-3 THREE-2-3). Informed Listening: Examples for Study |257 6.18. The Jimi Hendrix Experience, “Manic Depression,” from Are You Experienced? “Manic Depression” is in a very fast compound-triple meter, about 𝅘𝅥𝅼 = 148 bpm. The song could be notated in nine-eight, a very unusual meter for rock music. First, count along with the vocal line, which comprises mostly dotted quarter notes: Next, sing along with the rhythm, played by the bass and drums for most of the song. (Use “ta-ka-da,” as the tempo is too fast for numbers.) 6.19. Creedence Clearwater Revival, “I Put a Spell on You,” from Creedence Clearwater Revival This song is in compound-quadruple meter and could be notated in twelve-eight. The tempo is moderate, and the guitar plays eighth notes throughout most of the song. Count aloud as you listen, alternating one measure of dotted quarter notes with a measure of eighth notes. “I Put a Spell on You” is in a minor key, and for the most part it uses the harmonic minor scale. During the introduction, find the tonic; then sing up the scale to sol. Hold sol until about 0′19″ (take a breath and come back in when you need to); then move up a half step to le. You should hear it fit with the music. Return to do, and hold it until 0′38″; then move down a half step to ti. (See Chapter 9 for a more advanced version of this exercise.) INFORMED LISTENING: EXAMPLES WITH QUESTIONS Listen to each example several times. a. Find the pulse, and then the pulse division, and decide whether the piece is in simple or compound meter. In other words, does the pulse divide into two equal parts or three? b. Decide whether the piece is in triple or quadruple meter. That is, are there three pulses in each measure or four? (There are no duple meter examples in this section.) c. Answer any additional questions for each example. 258| Informed Listening: Examples with Questions 6.20. Carole King “(You Make Me Feel Like a) Natural Woman,” from Tapestry Meter type: [simple / compound] [triple / quadruple] 6.21. Alicia Keys, “Fallin’,” from Songs in A Minor Meter type: [simple / compound] [triple / quadruple] 6.22. Clara Schumann, “Allegro Moderato” (Movement I) from Piano Trio in G Minor, Op. 17 1. Meter type: [simple / compound] [triple / quadruple] 2. The scale degrees of the first four pitches of the melody are: a. sol-do-sol-la b. sol-do-sol-le c. me-do-me-fa d. do-|do-|do-|re 6.23. Claude-Michel Schönberg/Herbert Kretzmer, “At the End of the Day,” from Les Misérables 1. Meter type: [simple / compound] [triple / quadruple] 2. The lowest note in the melody is: a. do b. sol d. ti e. re 3. The highest note in the melody is: a. do b. sol c. le d. ti 6.24. Martin Nolan, “Goodman’s Slip Jig,” from Bright Silver Dark Wood Note: the meter does not become apparent until the pipes enter with the melody, at about 0′22″. Meter type: [simple / compound] [triple / quadruple] 6.25. The Ventures, “Walk Don’t Run,” from The Very Best of the Ventures 1. Meter type: [simple / compound] [triple / quadruple] 2. The piece begins with drums followed by bass and rhythm guitar. Which best represents the four-note repeating bass line? a. do-te-le-sol b. do-ti-la-sol c. do-ti-le-sol d. do-le-sol-fa 3. The melody, played by the lead guitar (beginning about 0′09 ″), features an ascending scale. What is the scale type? a. Major b. Natural minor c. Harmonic minor d. Melodic minor (ascending) 6.26. J. S. Bach, “Allegro” (Movement III) from Brandenburg Concerto No. 6, BWV 1051 Meter type: [simple / compound] [triple / quadruple] 6.27. Béla Fleck and the Flecktones, “Star of the County Down,” from Flight of the Cosmic Hippo Meter type: [simple / compound] [triple / quadruple] 6.28. Stephen Sondheim, “It Would Have Been Wonderful,” from A Little Night Music (performed by Len Cariou and Laurence Guittard) Note: after a short introduction, the meter becomes apparent beginning at about 0′25″. Meter type: [simple / compound] [triple / quadruple] Informed Listening: Examples with Questions |259 6.29. Chicago, “25 or 6 to 4,” from Chicago II 1. Meter type: [simple / compound] [triple / quadruple] 2. Which best represents the pitches of the vocal line when it enters at 0′27 ″ (“Waiting for the break of day”)? a. do-me-fa-sol-le-te-do b. do-me-fa-sol-la-ti-do c. do-re-me-fa-sol-ti-do d. do-re-me-fa-sol-te-do 6.30. Johann Sebastian Bach, “Minuet in G Minor,” BWV Anh. II 115, from the Notebook for Anna Magdalena Bach Recommended recording: J. S. Bach, Inventions and Sinfonias, Janos Sebestyen 1. Meter type: [simple / compound] [triple / quadruple] 2. The first three pitches of the melody are: a. me-re-do b. sol-fa-me c. sol-me-do d. do-te-le 3. The first four pitches of the bass are: a. me-re-do-ti b. do-ti-le-sol c. do-te-le-sol d. me-re-do-te 4. The last two pitches of the melody are: a. ti-do b. te-do c. re-do d. |sol-do 6.31. The Beatles, “Oh! Darling!” from Abbey Road Meter type: [simple / compound] [triple / quadruple] 6.32. BeauSoleil, “Chanson Pour Tommy,” from Cajunization Meter type: [simple / compound] [triple / quadruple] The next examples are all in six-eight (compound duple) meter. Listen to them several times and answer the questions that follow. 6.33. Georges Bizet, “Carillon” (Movement IV) from L’Arlésienne Suite No. 1, Op. 23 1. Which of the rhythmic figures is most prevalent throughout the melody of the middle section (beginning at 1′22 ″)? 260| Informed Listening: Examples with Questions 2. Which best represents the rhythm of the accompaniment throughout the middle section? 6.34. Franz Josef Haydn, “Allegro” (Movement III) from, Cello Concerto No. 2 in D major, Hob.VIIb:2 1. At the beginning of the piece, in measures 1–4 the cello plays this rhythm: 2. The melody in measures 3–4 is _____________ the melody of measures 1–2. a. A step higher than b. A step lower than c. The same as 3. In measures 5–6, the cello plays the rhythm twice: Informed Listening: Examples with Questions |261 6.35. Clara Schumann, “Andante” (Movement III) from Piano Trio in G Minor, Op. 17 1. The opening melody, played by the piano, begins on what pitch? a. do b. mi c. sol d. la 2. Which of these best represents the rhythm of the first two measures of melody? 3. The violin echoes the piano’s opening melody, beginning at 0′27 ″. At this point the piano begins playing: a. Dotted quarter notes b. Eighth notes c. Sixteenth notes d. Thirty-second notes DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 6.36. Sing these scales, up and down, with correct solfège. Start by singing one scale at a time. As you become fluent, try linking them together as shown in the example. • Major • Natural minor • Harmonic minor • Melodic minor 262| Drills to Go 6.37. Use this exercise to isolate scale degrees 5, 6, 7, and 8 for each of the scale forms you have learned so far. Sing each pattern repeatedly until you have memorized its sound. Then, mix up the patterns. & 43 .. œ œ œ .. œ œ œ .. œ bœ bœ OH .. œ bœ bœ .. n œ œ bœ .. œ bœ bœ .. n œ œ nœ D0DMRUE1DWXUDOPLQRU G W V O & 43 .. œ n œ b œ O W G WH F+DUPRQLFPLQRUG0HORGLFPLQRU G W V OH OH W G WH OH V V OH WH O W 3 & 4 œ œ œ œ œ œ œ bœ bœ œ nœ nœ œ nœ bœ œ bœ nœ H([DPSOHRIFRPELQHGSDWWHUQV G W 0DMRU O V O W G WH OH V 0HORGLFPLQRU O W G W OH V +DUPRQLFPLQRU OH W HWF 6.38. Starting on a comfortable note in the middle of your voice range, sing the minor scale in solfège, up and down, changing direction at any time you choose. Use all three forms of the minor scale as you sing. Experiment with the forms of scale degrees 6 and 7 (you will find that these guidelines work well): • Use le when proceeding downward to sol. • Use te when proceeding downward to le (and eventually to sol). • Use ti when proceeding upward to do. • Use la when proceeding upward to ti (and eventually to do). Your improvisation might look something like this: LE AL N CH ✪ GE 6.39. Choose a key for the day and repeat Exercise 6.38, substituting note names for that key. 6.40. Sing the basic and advanced tendency rows (Ex. 6.9) in solfège from memory. Then improvise patterns by leaping through the segments of the rows in random order. Drills to Go LE AL N CH ✪ GE 6.41. Choose a key for the day and repeat Exercise 6.40, substituting note names for that key. |263 CLASSROOM ACTIVITIES 6.42. Guided rhythm improvisation. 1. Choose eight rhythmic patterns, all in the same meter, from Exercise 6.1. 2. Write your choices on the board in two columns of four patterns each. (An example is given below.) Be sure to include the landing measure with each pattern. 3. Set your metronome at a slow tempo to establish a dotted-quarter-note pulse. Choose any pitch, and lead the class in singing the rhythms in order. Use a neutral syllable such as “nah” or “tah.” 4. Repeat step (3), but this time randomize the order of your choices. Start with any rhythm, and as the class reaches the landing measure, point to the next rhythm you want them to sing. (Be sure to give them enough time to anticipate where they’re going.) 5. If there are incorrect responses, repeat the pattern until the entire class sings it correctly, and then move on. 6. Continue the exercise for about one minute; then switch leaders. a. Use only the pitches |ti-do-re-me-fa-sol-le. b. Each pattern must begin on do, me, or sol. c. Use only stepwise motion (no leaps). d. Write your patterns on the board in the key you have chosen, but do not include solfège. e. As you point to each pattern, the class must respond by singing that pattern with correct solfège syllables. f. If there are incorrect responses, repeat the pattern until the entire class sings it correctly, and then move on. g. Continue the exercise for about one minute; then switch leaders. 6.44. Two ball games. Two versions of the song “Take Me Out to the Ball Game” are printed below. Version (A) is notated correctly, in six-eight meter. Version (B) is notated incorrectly, in three-four meter. 264| Classroom Activities ✪ CH Repeat Activity 6.42, but this time, choose a clef and key and compose notes on the staff for the rhythms you have chosen. Adhere to these guidelines: LE AL N GE 6.43. Rhythm improvisation with solfège. Although both versions use the exact same durations, you will find that version B “feels” wrong because its metric accents are displaced. 1. Divide the class in half. 2. Perform version (A), in six-eight. Group 1 will sing the melody, while Group 2 claps the pulse and speaks the counts as indicated. 3. Switch roles and perform version (B) in three-four. Group 2 will sing the melody while Group 1 claps the pulse and speaks the counts as indicated. It should feel very awkward and uncomfortable to sing the song this way. This is exactly the point–and why six-eight and three-four are not the same. A. “Take Me Out to the Ballgame,” beamed correctly, in six-eight Classroom Activities |265 B. “Take Me Out to the Ballgame,” beamed incorrectly, in three-four 6.45. Greensleeves, recomposed. Copy the melody for “Greensleeves” (Fig. 6.17) on the board. 1. Sing the song in solfège, it its original version. 2. Change the melody to natural minor by removing all D-sharps and C-sharps. Sing this version. 3. Change the melody to harmonic minor by changing all Ds to D-sharps. Sing this version. 266| Classroom Activities 4. Keep the D-sharps and change the melody to melodic minor (ascending form) by changing all Cs to C-sharps. Sing this version. 5. Create your own version of the song, drawing on the contrasting inflections of 6 and 7 as you prefer. 6. As a class, discuss which version you prefer, and why. WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 6 online drills and quizzes at www.oup.com/us/root. 6.46. Write the requested clef and key signature. 6.47. Identify the minor key represented by the given key signature, and then write the minor scale for that key in the form indicated. Written Exercises |267 6.48. For each question, draw dots on the correct piano keys to build the requested scale. Be sure to start the scale low enough that you don’t run out of keys. Check your work by playing the scale on an actual keyboard. Question #1 has been completed for you. 268| 1. F melodic minor (ascending) 2. A-flat harmonic minor 3. E-flat harmonic minor 4. D melodic minor (ascending) 5. G-sharp melodic minor (ascending) 6. B-flat harmonic 7. A melodic minor (ascending) 8. C-sharp harmonic minor Written Exercises 9. A-sharp harmonic minor 10. G melodic minor (ascending) 6.49. Write the requested scale degree in the key indicated. Do not use a key signature, but instead apply the accidental directly to the note. Remember that the syllables la and ti represent the raised form of scale degrees 6 and 7. 6.50. For each question, name the minor key indicated by the key signature; then write the correct solfège syllable for each note in the given key. Written Exercises |269 6.51. For each question, draw the clef indicated, and then write the scale using the clue given. LE AL N CH GE ✪ Apply sharps or flats directly to the scales; do not use key signatures. 1. Treble clef: write the major scale that is parallel to A-flat minor. 2. Treble clef: write the harmonic minor scale that is relative to C-sharp major. 3. Bass clef: write the melodic minor scale (up and down) that is parallel to C major. 4. Bass clef: write the major scale that is relative to B minor. 5. Treble clef: write the melodic minor scale (up and down) that is relative to F-sharp major. 6. Treble clef: write the major scale that is relative to C-sharp minor. 7. Bass clef: write the melodic minor scale (up and down) that is parallel to G major. 8. Bass clef: write the harmonic minor scale that is parallel to B-flat major. 270| Written Exercises 6.52. Each question contains the notes of a scale, out of sequential order. Unscramble the scale, and write the letter names in the correct order in the blank. Then circle the correct scale type from the choices given. Keep in mind: • For melodic minor only the ascending scale form is used. • Some questions have two possible correct answers. Sample question 1: F# E∫ C G B∫ D A _________________________ This scale is: major / natural minor / harmonic minor / melodic minor Answer: G A B∫ C D E∫ F# G harmonic Sample question 2: G# E A C# D# B F# _________________________ This scale is: major / natural minor / harmonic minor / melodic minor Possible answer: E F# G# A B C# D# major Possible answer: C# D# E F# G# A B natural minor 1. B# A# C# E# G‹ F‹ D# This scale is: major / natural minor / harmonic minor / melodic minor 2. B∫ A C G∫ D∫ F E∫ _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 3. G B F# D E A C# _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 4. C# A F# G# B E# D _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 5. B∫ E∫ D∫ A∫ C∫ F∫ G∫ _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 6. A F# B D# C# G E _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 7. B∫ G E∫ F D∫ A∫ C _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 8. D# C# F# A# B G# E _________________________ This scale is: major / natural minor / harmonic minor / melodic minor 9. B E A D G C F# _________________________ This scale is: major / natural minor / harmonic minor / melodic minor Written Exercises |271 6.53. Complete each measure using just one rhythmic value. Use only notes; do not use rests. Be sure to observe the rules for proper beaming. Where necessary, beam your answers to the notes that are given. After you have finished, perform each example. 6.54. Rewrite each example so that it is beamed properly for the meter given. The first beat of Question 1 has been completed. 272| Written Exercises 6.55. Each question contains an excerpt from a song written in vocal notation. Rewrite the music with correct beaming for the meter indicated. Question #1 has been completed for you. 1. Hector Berlioz, “Le spectre de la rose,” from Les nuits d’été, Op. 7, mm. 31-32 2. Emmanuel Chabrier, “A la musique,” mm. 18-20 Written Exercises |273 3. Claude Debussy, “Clair de Lune,” from Fêtes galantes, mm. 6-11 274| Written Exercises 4. Gabriel Faure, “Notre Amour,” Op. 23, No. 2, mm. 3-6 M leggiero e legato 6 O O O œ œ œ œ œ G O O O œ œ œ œ œ 8 œ œ œ 0 ( 00( œ œ œ œ 0 ( 0 0 ( œ œ 0 0 Notre a - mor est cho - se lé - gè - re, Com - me les par - fums que le vent Prend aux O O O G œ O œ œ œO O O O œ œ œ G œ ( 0 œ œ œ 0 œ œ œ œ œ ci - mes de la fou - gè - re, Pour qu'on les res - pire en rê - vant; O œ œ 0 Notre a- 68 Rewrite: 5. Henri Duparc, “Sérénade,” mm. 3-10 Written Exercises |275 6. Gabriel Fauré, “Aubade,” Op. 6, No. 1, mm. 6-12 2 œ 8 œ voir œ œ œG œG œ . ( ( L'ho - ri - zon se co - lo - C G± G œ œ œ re. Voi - -ci œ œ œ œG œ œ œG œ œ œ ( ( les fleurs à la œ Mœ ( ± ( œ œG œ œ œ . ( ( ( œ ± œ ( ( le frais mat - in! lu - miè - re. S'ou - vrir de tou - te Kœ œ œ œ œ œ . œ ± œ Ç. ( ( ( ( tr'ou - vre ta œ œ K œ( œ . ( pau- piè - re, O vier - part. Pour œ œ œ œ œG œ . Ç . ( ge au doux re - gard! 2 8 Rewrite: COMPOSITION 6.56. Compose an eight-measure melody in six-eight meter, according to these guidelines. 1. Use only these rhythmic figures, and do not use rests or ties. 276| Composition Eu - œ . O 2. Your composition will be in a minor key, beginning and ending on high do. 3. Use a combination of all three forms of the minor scale. Alter scale degrees 6 and 7 according to the guidelines given in Exercise 6.38. 4. Use only stepwise motion, in any direction you choose. In other words, your composition may go up and down the scale, changing direction at any time. 5. Measure 8 will contain only do, with a dotted-half note duration. 6. Measure 4 will contain only re and sol, in the rhythm given. (Use the low re and the sol in the middle of the scale.) 7. The last note of measure 3 will be do or me (in order to lead stepwise into re). 8. Measure 5 will begin on the low do. 9. The last note of measure 7 will be re or ti (in order to lead stepwise into do). 10. The highest note in your piece will occur somewhere in measure 7, and it may only happen once. 11. The lowest note in your piece may occur anywhere but may only happen once. Use the blank template given to compose your melody in solfège. Then write the melody on staff paper in a clef and key of your instructor’s choice. Perform your composition at the piano or on your instrument, or lead the class in singing it. Here is a sample composition written first in solfège, and then in treble clef, F-sharp minor. Composition |277 6.57. For each example: a. Label each note with the correct solfège syllable. (The key is given.) b. Compose your own rhythm for each measure, using only the notes included for that measure. You may use rests and ties within a measure, but do not tie any notes over a bar line. Take care to use proper beaming. c. Lead the class in performing your composition. D major, six-eight meter 278| Composition Chapter Goals Revisited B-flat minor, nine-eight meter Be sure that you have achieved all Chapter 6 Goals before proceeding to Chapter 7. Understand the difference between simple and compound meters. (pages 230–237) Perform, recognize, and notate basic rhythms in six-eight, nine-eight, and twelveeight meter. (pages 245–246, 247–250) Distinguish between simple and compound meters in music you hear. (pages 257– 258) Sing harmonic and melodic minor scales with solfège and letter names for all keys. (pages 251–252) Play harmonic and melodic minor scales for all keys at the piano. (pages 250–252) Write harmonic and melodic minor scales for all keys in treble clef, bass clef, and letter names. (pages 237–245) Distinguish major, natural minor, harmonic minor, and melodic minor scales by sound. (pages 244–246, 254) Sing and resolve tendency tones in the minor scale. (pages 245, 253–254) Hear and identify tendency tones with their resolution tones in the minor scale. (pages 245, 254–256) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. Composition |279 CHAPTER 7 PITCH: INTERVALS/ RHYTHM: COMPOUND METER REVIEW Chapter Goals After you finish this chapter, you should be able to do the following, quickly and accurately: • Identify simple intervals by number and quality. • Build simple intervals above and below a given note. • Sing intervals above and below do in the major and minor scales, naming each interval by number and quality. • Hear and identify intervals above and below do in the major and minor scale, naming each interval by number and quality. • Invert a melody diatonically. • Invert a melody chromatically. • Invert an interval, and identify the resulting interval by number and quality. • Recognize pairs of enharmonic intervals. • Identify compound intervals by number and quality. • Build compound intervals above and below a given note. • Hear and identify intervals between melody notes in a piece of music. INTERVAL NUMBER AND QUALITY You may recall that at the beginning of this book you sang a melody made up of pitches, and that each pitch had a duration. Your melody was also made up of intervals; an interval measures the distance between two pitches. Every interval name is made up of a number and a quality. The number identifies the visual space between two notes as they appear on the staff. We describe intervals by saying “second” “third,” “fourth,” etc., but we write the number as an Arabic numeral with no suffix (i.e., 2, 3, 4, not 2nd, 3rd, 4th). Always use the words unison and octave (never first and eighth) to describe the intervals 1 and 8, respectively. EBSIT E W Figure 7.1. Interval numbers. When finding an interval number, you must count both the lower and higher notes in your calculation. For example, C ↑ E is a third because “C-D-E” is counted as “1-2-3.” Although the number describes an interval in very general terms, quality is a more precise label used to pinpoint the exact distance between the pitches. For example, F up to A 280| (or F ↑ A) and F ↑ A-flat are both thirds, but they are not the same size; F ↑ A is larger by one half step and therefore has a different quality. There are seven interval qualities, found in music with varying degrees of frequency: Most Common Less Common Very Rare Major (M) Augmented (A) Doubly augmented (AA) Minor (m) Diminished (d) Doubly diminished (dd) Perfect (P) EP L A Y R • An interval measures the distance between two pitches. • Every interval name is made up of a number and quality. • The interval number describes the visual distance between notes on the staff. To find it, count the letter names between the notes, and be sure to count the lower note as “one.” C ↑ F is a fourth because “C-D-E-F” is counted “1-2-3-4.” • The most common interval qualities are major, minor, and perfect. Augmented and diminished intervals are less common, and doubly augmented and doubly diminished intervals are very rare. MAJOR, MINOR, AND PERFECT INTERVALS Before proceeding, it is important to know some basic information about the quality labels “major,” “minor,” and “perfect.” • The label perfect (P) applies only to unisons, fourths, fifths, and octaves (1, 4, 5, 8). There is no such thing as a “perfect third,” “perfect sixth,” etc. • The labels major (M) and minor (m) apply only to seconds, thirds, sixths, and sevenths (2, 3, 6, 7). There is no such thing as a “major fifth,” “major octave,” “minor fourth,” etc. Perfect 1, 4, 5, 8 2, 3, 6, 7 Major and Minor 2, 3, 6, 7 1, 4, 5, 8 Once you know the interval number, you can determine its quality by treating the lower of the two notes as tonic (do) in a major key. If the upper note exists in that key, the interval is either major or perfect, depending on its number. For example, the interval A ↑ C-sharp is a major third because: • The letter names are three counts apart (A-B-C = 1-2-3). • There is a C-sharp in the key of A major (not a C-natural, a C-flat, or any other kind of C; only C-sharp). • Remember that the C-sharp is present because the key of A contains three sharps (F-sharp, C-sharp, and G-sharp). Here is another method: • The letter names are three counts apart (A-B-C = 1-2-3). • Think of A as do, and count up the scale do-re-mi. • In the key of A, mi is C-sharp. • Therefore, A ↑ C-sharp is a major third. Pitch: Intervals/Rhythm: Compound Meter Review |281 The following intervals are all perfect (P) or major (M) in quality. Refer to the numbered list below the staff for an explanation of each interval’s quality. 1. This interval is a major second because B is present in the key of A major. 2. This interval is a major second because E-flat is present in the key of D-flat major. 3. This interval is a major third because A is present in the key of F major. 4. This interval is a major third because F-sharp is present in the key of D major. 5. This interval is a major third because G is present in the key of E-flat major. 6. This interval is a perfect fourth because B-flat is present in the key of F major. 7. This interval is a perfect fifth because E-flat is present in the key of A-flat major. 8. This interval is a major sixth because G-sharp is present in the key of B major. 9. This interval is a major sixth because E is present in the key of G major. If a major interval is reduced in size by one half step, the resulting quality is minor. The reduction in size may be accomplished by lowering the top note of the interval, or raising its bottom note. In either case, the letter names of the two notes (and therefore the interval number) should stay the same. EBSIT E W Figure 7.2. Major third reduced to minor third, two ways. 1. F ↑ A is a major third because A is present in the key of F major. 2. F ↑ A-flat is a minor third, because the upper note of the major third has been lowered by one half step. 3. F-sharp ↑ A is a minor third, because the lower note of the major third has been raised by one half step. The following intervals are all minor (m) in quality. Refer to the numbered list below the staff for an explanation of each interval’s quality. 1. This interval is a minor second, because: • A ↑ B would be a major second • Changing B to B-flat reduces the interval space by one half step, creating a minor second 282| Pitch: Intervals/Rhythm: Compound Meter Review 2. This interval is a minor second, because: • F ↑ G would be a major second • Changing F to F-sharp reduces the size of the interval space by one half step • In this case, the top note stays the same and the bottom note is raised 3. This interval is a minor third, because: • F ↑ A would be a major third • Changing A to A-flat reduces the size of the interval space by one half step 4. This interval is a minor third, because: • D ↑ F-sharp would be a major third • Changing D to D-sharp reduces the size of the interval space by one half step • In this case, the top note stays the same and the bottom note is raised 5. This interval is a minor third, because: • B ↑ D-sharp would be a major third (there is a D-sharp in the key of B major) • Changing the D-sharp to D reduces the interval space by one half step, resulting in a minor third 6. This interval is a minor sixth because: • F ↑ D would be a major sixth • Changing D to D-flat reduces the size of the interval space by one half step 7. This interval is a minor sixth because: • G ↑ E would be a major sixth • Changing G to G# reduces the size of the interval space by one half step • In this case, the top note stays the same and the bottom note is raised 8. This interval is a minor seventh, because: • D ↑ C-sharp would be a major seventh (there is a C# in the key of D major) • Changing the C-sharp to C reduces the interval space by one half step, resulting in a minor seventh 9. This interval is a minor seventh, because: • C ↑ B-natural would be a major seventh • Changing the B to B-flat reduces the interval space by one half step, resulting in a minor seventh You can change a minor-quality interval to major quality by increasing its size by one half step. This can be done by raising the top note or lowering the bottom. Again, the interval number does not change. EBSIT E W Figure 7.3. Minor seventh increased to major seventh, two ways. 1. D ↑ C is a minor seventh. (See item 8 in the previous list.) 2. D ↑ C-sharp is a major seventh because the upper note has been raised by a half step (and also because C-sharp is present in the key of D major). Pitch: Intervals/Rhythm: Compound Meter Review |283 3. D-flat ↑ C is a major seventh because the lower note has been lowered by a half step (D to D-flat), and also because C-natural is present in the key of D-flat major. Keep in mind that minor quality exists only for seconds, thirds, sixths, and sevenths (2, 3, 6, 7), because a minor interval is always derived from a major interval. Accidentals alone are of little help in determining interval quality. Do not assume, for example, that intervals containing a sharp will necessarily be major, or that those with flats will always be minor. Compare the intervals shown below; even though each one uses its own arrangement of accidentals, all are major sixths. 1. C-sharp is present in the key of E major. 2. D is present in the key of F major. 3. G is present in the key of B-flat major. 4. B-flat is present in the key of D-flat major. Some students may find a visual technique helpful for understanding the relationship between major and minor intervals. Place two pencils parallel to each other on a table, one above the other (that is, farther away from you). Imagine that the nearer one is the floor of a room and the other is the ceiling. To make the room smaller, you can either lower the ceiling (the top note) or raise the floor (the bottom note). To make the room larger, you can either raise the ceiling (the top note) or lower the floor (the bottom note). 284| Pitch: Intervals/Rhythm: Compound Meter Review EP L A Y • Major quality applies only to seconds, thirds, sixths, and sevenths (2, 3, 6, 7). An interval is major if the higher note exists in the major scale of the lower note. R • Perfect quality applies only to unisons, fourths, fifths, and octaves (1, 4, 5, and 8). An interval is perfect if the higher note exists in the major scale of the lower note. • Minor quality applies only to seconds, thirds, sixths, and sevenths (2, 3, 6, 7). A minor interval is one half step smaller than a major interval. • The size of an interval may be changed by altering either of its notes: o To make an interval larger, raise the top note, or lower the bottom note. o To make an interval smaller, lower the top note, or raise the bottom note. MELODIC AND HARMONIC INTERVALS In the English language, a single word can have several meanings; the same is true of musical terminology. In the previous chapter, you learned about harmonic and melodic minor scales. Even though these terms refer to specific scale types, they also have much broader meanings. Generally speaking: • Harmonic describes sounds that happen at the same time. • Melodic describes sounds that happen one after another. Simply put, a harmonic interval occurs when two notes are played at the same time; a melodic interval occurs when one note is played after the other. Figure 7.4 is an excerpt from a two-part choral work. Melodic intervals occur in each part, connecting one note to the next. Harmonic intervals occur vertically, as a result of the interaction of the two parts. R EP L A Y • A melodic interval is the distance between two pitches played one after the other. EBSIT E W Figure 7.4. Anon., “Ecco Il Messia,” mm. 11–15. • A harmonic interval is the distance between two pitches played at the same time. Pitch: Intervals/Rhythm: Compound Meter Review |285 RECOGNIZING MAJOR, MINOR, AND PERFECT INTERVALS Here are six examples to help you develop a method for recognizing intervals quickly and accurately. Example 1. Identify the interval number and quality seen here. Step 1. What is the interval number? (Always calculate the number first.) Answer: 6 Step 2. Treat the bottom note (B) as do in a major key. Is the top note (G-sharp) present in the key of B major? Answer: Yes. Hence the interval is a major sixth (M6). Example 2. Identify this interval number and quality. Step 1. What is the interval number? Answer: 3 Step 2. Treat the bottom note (E-flat) as do in a major key. Even though E-flat is not the first note of the interval, it is still the lower note and should be used as the basis for the interval calculation. Is the top note (G-flat) present in the key of E-flat major? Answer: no. The interval is not a major third. Step 3. How does this interval compare to what is found in the key of E-flat major? Answer: there is a G-natural in the key of E-flat major. G-flat makes the interval one half step smaller by lowering the top note. Hence the interval is a minor third (m3). Example 3. Identify the next interval number and quality. Step 1. What is the interval number? Answer: 5 Step 2. Treat the bottom note (B-flat) as do in a major key. Is F present in the key of B-flat major? Answer: yes. Hence the interval is a perfect fifth (P5). 286| Pitch: Intervals/Rhythm: Compound Meter Review Example 4. Identify the interval number and quality. Step 1. What is the interval number? Answer: 3 Step 2. Treat the bottom note (F-flat) as do in a major key. Problem: there is no key of F-flat major. Solution: a. Cover both flats with your finger, and calculate the resulting interval (F ↑ A). b. F ↑ A is a major third, because A is in the key of F. c. Uncover the flats. Since both notes are altered by the same amount (one half step downward), the distance between the notes does not change, and the interval size remains the same. Hence the interval is a major third (M3). Example 5. Identify the interval number and quality. Step 1. What is the interval number? Answer: 2 Step 2. Treat the bottom note (E-sharp) as do in a major key. Problem: there is no key of E-sharp major. Solution: a. Cover both sharps, and calculate the resulting interval (E ↑ F). b. E ↑ F is a minor second. c. Reinstate the sharps. Since both notes are altered by the same amount (one half step upward), the distance between the notes does not change, and the interval size remains the same. Hence the interval is a minor second (m2). Example 6. Identify the interval number and quality. Step 1. Don’t panic. What is the interval number? Answer: 7 Step 2. Treat the bottom note (A-double-flat) as do. Problem: there is no key of A-double-flat major. Solution: a. Remove one flat from each note. Calculate the resulting interval (A-flat ↑ G). b. A-flat ↑ G is a major seventh, because G is present in the key of A-flat. c. Reinstate the flats. Since both notes were altered by the same amount (one half step downward), the distance between the notes does not change, and the interval size remains the same. Hence the interval is a major seventh (M7). Pitch: Intervals/Rhythm: Compound Meter Review |287 BUILDING MAJOR, MINOR, AND PERFECT INTERVALS The next nine examples will help you develop a method for building intervals quickly and accurately. Building Intervals Above a Given Note Example 1. Build a major third above this note. Step 1. Calculate the letter name of the note first. B is a third above G. Step 2. Analyze the resulting interval. Is it a major third? Answer: yes Step 3. You’re done. Example 2. Build a perfect fourth above this note. Step 1. Calculate the letter name of the note first. A is a fourth above E-flat. Step 2. Analyze the resulting interval. Is it a perfect fourth? Answer: no. A perfect fourth above E-flat is A-flat, because A-flat is present in the key of E-flat major. Step 3. Adjust the top note to A-flat. Example 3. Build a minor sixth above this note. Step 1. Calculate the letter name of the note first. D is a sixth above F. Step 2. Analyze the resulting interval. Is it a minor sixth? Answer: no. F ↑ D is a major sixth, because D is present in the key of F major. In other words, the interval is one half step too large. Step 3. Reduce the interval size by adjusting the top note down a half step, to D-flat. Example 4. Build a major sixth above this note. 288| Pitch: Intervals/Rhythm: Compound Meter Review Step 1. Since the bottom note (A-sharp) is not the tonic of a major key, cover the sharp temporarily. Step 2. What note is a major sixth above A-natural? Answer: F-sharp Step 3. Reinstate the A-sharp and adjust the top note accordingly (up a half step, to F-double-sharp). Building Intervals Below a Given Note Example 5. Build a minor seventh below this note. Step 1. Calculate the letter name of the note first. G is a seventh below F. Step 2. Analyze the resulting interval. Is it a minor seventh? Answer: yes, because a major seventh above G is F-sharp. G ↑ F-natural is one half step smaller, so it is a minor seventh. Step 3. You’re done. Example 6. Build a perfect fifth below this note. Step 1. Calculate the letter name of the note first. D is a fifth below A-flat. Step 2. Analyze the resulting interval. Is it a perfect fifth? Answer: no. A perfect fifth above D-natural is A-natural. This interval is one half step too small to be a perfect fifth. Step 3. Increase the size of the interval by one half step. To do this, you must lower the bottom note, D, to D-flat. Keep in mind that you cannot alter the given note. A note about Example 6: if you are using the “ceiling and floor” method, this is a case where you must lower the floor to make the interval larger, because the ceiling is the given note and cannot be changed. Example 7. Build a major third below this note. Step 1. Calculate the letter name of the note first. A is a third below C-sharp. Step 2. Analyze the resulting interval. Is it a major third? Answer: yes (because C-sharp is present in the key of A major). Step 3. You’re done. Pitch: Intervals/Rhythm: Compound Meter Review |289 Example 8. Build a major sixth below this note. Step 1. Calculate the letter name of the note first. D is a sixth below B-flat. Step 2. Analyze the resulting interval. Is it a major sixth? Answer: no. A major sixth above D is B (natural), so this interval is one half step too small. Step 3. Increase the size of the interval by one half step. To do this, you must lower the bottom note, D, to D-flat. Example 9. Build a major third below this note. Step 1. Calculate the letter name of the note first. B is a third below D-double-sharp. Step 2. Analyze the resulting interval. Is it a major third? Answer: no. A major third above B is D-sharp. This interval is one half step too large. Step 3. Reduce the size of the interval by one half step. To do this, you must raise the bottom note (B) to B-sharp. (Remember, you cannot change the given note.) A note about Example 9: if faced with this example on a homework assignment or exam, you might be tempted to notate a C, instead of a B-sharp, as the answer. Even though C and B-sharp are enharmonically equivalent, C is not a major third below D-double-sharp and would in fact be an incorrect answer. This is because the interval number is always based on the distance between the two letter names of the notes. Any type of B ascending to any type of D is always a third. Any type of C up to any type of D is always a second. AUGMENTED AND DIMINISHED INTERVALS The labels augmented or diminished may apply to any interval number. • An augmented interval (A) is one chromatic half step larger than a major or perfect interval. • A diminished interval (d) is one chromatic half step smaller than a minor or perfect interval. To begin, let us consider only the perfect intervals: 1, 4, 5, and 8. If a perfect interval is increased in size by one chromatic half step, the result is an augmented interval (A). This may be accomplished by raising the top note (the “ceiling”) or lowering the bottom note 290| Pitch: Intervals/Rhythm: Compound Meter Review (the “floor”). Play the next example at the piano, and then refer to the text below for an explanation of each interval. EBSIT E W Figure 7.5. Perfect intervals expanded to augmented intervals. 1a. This interval is a perfect fifth because E is present in the key of A major. 1b. This interval is an augmented fifth because its size has been increased by one half step from the perfect fifth (by raising the top note from E to E-sharp). 1c. This interval is an augmented fifth because its size has been increased by one half step from the perfect fifth (by lowering the bottom note from A to A-flat). 2a. This interval is a perfect fourth because D-flat is present in the key of A-flat major. 2b. This interval is an augmented fourth because its size has been increased by one half step from the perfect fourth (by raising the top note from D-flat to D-natural). 2c. This interval is an augmented fourth because its size has been increased by one half step from the perfect fourth (by lowering the bottom note from A-flat to A-double-flat). 3a. This interval is a perfect fifth because F-sharp is present in the key of B major. 3b. This interval is an augmented fifth because its size has been increased by one half step from the perfect fifth (by raising the top note from F-sharp to F-double-sharp). 3c. This interval is an augmented fifth because its size has been increased by one half step from the perfect fifth (by lowering the bottom note from B to B-flat). If a perfect interval is reduced in size by one half step, the result is a diminished interval (d). The reduction may be accomplished by lowering the top note or raising the bottom note. Play the following example at the piano; then refer to the text below for an explanation of each interval. EBSIT E W Figure 7.6. Perfect intervals reduced to diminished intervals. 1a. This interval is a perfect fourth because B-flat is present in the key of F major. 1b. This interval is a diminished fourth because its size has been reduced by one half step from the perfect fourth (by lowering the top note from B-flat to B-double-flat). 1c. This interval is a diminished fourth because its size has been reduced by one half step from the perfect fourth (by raising the bottom note from F to F-sharp). 2a. This interval is a perfect fifth because G-sharp is present in the key of C-sharp major. Pitch: Intervals/Rhythm: Compound Meter Review |291 2b. This interval is a diminished fifth because its size has been reduced by one half step from the perfect fifth (by raising the bottom note from C-sharp to C-double-sharp). 2c. This interval is a diminished fifth because its size has been reduced by one half step from the perfect fifth (by lowering the top note from G-sharp to G-natural). 3a. This interval is a perfect fifth because D is present in the key of G major. 3b. This interval is a diminished fifth because its size has been reduced by one half step from the perfect fifth (by lowering the top note from D to D-flat). 3c. This interval is a diminished fifth because its size has been reduced by one half step from the perfect fifth (by raising the bottom note from G to G-sharp). Major and minor intervals may also be altered in size to produce augmented and diminished intervals. If a major interval is increased in size by one half step, the result is an augmented interval. Play this example at the piano, and then refer to the text below for an explanation of each interval. EBSIT E W Figure 7.7. Major intervals expanded to augmented intervals. 1a. This interval is a major sixth because D is present in the key of F major. 1b. This interval is an augmented sixth because its size has been increased by one half step from the major sixth (by raising D to D-sharp). 1c. This interval is an augmented sixth because its size has been increased by one half step from the major sixth (by lowering F to F-flat). 2a. This interval is a major third because F-sharp is present in the key of D major. 2b. This interval is an augmented third because its size has been increased by one half step from the major third (by raising F-sharp to F-double-sharp). 2c. This interval is an augmented third because its size has been increased by one half step from the major third (by lowering D to D-flat). 3a. This interval is a major seventh because F-sharp is present in the key of G major. 3b. This interval is an augmented seventh because its size has been increased by one half step from the major seventh (by raising F-sharp to F-double-sharp). 3c. This interval is an augmented seventh because its size has been increased by one half step from the major seventh (by lowering G to G-flat). If a minor interval is reduced in size by one half step, it becomes a diminished interval. The reduction may be accomplished by lowering the top note or raising the bottom note. Play the following example at the piano; then refer to the text below for an explanation of each interval. 292| E W Figure 7.8. Minor intervals reduced to diminished intervals. EBSIT Pitch: Intervals/Rhythm: Compound Meter Review 1a. This interval is a minor sixth because it is one half step smaller than a major sixth (F ↑ D). 1b. This interval is a diminished sixth. It is one half step smaller than the minor sixth because the top note has been lowered from D to D-flat. 1c. This interval is a diminished sixth. It is one half step smaller than the minor sixth because the bottom note has been raised from F-sharp to F-doublesharp. 2a. This interval is a minor third because it is one half step smaller than a major third (F ↑ A). 2b. This interval is a diminished third. It is one half step smaller than the minor third because the top note has been lowered from A-flat to A-double-flat. 2c. This interval is a diminished third. It is one half step smaller than the minor third because the bottom note has been raised from F to F-sharp. 3a. This interval is a minor seventh because it is one half step smaller than a major seventh (G ↑ F-sharp). 3b. This interval is a diminished seventh. It is one half step smaller than the minor seventh because the top note has been lowered from F to F-flat. EP L A Y • An augmented interval is one chromatic half step larger than a major or perfect interval. R 3c. This interval is a diminished seventh. It is one half step smaller than the minor seventh because the bottom note has been raised from G to G-sharp. • A diminished interval is one chromatic half step smaller than a minor or perfect interval. SUMMARY OF INTERVAL QUALITIES Here are two charts illustrating the relationship between interval sizes; memorize them separately to avoid confusion. (Remember that a perfect interval can never become major or minor, and a major/minor interval can never become perfect.) Smaller qualities are found to the left, and larger qualities to the right. The symbol ↔ indicates that the interval size is increased or decreased by a chromatic half step. For Intervals 1, 4, 5, 8 Diminished (o) Perfect ←⎯⎯⎯→ ←⎯⎯⎯→ (P) Augmented (+) ←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ Smaller Larger For Intervals 2, 3, 6, 7 Diminished ←⎯→ Minor ←⎯→ Major ←⎯→ Augmented (o) (m) (M) (+) ←⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ Smaller Larger Pitch: Intervals/Rhythm: Compound Meter Review |293 If you prefer, you can also memorize the interval qualities using the equations listed below. In this case, “+1” means a half step increase, and “−1” means a half step decrease in the distance between the two notes. • Perfect − 1 = Diminished • Perfect + 1 = Augmented • Major + 1 = Augmented • Major − 1 = Minor • Minor + 1 = Major • Minor − 1 = Diminished DOUBLY AUGMENTED AND DOUBLY DIMINISHED INTERVALS It is possible to construct doubly augmented (AA) and doubly diminished (dd) intervals. A doubly augmented interval is one chromatic half step larger than an augmented interval. A doubly diminished interval is one chromatic half step smaller than a diminished interval. 294| Pitch: Intervals/Rhythm: Compound Meter Review Although these intervals are theoretically possible, they seldom occur in actual music. The Joplin excerpt in Figure 7.9 is a rare exception. In measure 2, G-flat (in the bass) and C-sharp (in the middle of the right hand) form a doubly augmented fourth. EBSIT E At first, Joplin’s choice of G-flat and C-sharp may seem unnecessarily complex. But notice the direction of each note in the interval: G-flat moves downward to F in the following measure, while C-sharp proceeds upward to D natural. In this case, writing a doubly augmented fourth is the only way to avoid unnecessary courtesy naturals. W Figure 7.9. Scott Joplin, “The Chrysanthemum.” INVERSION Inversion is another musical term (like “harmonic” and “melodic”) that has several meanings. In a general sense, to invert something is to turn it upside-down. In music, there are several types of inversion. This book will cover three of them: diatonic inversion, chromatic inversion, and interval inversion. Diatonic Melody Inversion Figure 7.10 contains two short melodic figures or motives in a work by J. S. Bach. The motives are related by a process called diatonic inversion. The inverted motive is generated from Motive A by reversing the direction of each interval, while keeping the notes within the overall key signature (in this case, C major). In other words, only the interval numbers are inverted, without regard to each interval’s quality. Pitch: Intervals/Rhythm: Compound Meter Review EBSIT E W Figure 7.10. Bach, Invention No. 1 in C major. |295 Chromatic Melody Inversion Figure 7.11 is an excerpt from an organ piece that uses the technique of chromatic inversion. The intervals of the inverted motives are identical in number and quality to those of the original motives, but the direction of each interval is reversed. Figure 7.11. Jena Root, “Variations on a Southern Harmony Tune,” mm. 55–60. Motive A ĻP5 Ĺm3 I II Pedals ± O Ç O Ç Manuals ĻP5 ĹM7 ĻP5 Ĺm3 Ļm2 ± 55 Ç K Chromatic inversion of Motive A ĹP5 Ļm3 ± 57 @ @ Ĺm3 Ç 0 59 ± ( Ļm3 @ ĻM2 Ç Ļm3 ĻM2 O Ç ( ĻM2 Motive B K ± ĹM2 O Ç 296| ĹP5 ĻM7 ĹP5 Ļm3 Ĺm2 ± ĹM2 K Ĺm3 ĹM2 Chromatic inversion of Motive B Pitch: Intervals/Rhythm: Compound Meter Review O Ç Interval Inversion To invert a single interval, turn it upside down by moving the bottom note above the top note, or vice versa. Study the pairs of inverted intervals below; do you see a pattern? An interval number and its inversion will always add up to nine. Thus: • 1 inverts to 8 and vice versa. • 2 inverts to 7 and vice versa. • 3 inverts to 6 and vice versa. • 4 inverts to 5 and vice versa. The interval quality “flips” when inverted. • Augmented inverts to diminished and vice versa. • Major inverts to minor and vice versa. • Perfect inverts to perfect. EP L A Y • To invert a melody chromatically, reverse the direction of each interval number and quality. For example, a major third up (C ↑ E) inverts to a major third down (C ↓ A-flat). R • To invert a melody diatonically, reverse the direction of each interval number, while keeping all of the pitches within the same key. For example, a third up (C ↑ E) inverts to a third down (C ↓ A). • To invert a single interval, exchange the positions of the two notes: move the lower note above the higher note. For example, F ↑ A inverts to A ↑ F. • An interval number and its inversion will always add up to nine. The interval quality flips when inverted: o Major inverts to minor. o Augmented inverts to diminished. o Perfect inverts to perfect. ENHARMONIC INTERVALS The two intervals below are enharmonic, because the augmented fifth A to E# sounds exactly the same as the minor sixth A to F. In fact, any augmented fifth is enharmonic to a minor sixth. Take care not to confuse enharmonic intervals. Remember that interval number always depends on the distance between the letter names: • Any kind of A going up to any kind of E is always some kind of fifth. • Any kind of A going up to any kind of F is always some kind of sixth. Pitch: Intervals/Rhythm: Compound Meter Review |297 Figure 7.12 lists pairs of enharmonic intervals. (Doubly augmented and doubly diminished intervals are not included.) Notice that every interval can be spelled as major, minor, or perfect quality, except for the augmented fourth/diminished fifth. This interval is sometimes called a tritone, because it is made up of three whole steps (“tri-” = three). The tritone spans exactly half an octave (six half steps out of twelve), so it inverts to itself. (The augmented fourth inverts to the diminished fifth, and they are also enharmonic.) EBSIT E W Figure 7.12. Enharmonic intervals. COMPOUND INTERVALS The intervals you have learned so far–those one octave and smaller–are called simple intervals. Any interval that is larger than an octave is called a compound interval. To number a 298| Pitch: Intervals/Rhythm: Compound Meter Review compound interval, start with the simple interval number (as if the two notes appeared within an octave), and add seven. The interval quality remains the same. EBSIT E W Figure 7.13. Simple and compound intervals. “Ecco Il Messia” (Fig. 7.14) contains two compound harmonic intervals. EBSIT E W Figure 7.14. Anon., “Ecco Il Messia,” mm. 1–5. OTHER INTERVAL PATTERNS Intervals in the Descending Major Scale As you have already learned, measuring from do up to any note in the major scale will result in a major interval (2, 3, 6, and 7) or a perfect interval (1, 4, 5, 8). Pitch: Intervals/Rhythm: Compound Meter Review EBSIT E W Figure 7.15. Intervals measured upward from do in the major scale. |299 On the other hand, if you measure downward from the high do to any note in a major scale, the resulting interval is either minor (2, 3, 6, and 7) or perfect (1, 4, 5, 8). Remember that a major interval always inverts to a minor interval. In this case, we are simply inverting the intervals of the scale. For example, do up to mi (M3) becomes do down to mi (m6). EBSIT E W Figure 7.16. Intervals measured downward from do in the major scale. Intervals in the Natural Minor Scale Recall that the natural minor scale contains a lowered third, sixth, and seventh (me, le, and te) compared to the major scale. This means that a minor third (m3), minor sixth (m6), and minor seventh (m7) exist above its tonic note. Since re is unaltered in the minor scale, its distance above do remains a major second (M2). Likewise, the unaltered fourth and fifth remain perfect. In other words, all intervals in the natural minor scale, measured upward from the tonic, are minor and perfect, except for the second, which is major. E W Figure 7.17. Intervals measured upward from do in the natural minor scale. EBSIT Measuring downward from the upper tonic of a natural minor scale will yield intervals that are all major or perfect, except for the seventh, which is minor. Figure 7.18. Intervals measured downward from do in the natural minor scale. 300| Pitch: Intervals/Rhythm: Compound Meter Review EP L A Y • An interval larger than an octave is called a compound interval. Compound intervals are numbered by adding seven to the simple interval number. For example, C3 to D3 is a major second. C3 to D4 is a major ninth. R • Enharmonic intervals sound the same but are notated differently. For example, an augmented second (C ↑ D-sharp) and a minor third (C ↑ E-flat) are enharmonic. • In the major scale, all intervals measured upward from do are major and perfect. All intervals measured downward from do are minor and perfect. • The natural minor scale contains a major second, minor third, minor sixth, and minor seventh above do. The fourth, fifth, and octave are perfect. NOTATION When writing the harmonic interval of a second, place the higher of the two notes on the right. If the notes require a stem, let the note that is farther from the middle line dictate stem direction. If both notes of the second take an accidental, add the upper accidental first, writing it close to the chord. Write the lower symbol to its left, a bit farther away from the chord. When both notes of a third require an accidental, the same rule applies. Notate the higher note of a second on the right. ÇÇ Place the higher accidental on the right, closer to the interval. @ @ @ @ @ @ @ ÇÇ Note that is farther from the center line dictates stem direction @ @ @ @ @ K ÇÇ Place the higher accidental on the right, closer to the interval. @ @ @ @ @ @ Ç @Ç Pitch: Intervals/Rhythm: Compound Meter Review |301 This page intentionally left blank MEMORIZATION STRATEGIES Interval Shapes Train your eye to immediately recognize numerical distances between notes on the staff; you can think of these as interval “shapes.” As you learn to do this, don’t think about the letter names of the pitches, but only the amount of space between the notes. Odd-numbered intervals (1, 3, 5, and 7) are always line-to-line or space-to-space. Even-numbered intervals are always line-to-space or space-to-line. Create flash cards to help you memorize the interval shapes. On the front of each card, write an interval on the staff. Do not use a clef; this will allow you to focus on the distance without worrying about letter names. On the back of each card, write the interval number. Letter-name Distances Memorize interval distances between letter names without using the staff (see Ex. 7.22). Your flashcards might look something like this: Plain Interval Qualities You might find it helpful to memorize all of the “plain” or “white-key” intervals—those that contain no sharps or flats. Once you have done this, simply use the accidentals (if present) to find the quality. If you practice this method diligently, you will find that even large intervals with accidentals will simply come to you. (For example, you will look at Memorization Strategies |303 C-sharp ↑ A and just know it’s a minor sixth, without any intervening calculations.) As a further shortcut, you need memorize only seconds, thirds, and fourths, and then remember to flip the quality when they invert to sevenths, sixths, and fifths. Seconds and Sevenths: all plain seconds are major, except E ↑ F, and B ↑ C (both m2). Inverted: all plain sevenths are minor, except F ↑ E and C ↑ B (both M7). Thirds and Sixths: plain major thirds occur on C, F, and G. Plain minor thirds occur on D, E, A, and B. Inverted: plain minor sixths have C, F and G as the upper note. Plain major sixths have D, E, A, and B as the upper note. Fourths and Fifths: all plain fourths are perfect except F ↑ B (augmented fourth). 304| Memorization Strategies Inverted: all plain fifths are perfect except B ↑ F (diminished fifth). For half steps and whole steps: • All whole steps are major seconds (for example, A-flat ↑ B-flat). • All diatonic half steps are minor seconds (for example, F-sharp ↑ G). • All chromatic half steps are augmented unisons (for example, C ↑ C-sharp). Although it is true that every interval is made up of a series of half steps (for example, a major third is four half steps), you should avoid counting half steps to calculate interval qualities. It simply takes too long; interval recognition should be fluent and instantaneous. IDENTIFYING INTERVALS IN A MUSICAL CONTEXT When identifying the intervals in a notated piece of music, keep in mind: • Always remember to apply the key signature. For example, what appears to be a C on the staff may actually be a C-sharp. • An interval is a distance, not a direction. For example, the distance between F-sharp and the D above it is always a minor sixth. It does not matter whether the interval ascends melodically, descends melodically, or is played harmonically. • If you prefer to use the lower note to calculate the interval, remember to do so even when the higher note comes first. • If you calculate intervals using the major scale, remember to treat the bottom note of the interval as do, regardless of the overall key signature. In Figure 7.19, several intervals are labeled, and an explanation of each is given in the text below. Identifying Intervals in a Musical Context EBSIT E W Figure 7.19. Hymn Tune “St. Louis” (“O Little Town of Bethlehem”). |305 Intervals 1 and 2. The distance between E-sharp and F-sharp is a minor second; this true for both directions, up and down. Measure from the E-sharp. E-natural to F-sharp is a major second, so E-sharp to F-sharp is a minor second. (It is also a diatonic half step.) 3. Measure from the F-sharp. In the key of F-sharp major, there is an A-sharp, which would create a major third. Because this interval, F-sharp to A, is one half step smaller, it is a minor third. 4. Measure from the G up to the A. Because A is present in the key of G, this interval is a major second. 5. Measure from the B up to the G. In the key of B major, there is a G-sharp, which would create a major sixth. Because this interval, B to G, is one half step smaller, it is a minor sixth. 6. Measure from the B up to the E. Because there is an E in the key of B major, this interval is a perfect fourth. 7. Measure from the D up to the E. Because E is present in the key of D major, the interval is a major second. 8. Measure from the A up to the E. Because E is present in the key of A major, this interval is a perfect fifth. 9. Measure from A up to F-sharp. Because there is an F-sharp in the key of A major, this interval is a major sixth. KEYBOARD AND SINGING EXERCISES 7.1. Compound meter review. Review Exercises 6.1 and 6.2 from the previous chapter. Then sing the rhythm exercises below, individually or as a class. Sing using a neutral syllable and a pitch that is comfortable for your voice. 1. 2. 3. 306| Keyboard and Singing Exercises 4. 5. 7.2. Intervals. In Chapters 3 through 6, you learned to sing intervals in the major and minor scales. The following exercises use the same “tune” as the ones you already know, but this time you will name each interval after you sing it. 1. Intervals in the major scale. Ascending do do re, sol, ma - jor sec- ond, do per - fect fifth do ti, mi - nor sec- ond, do re, mi - nor sev - enth, do do fa, do, per - fect fourth, ti, ma - jor sev - enth, do per - fect fifth, fa, do do do per- fect oc- tave. per - fect fourth, ma - jor third, ma - jor sixth, Descending do, sol, mi, la, do do do la, mi, mi - nor third, mi - nor sixth, per- fect oc - tave. Keyboard and Singing Exercises |307 2. Intervals in the minor scale. @ @ @ Ascending @ @ @ @@ do do re, ma - jor sec- ond, do sol, per - fect fifth, do do, per- fect oc- tave. @ @ @ do @@ @ do sol, re, do @ do mi - nor sixth, fa, per - fect fourth, do te, mi - nor sev - enth, Descending do te, do mi - nor sev - enth, mi, mi - nor third, le, per - fect fourth, do fa, do, ma - jor sec ond, per - fect fifth, do do le, me, ma - jor third, mi - nor sixth, per- fect oc- tave. 3. Repeat the exercise using the harmonic and melodic minor scales. 4. Once you have mastered this exercise, try singing the intervals in random order. (For example: P5, M2, M6, etc.) 308| Keyboard and Singing Exercises 7.3. Intervals with inversions. This drill is based on Exercise 7.2. Sing each interval up from do, followed immediately by its inversion (singing from the high do to the same scale tone). 1. Intervals in the major scale. Keyboard and Singing Exercises |309 2. Intervals in the minor scale. @ @ @ do re, ma - jor sec- ond, @ @ @ do me, sol, ma - jor sixth, do @ @ @ 7.4. do le, ma - jor third, re, fa, do mi - nor sev - enth, do do do, per- fect oc- tave, do te, per - fect fourth, do mi - nor sev - enth, do me, mi - nor third, per - fect fourth, sol, per - fect fifth, @ @ @ do @ @ @ do do fa, per - fect fifth, mi - nor sixth, te, ma-jor sec-ond do do, per- fect oc - tave. Intervals with note names. Repeat Exercises 7.2 and 7.3, singing note names for each major and minor key instead of solfège. Goal for Exercises 7.5–7.8: ten consecutive correct answers. Compound meter patterns. a. Compose ten rhythmic figures, each worth one dotted-quarter-note beat in compound meter. (Choose from the patterns given in Chapter 6, Ex. 6.1, or make up your own.) b. Write each figure on a separate index card. c. For each drill, your instructor or study partner will choose one or more cards (as indicated.) d. She or he will then play the rhythmic figure given below, substituting the chosen rhythm(s) for the blank beat(s). Notate the missing beat(s). 310| Hearing Exercises le, HEARING EXERCISES 7.5. 1. Instructor chooses one card. Notate beat 2 of measure 1. 2. Instructor chooses two cards. Notate beats 2 and 3 of measure 1. GE 7.6. LE AL N ✪ CH 3. Instructor chooses three cards. Notate beats 2, 3, and 4 of measure 1. Hearing ascending intervals. Your instructor (or study partner) will play an ascending interval, chosen from those present above do in the major and natural minor scales (see Ex. 7.2). Ascending intervals: M2, m3, M3, P4, P5, m6, M6, m7, M7, P8 Sing back the interval first on a neutral syllable, then with solfège, and then with the interval name. (Calculate the interval by treating the bottom note as do.) 7.7. Hearing descending intervals. Your instructor (or study partner) will play a descending interval, chosen from those present below do in the major and natural minor scales. (See Singing Ex. 7.2 and 7.3.) Descending intervals: m2, M2, m3, M3, P4, P5, m6, M6, m7, P8 Hearing Exercises |311 Sing back the interval first on a neutral syllable, then with solfège, and then with the interval name. (Calculate the interval by treating the upper note as do.) Your instructor plays this. Listen, and sing back the pitches on a neutral syllable… nah …then with solfège… nah do sol …then with the interval name. perfect fourth Hint: If you have trouble with Exercises 7.6 and 7.7, sing the major and natural minor scales to help you measure the interval with your voice. 7.8. LE AL N CH GE ✪ Hearing harmonic intervals. Repeat Exercises 7.6 and 7.7, but this time your instructor will play each interval harmonically (both notes together). You will then need to separate the notes in your mind, sing the two notes melodically, and name the solfège syllables and the interval. Your instructor plays this. Listen, separate the pitches in your mind, and sing them back on a neutral syllable… nah …then with solfège… nah do re …then with the interval name. minor seventh INFORMED LISTENING: EXAMPLES FOR STUDY Each of the following pieces highlights a specific interval. Listen to each, and read the explanation that follows. Then sing back the pitches that make up the interval(s) described. If you have trouble recognizing the interval, try matching the notes on the piano or on your instrument. Then calculate the interval from the pitch names. The key for each piece is given; this will allow you to hear solfège syllables for all the intervals and place them in the context of the key. 312| Informed Listening: Examples for Study 7.9. Johannes Brahms, Waltz, Op. 39, No. 15 Key: A major What to listen for: • The melody begins with a major third down and up: mi-do-do-mi-mi C# ↓ A – A ↑ C# – C# 7.10. Carole King “(You Make Me Feel Like a) Natural Woman,” from Tapestry Key: A major What to listen for: • The singer’s melody begins with a minor third down and up on the words “Lookin’ out. . . .” sol-mi-sol E ↓ C# ↑ E • The first chorus is entered via a major sixth on the words “‘Cause you . . .” (at about 0′48″). sol-|mi E ↑ C# 7.11. Ben Folds Five, “Boxing,” from Ben Folds Five Key: D major What to listen for: • The first four melody notes of the piano introduction contain a perfect fifth up, major second up, and augmented fifth down. Try matching these four notes at the piano. sol-|re-|mi-le A ↑ E ↑ F# ↓ B∫ Note the use of le (B-flat) in a major key. Why does it make sense to call this pitch B-flat instead of A-sharp? 7.12. Martin Nolan, “Goodman’s Slip Jig,” from Bright Silver Dark Wood Key: D major1 What to listen for: • The tonic is heard first; then the melody begins with a quick leap of an ascending perfect fifth. do-sol D↑A 1 A more accurate interpretation would be D Mixolydian, as a lowered seventh (C-natural) is prevalent throughout the melody. Modes are discussed in Appendix D. Informed Listening: Examples for Study |313 7.13. Wolfgang Amadeus Mozart, “Allegro” (Movement I) from Eine Kleine Nachtmusik Key: G major What to listen for: • The piece begins with a perfect fourth, down and up: do-|sol-do G↓D↑G • Beginning at about 0’ 21”, a contrasting melody begins with a major second up. The interval is heard again at about 0’29”. sol-la D↑E 7.14. Frederic Chopin, Prelude in C minor, Op. 24, No. 20 Key: C minor What to listen for: • The first interval heard is a minor second up and down: sol-le-sol G ↑ A∫ ↓ G • The last interval of the piece is a perfect octave up: do-|do C4 ↑ C5 INFORMED LISTENING: EXAMPLES WITH QUESTIONS Listen to each example several times, and answer the questions that follow. If you have trouble with some of the questions, find the notes on the piano, and then calculate the interval and solfège from the pitch names. 7.15. Booker T. and the MG’s, “One Who Really Loves You,” from Green Onions Key: C major For the first twenty seconds of the piece, the bass and rhythm guitar alternate between two pitches. 1. In solfège, they are ___ and ___. 2. In note names, they are ___ and ___. 3. The interval between the two pitches is ___. 314| Informed Listening: Examples with Questions 7.16. Shelby Lynne, “How Can I Be Sure,” from Just a Little Lovin’ Key: D major In the introduction to the song, the guitar alternates between two pitches. 1. In solfège, they are ___ and ___. 2. In note names, they are ___ and ___. 3. The interval between the two pitches is ___. 7.17. John Philip Sousa, “The Thunderer” Key: F major After a very short introduction, the melody begins in the flutes, trumpets, and clarinets at 0’04”. Identify the first two melody pitches. 1. In solfège, they are ___ and ___. 2. In note names, they are ___ and ___. 3. The interval between the two pitches is ___. 7.18. The Beatles, “Oh! Darling!” from Abbey Road Key: A major Identify the first two pitches of the song, occurring on the word “Oh.” 1. In solfège, they are ___ and ___. 2. In note names, they are ___ and ___. 3. The interval between the two pitches is ___. 7.19. Josef Haydn, “Kyrie,” from Mass No. 11 in D Minor (Nelson) Key: D minor Identify the two pitches sung at the first choral entrance on the word “Kyrie” (about 0’29”). 1. In solfège, they are ___ and ___. 2. In note names, they are ___ and ___. 3. The interval between the two pitches is ___. Key: See Question 3. LE AL N CH ✪ GE 7.20. Peter Gabriel, “I Have the Touch,” from Security 1. Listen from 3’41” to the end of the song. Name the descending interval you hear every time the word contact is sung: ___ 2. The first pitch of this interval is F-sharp. What is the second pitch? ___ 3. Listen through to the end of the song, and hum the note you think is the tonic. What pitch is it? (Answer with a letter name.) ___ 4. On the basis of the tonic you chose, what is the solfège of the interval above? ___ Informed Listening: Examples with Questions |315 DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 7.21. Memorize Exercises 7.2 and 7.3, and sing them where appropriate. 7.22. Drill interval numbers by speaking this exercise in a slow, steady rhythm: Repeat the exercise starting from each of the seven letter names. (Start on B, then C, etc.) 7.23. Drill plain interval qualities by speaking the next exercise in a slow, steady rhythm. œ œ $ % œ œ $ ' œ œ œ œ Œ œœ œ œ œ œ œ Œ œœ œœœ PD MRU VHF RQG SHU IHFW IRXUWK $ % $ % & $ & ' ( œ œ œ œ Œ & PL QRU WKLUG œ œ $ ( œ œ œ SHU IHFW ILIWK œœœœ $ % & ' HWF 7.24. Listen carefully to any music that you happen to hear as you go about your day, and try to analyze the intervals you hear: a. Decide if the piece is in a major or minor key. b. Sing the tonic, and then the first note; name the interval. (Use solfège to help you.) c. Sing another important note in the song, compare it with the tonic, and name the interval. (You might choose the highest note in a passage, or the first note of the chorus, or a note that occurs on a certain lyric, etc.) CLASSROOM ACTIVITIES 7.25. Intervals in the scale (Point and Sing) This activity is based on Exercise 7.2. a. On the board, write solfège syllables for the major scale in a vertical line from lowest to highest. b. A leader will establish a tonic and then dictate an interval by pointing to do, and then another scale degree. The leader may dictate ascending intervals starting with the low do, or descending intervals starting from the high do. 316| Classroom Activities c. The class responds by singing the correct pitches with the solfège syllables, and then with the name of the interval. For example: 7.26. Variation. Repeat Exercise 7.25 using the natural minor scale. (For an extra challenge, use the harmonic and ascending melodic minor scales.) For example: 7.27. Interval inversions. Perform Exercise 7.3 as a call-and-response: One leader will sing do up to any scale degree. a. The class repeats the pitches and names the interval. b. The class then sings the high do down to the same scale degree. c. The class repeats the new pitches with the name of the inverted interval. For example: 7.28. Variation. Repeat Exercise 7.27 using the natural minor scale. (For an extra challenge, try harmonic and ascending melodic minor scales.) For example: Classroom Activities |317 7.29. Variation. Choose a key for the day and repeat Exercises 7.25–7.27 using pitch names. For example: 7.30. Quick intervals. Use this activity at the beginning of class (or your study session) to warm up your mind: a. Write a clef of your choice and six blank measures on the board. b. Student 1 chooses two flat notes and writes them in measures 1–2. c. Student 2 chooses two sharp notes and writes them in measures 3–4. d. Student 3 chooses two natural notes and writes them in measures 5–6. e. The instructor announces an interval for the day and chooses six students, one for each note on the board. Each student must write that interval above and below his assigned note. 7.31. Impromptu rhythm composition (compound meter review). 1. Each student composes one dotted-quarter-note beat of rhythm on an index card, choosing from the patterns given in the previous chapter (Ex. 6.1) or composing new ones. If the class has a small number of students, each student may compose two or three cards. 2. Collect and shuffle the cards. 3. Choose a compound meter (six-eight, nine-eight, or twelve-eight) and compose a rhythmic exercise by selecting several cards at random. For example, if you want a four-measure exercise in nine-eight, choose twelve cards. 4. Write the exercise on the board, and perform it as a class. 5. Optional: choose several students to go to the board; each will replace one note with a rest of the same value. Perform the altered rhythm. 6. Optional: choose several students to go to the board; each will add one tie between beats or over a bar line. Perform the altered rhythm. WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 7 online drills and quizzes at www.oup.com/us/root. 318| Written Exercises 7.32. Identify each interval in the next example by number and quality. All intervals in this exercise are major, minor, or perfect. Question 1 has been completed for you. 7.33. Identify each interval by number and quality. This exercise includes major, minor, perfect, augmented, and diminished intervals. The first answer is given. Written Exercises |319 7.34. These intervals are all thirds. Identify the quality of each. 320| Written Exercises 7.35. These intervals are all sixths. Identify the quality of each. Written Exercises |321 7.36. The next intervals are all sevenths. Identify the quality of each. 322| Written Exercises 7.37. For each question, build the requested interval above and below the given note. Write your two answers as quarter notes, and be sure to write the interval above first. The first answer is given. 7.38. Each interval given is major, minor, or perfect in quality. a. Identify the given interval. b. In the two blank measures, alter the interval to make it augmented in two ways. c. Do not change the letter names of the given notes; only add accidentals. Three sample questions are given. Written Exercises |323 324| Written Exercises 7.39. Each interval given is major, minor, or perfect in quality. a. Identify the given interval. b. In the two blank measures alter the interval to make it diminished in two ways. c. Do not change the letter names of the given notes; only add accidentals. Three sample questions are given. Written Exercises |325 7.40. For each question, build the requested interval above and below the given note. Write your two answers as quarter notes, and be sure to write the interval above first. The first answer is given. 326| Written Exercises 7.41. For each question, write the correct interval in the blank, using the proper abbreviation and numeral. Do not include any doubly augmented or doubly diminished intervals in your answers. Question #1 has been completed for you. What interval is . . . 1. The inversion of a minor third? M6 2. The inversion of a major seventh? ___ 3. The inversion of a perfect fifth? ___ 4. The inversion of a major sixth? ___ 5. The inversion of a major third? ___ 6. The inversion of a minor second? ___ 7. The inversion of a perfect fourth? ___ 8. The inversion of a minor seventh? ___ 9. The inversion of an augmented second? ___ 10. The inversion of a diminished third? ___ 11. The inversion of a perfect unison? ___ 12. The inversion of an augmented fourth? ___ 13. The inversion of an augmented sixth? ___ What interval is . . . 14. Enharmonic to a minor third? ___ 15. Enharmonic to a diminished seventh? ___ 16. Enharmonic to a minor sixth? ___ 17. Enharmonic to an augmented fifth? ___ 18. Enharmonic to a perfect fourth? ___ 19. Enharmonic to a perfect unison? ___ 20. Enharmonic to a major second? ___ 21. Enharmonic to a diminished fifth? ___ 22. Enharmonic to a diminished fourth? ___ 23. Enharmonic to a minor second? ___ 24. Enharmonic to a diminished sixth? ___ 25. Enharmonic to an augmented seventh? ___ 26. Enharmonic to a minor seventh? ___ Written Exercises |327 EBSIT 328| E W 7.42. Identify the harmonic intervals in this piece, and write them in the blanks between the staves. The exercise contains both simple and compound intervals. The first four answers are given. J. S. Bach, Minuet in A minor, measures 1–12 Written Exercises 7.43. For each example: a. Write the requested intervals above the given whole notes. Where only interval numbers are given, use only notes in the given key. If an interval quality is given, notate that quality of interval using the appropriate accidental. b. Use half notes in measures that require two intervals, and whole notes in measures that require one interval. c. Perform the resulting music with a classmate, singing, at the piano, or on your instruments. Canti firmi and counterpoint for exercises 7.43 and 7.44 composed by Steven B. Reale. 7.44. For each example: a. Write the requested intervals below the given whole notes. Where only interval numbers are given, use only notes in the given key. If an interval quality is given, notate that quality of interval using the appropriate accidental. b. Because there are two intervals per measure, use half notes for all your answers. Written Exercises |329 c. Perform the resulting music with a classmate, singing, at the piano, or on your instruments. 7.45. Compound meter review. Each question contains an excerpt from a song written in vocal notation. Rewrite the music with correct beaming for the meter indicated. a. The first example has been started for you. 1. Hector Berlioz, “Sur les lagunes, (Lamento)” from Les nuits d’été, Op. 7, No. 3, mm. 84–90 330| Written Exercises 2. Gabriel Fauré, “Tristesse,” Op. 6, No. 2, mm. 3–9 Written Exercises |331 3. Gabriel Fauré, “Aubade,” Op. 6, No. 2, mm. 23–27 b. Unscramble the notes to create an ascending scale, and write it in the blank measure given. c. Write the name of the scale in the blank beneath it. d. Two sample questions with answers are given. e. Only four scale types are used: major, natural minor, harmonic minor, and melodic minor (ascending). In some cases there are two possible correct answers (see Sample Question 2). 332| Written Exercises GE a. Identify the interval between notes, and write your answers in the blanks. LE AL N ✪ CH 7.46. Each question contains the notes of a scale, in random order. Written Exercises |333 For each example: b. Starting on the given note, rewrite the melody and invert it diatonically. In other words, reverse the direction of each interval, but keep all notes within the key signature. c. Keep all unisons as unisons; do not change them to octaves. d. Play the resulting melody on the piano or your instrument. e. The first few answers of each example are given. 1. Katherine Bates and Samuel Ward, “America the Beautiful,” mm. 9–16 2. Johannes Brahms, “Wiegenlied,” from Five Songs, Op. 49, mm. 3–10. 334| Written Exercises LE AL N ✪ GE a. Write the interval number only in the blanks between the notes. (Do not write the quality.) CH 7.47. b. Starting on the given note, rewrite the melody and invert it chromatically. In other words, reverse the direction of each interval exactly. Add accidentals wherever necessary to achieve the correct interval quality. GE a. Write the interval number and quality between the notes. LE AL N ✪ CH 7.48. For each example: c. Keep all unisons as unisons; do not change them to octaves. d. Play the resulting melody on the piano or your instrument. e. The first few answers of each example are given. 1. Jack Norworth and Albert Von Tilzer, “Take Me Out to the Ball Game” Written Exercises |335 2. Francis Scott Key and John Stafford Smith, “The Star-Spangled Banner,” measures 1–8 ANALYSIS AND COMPOSITION 7.49. Choose any melody from this book. a. If the melody uses a key signature, rewrite it without the key signature, applying the sharps/flats directly to the notes they affect. b. Identify the interval number and quality between each pair of the melody notes. c. Rewrite the melody, enlarging each interval by one half step. Keep the original direction (up or down) for each interval. Use enharmonic spellings wherever necessary to keep the notation uncluttered. d. Use accidentals and enharmonic intervals where appropriate to keep the notation simple. (Avoid double sharps and double flats wherever possible.) e. Keep all unisons as unisons. 336| Analysis and Composition f. Perform the resulting melody on the piano or your instrument. g. A sample melody is given. 3 0 0 4 &4 œ œ œ œ œ œ Ç D2ULJLQDOVRQJ G P P 4 & 4 œ œ œ #œ œ œ #Ç E5HZULWWHQVRQJ œ œ œ œ 0 0 œ œ #œ œ P P 0 Ç. 3 $ G Ç. œ HWF HWF œ 7.50. We will analyze the melody of the song “Silent Night,” and then you will write a composition based on it. Play or sing the song several times; then read the measure-by-measure analysis that follows. Measure 1 The first four notes of the song, labeled “Motive A,” have a distinct rhythm and shape (up a major second, down a major second, down a minor third). Analysis and Composition |337 Measure 2 Motive A is repeated exactly. Measure 3 The melody for this measure comes directly from Motive A: simply remove the second note of Motive A, and the result is note, repeated note, descending third. Measure 4 This measure is an exact repeat of measure 3, but the descending third is expanded to a descending fourth (B-flat ↓ F). Measures 5–6 Motive B is developed from the repeated note, an ascending third (inverted from the descending third), a short stepwise descent, and the original motive A. Measures 7–8 These measures contain an exact repeat of Motive B. Measure 9 The repeated note, ascending third, and the original rhythm from motive A are used. The descending thirds (E-flat ↓ C ↓ A) are an expansion of the descending seconds from measure 5 (B-flat ↓ A ↓ G). The highest note in the piece (E-flat 5) occurs in the middle of measure 9 and happens only once in the song. Measure 10 This measure contains an ascending third. Measure 11 This is the only measure that contains a second, third, and fourth–the most frequently used intervals in the song. Measure 12 The final note is the lowest in the song, and it happens only once. The song “Silent Night” is an example of a melody that works well because it is unified: • It contains a lot of repeated material, making the melody easy to remember. • It is constructed organically; that is, the entire song is essentially developed from the first four notes. • It uses very few intervals; seconds, thirds, and fourths predominate. (One minor seventh, D4 to C5, is used twice.) • It uses only a few rhythmic figures. With these observations in mind, compose your own piece based on the melody of “Silent Night.” Your composition will have the same structure and rhythm as the original, but with different pitches. Observe these guidelines to ensure that your composition is unified and consistent with itself: A. Preparing to compose your piece. 1. Choose a clef (treble or bass) and keep the range of your melody within the staff; use no more than two ledger lines above or below the staff. If your teacher recommends it, write for your own instrument. 338| Analysis and Composition 2. Choose any two simple intervals; each one should be major, minor, or perfect. You may use only these two intervals, plus their inversions. You may use the intervals in either direction, up or down. This will ensure that you have a variety of pitches but that your piece is still unified. 3. Write your two intervals here: ___ ___ And their inversions here: _______ _______ 4. Do not use a key signature in your piece. The fact that it is based only on intervals will cause it to use a variety of pitches that are not in a single key. 5. Use six-eight meter and the exact same rhythm as the original song. B. Putting your piece together: 1. Write your own Motive A in measure 1, using the rhythm above, but write new pitches using your chosen intervals. 2. Measure 2 should be an exact repeat of measure 1. Or, optionally, you may transform your Motive A in measure 2. (See Part C here for a list of transformations.) Label all transformations that you use. 3. In measure 3, the first two notes should be the same pitch, just as in the original song. The same goes for measures 4 and 5. 4. Measure 6 should contain an exact repeat or a transformation of Motive A. Measures 5–6 together will form Motive B, which should be repeated or transformed in measures 7–8. 5. Measure 9 should begin with a repeated note, just as in the original song. 6. The third note of measure 9 should be the highest note in your piece, and that note should happen only once. 7. The last note of your piece should be the lowest note, and that note should happen only once. 8. Label all intervals in your composition. C. If you wish, use the following transformations in place of exact repeats. 1. For reference, here is an exact repeat (no transformation). . & 68 b œ . œ œ œ 0RWLYH$ 0 3 3 bœ. œ œ œ. 0RWLYH$UHSHDWHG $ 0 3 3 (YHQWKRXJKLWLVQRWRQHRIWKHFKRVHQLQWHUYDOVIRUWKHSLHFHWKH DXJPHQWHGIRXUWKLVSHUPLVVLEOHEHFDXVHLWLVQHFHVVDU\IRUWKHUHSHDW 2. Invert the motive chromatically. Analysis and Composition |339 3. Write the motive backwards by reversing the order of the pitches. This is called retrograde. 4. Invert the motive, and then write the inverted result backwards. This is called retrograde inversion. 5. Label all the transformations that you use. D. Other considerations: 1. Use occasional enharmonic equivalents to avoid writing double-sharps and double-flats. 2. Do not repeat the same note twice in a row, except: • Where it happens in the original song (these places are marked) • When you are using an exact retrograde (see C.3 above; the D5 is repeated) 3. The melody you write may sound strange to you because it is not in a major or minor key. This is by design; when constructing a piece based only on intervals, you can be sure that you are creating something entirely new, something that doesn’t sound like music you already know. Enjoy the creative process of constructing the melody. Once it is finished, listen for the musical unity that results from adhering to an organic structure. 4. Be sure to label all intervals and transformations in your finished composition. E. Sample compositions. Two sample compositions are given below. Sample 1 uses only exact repeats in the designated measures. Sample 2 uses the transformations explained in Part C. The intervals chosen for this composition are: • Perfect fourth and major third, and their inversions, namely, • Perfect fifth and minor sixth 340| Analysis and Composition 1. Sample composition using exact repeats (no transformations) Rufus Jaye, “Noisy Night” 2. Sample composition using transformations Rufus Jaye, “Noisy Night 2” Analysis and Composition |341 Chapter Goals Revisited Be sure that you have achieved all Chapter 7 Goals before proceeding to Chapter 8. • Identify simple intervals by number and quality. (pages 280–285, 286–287, 290– 294) • Build simple intervals above and below a given note. (pages 288–290) • Sing intervals above and below do in the major and minor scales, naming each interval by number and quality. (pages 299–301, 307, 310) • Hear and identify intervals above and below do in the major and minor scale, naming each interval by number and quality. (pages 311–312) • Invert a melody diatonically. (page 295) • Invert a melody chromatically. (page 296) • Invert an interval, and identify the resulting interval by number and quality. (page 297) • Recognize pairs of enharmonic intervals. (pages 297–298) • Identify compound intervals by number and quality. (pages 298–299) • Build compound intervals above and below a given note. (pages 298–299) • Hear and identify intervals between melody notes in a piece of music. (pages 305–306, 312–314) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. 342| Analysis and Composition CHAPTER 8 Chapter Goals PITCH: TRIADS RHYTHM: FOUR- AND SIXTEEN-BASED COMPOUND METER After you finish this chapter, you should be able to do the following, quickly and accurately: • Identify the root, quality, and inversion of any triad in simple position. • Spell any quality triad from a given root, third, or fifth. • Identify the root and quality of any triad in a musical context, arranged in multiple voices and octaves. • Sing triads of any quality, with and without the piano. • Hear and identify triad qualities in a piece of music. • Perform and notate basic rhythms in six-sixteen, nine-sixteen, and twelve-sixteen meter. • Perform and notate basic rhythms in six-four, nine-four, and twelve-four meter. TRIAD STRUCTURE AND QUALITY The following excerpt from a work by J. S. Bach was introduced in Chapter 6; you may recall that it features the melodic minor scale. Listen to the example online; if your class is large enough, try singing it in four parts. EBSIT E W Figure 8.1. Bach Chorale No. 16: “Es woll’ uns Gott genädig sein,” mm. 1–3 This example is made up of chords and passing tones. A chord is any group of pitches sounding together, though the term is generally accepted to mean three or more. (As you already know, two simultaneous pitches form a harmonic interval.) The passing tones (in parentheses) normally occur on the weak part of a beat, allowing a single voice to move stepwise between chord tones. Passing tones do not belong to the chord they embellish, so we will ignore them for now. In order to examine the chords more closely, we will take an inventory of all of the notes in each chord, remove any duplicates, and stack the chord in its most compact arrangement. We discover that all of the chords except one are triads. A triad is a three-note chord that can be arranged as two stacked thirds, with a fifth on the outside. When a triad is |343 arranged this way, we say that it is in root position. The three members of the triad are called the root, third, and fifth, as indicated in the example. A triad may be one of four qualities (or types), according to the type of third and fifth it contains above its root. 344| Quality Symbol Structure Major M Major third, perfect fifth Minor m Minor third, perfect fifth Diminished o Minor third, diminished fifth Augmented + Major third, augmented fifth Example Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter You can also the determine quality of a triad by examining its stacked thirds: Quality Symbol Structure Major M Major third, minor third Minor m Minor third, major third Diminished o Minor third, minor third Augmented + Major third, major third Example The Bach example contains major, minor, and diminished triads. We can identify each one by naming its root and quality. Although labeling systems vary, one popular method is to use uppercase letters for major and augmented triads (those with a major third on the bottom) and lowercase letters for minor and diminished triads (those with a minor third on the bottom). EBSIT E The major triad contains a major third and a perfect fifth above its root. Figure 8.2 shows several major triads, each written harmonically (with all notes sounding together) and melodically (with the notes sounding one at a time). A melodic triad is sometimes called a broken chord or arpeggio. W Major Triads Figure 8.2. Major triads written harmonically and melodically. Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter |345 Notice that each triad in Figure 8.2 contains its own arrangement of sharps or flats. In other words, there is no set pattern of accidentals that determines a triad’s quality. Instead, you may build a major triad easily and quickly by combining do, mi, and sol of any major scale. EBSIT E W Minor Triads A minor triad contains a minor third and a perfect fifth above its root. You can build a minor triad by combining do, me, and sol of any minor scale. To change a major triad to a minor triad, simply lower its third. Figure 8.3 shows all the major triads from the previous example, converted to minor triads. Figure 8.3. Major triads changed to minor triads. 346| Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter EBSIT E An augmented triad contains a major third and an augmented fifth above its root. To convert a major triad to an augmented triad, simply raise its fifth by a chromatic half step (Fig. 8.4). W Augmented Triads Figure 8.4. Major triads changed to augmented triads. The plus sign (+) is used to label an augmented triad. When building augmented triads, be sure to spell the fifth of the chord as an augmented fifth and not a minor sixth. For example, the fifth of the B augmented triad must be spelled as F-double sharp, not G-natural. Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter |347 EBSIT E W Diminished Triads A diminished triad contains a minor third and a diminished fifth above its root. To convert a minor triad to a diminished triad, lower its fifth by a chromatic half step. In the example below, minor triads are converted to diminished triads. Figure 8.5. Minor triads changed to diminished triads. The degree sign (°) is used to label a diminished triad. When building diminished triads, be sure to spell the fifth of the chord as a diminished fifth and not an augmented fourth. For example, the fifth of the A diminished triad above must be spelled as E-flat, not D-sharp. Summary of Triad Qualities The following chart shows the relationship of the four triad qualities to one another. For additional guidance as you study triads, see Memorization Strategies near the end of this chapter. a. Triad qualities, smallest to largest b. Triad qualities, largest to smallest 348| Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter • A chord is a group of pitches sounding together. • A triad is made up of three pitches that can be stacked as two thirds with a fifth on the outside. • The three members of a triad are called the root, third, and fifth. EP L A Y R • There are four triad qualities: o A major triad (M) contains a major third and a perfect fifth above its root. o A minor triad (m) contains a minor third and a perfect fifth above its root. o An augmented triad (+) contains a major third and an augmented fifth above its root. o A diminished triad (o) contains a minor third and a diminished fifth above its root. TRIAD INVERSIONS All of the chords in Figure 8.6 are G major triads, because they are all some arrangement of the notes G, B, and D. We say that triad 1 is in root position, because the root, G, is the lowest sounding tone or bass tone. When the third or the fifth is the bass tone, we say that the triad is inverted, as in triads 2 and 3. Every triad has three possible positions: root position (root in the bass), first inversion (third in the bass), and second inversion (fifth in the bass). EBSIT E W Figure 8.6. Triad positions. In addition to the labels “root position,” “first inversion,” and “second inversion,” the three triad positions are each assigned a number that labels the intervals above the bass note. • In root position, or % , the upper voices form a fifth and a third above the bass. # Because root-position triads are so common in music, they are often not labeled. If you see a triad without a numeric designation, assume it is in root position. • In first inversion, or ^ , a sixth and a third are present above the bass. This des# ignation is often abbreviated to “6.” • In second inversion, or ^ , a sixth and a fourth are present above the bass. $ Take care not to confuse the terms root and bass. In the example above, any of the three tones may appear in the bass, but the root is always G, no matter where it appears in the chord. (Likewise, B is always the third and D is always the fifth.) • The lowest-sounding tone in a triad is called the bass. EP L A Y R • When the root is in the bass, the triad is in root position. • When the third of the triad is in the bass, the triad is in first inversion, which is identified by the numeral 6. • When the fifth of the triad is in the bass, the triad is in second inversion, which is identified by the numerals ^ . $ Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter |349 EBSIT E W IDENTIFYING TRIADS IN A MUSICAL CONTEXT The three G major triads in Figure 8.6 are all voiced in simple position, meaning the notes are arranged immediately above the bass tone, within one octave, and without duplications. In actual music, triads may be spread across several octaves, with some pitches doubled. The bass note will always tell you the inversion, no matter how the tones above it are arranged. The two musical excerpts in Figure 8.7 demonstrate how to condense complex triads into simple position on paper. Notice that each triad is named according to its root, which is not necessarily its bass note. For inverted triads, the root-position spelling is given immediately below the pitch inventory for that chord. Figure 8.7. a. J. S. Bach, Chorale No. 16, “Es woll’ uns Gott genädig sein, mm. 1–3.” b. Johann Crüger, “Nun Danket All” (Second Tune), mm. 1–6. 350| Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter W EBSIT E In Figure 8.8, each triad is played as an arpeggio. We use the same process to identify the triads, stacking the notes in simple position as if all of them sounded simultaneously. Figure 8.8. W. A. Mozart, Piano Sonata No. 16 in C major, K. 545, mm., 18–22. EP L A Y • Condense all of its pitches into a single octave, keeping the original bass note on the bottom. This is called simple position. R To identify a triad in a piece of music: • Find the root of the triad. • Name the triad by its root, quality, and inversion. SIXTEEN- AND FOUR-BASED COMPOUND METER We will begin this section with a brief review of compound meter: • In compound meter, the pulse divides into three equal parts. • The pulse in compound meter is always represented by a dotted note. Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter |351 • In six-eight meter, there are six eighth notes per measure, packaged in two groups of three. The result is two dotted-quarter-note pulses. • In nine-eight meter, there are nine eighth notes per measure, packaged in three groups of three. The result is three dotted-quarter-note pulses. • In twelve-eight meter, there are twelve eighth notes per measure, packaged in four groups of three. The result is four dotted-quarter-note pulses. Sixteen-based Compound Meter In a sixteen-based compound meter, each pulse contains three sixteenth notes, resulting in a dotted-eighth-note pulse. (Remember, three of any nondotted note add up to a dotted note.) Each of the examples below contains a melody written in an eight-based compound meter, and then rewritten in a sixteen-based compound meter. Notice that the speed of 352| Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter the music does not change, even though the music “looks” faster. This is because the pulse note (either the dotted quarter or the dotted eighth) is set at the same speed. To convert an eight-based meter to a sixteen-based meter, reduce all of the note durations by half: dotted eighth notes become dotted sixteenth notes, sixteenths become thirty-seconds, etc. Six-sixteen is a compound duple meter. Six sixteenth notes are packaged as two dottedeighth-note pulses per measure. EBSIT E W Figure 8.9. “Silent Night” in six-eight and six-sixteen. Although the six-sixteen version of “Silent Night” looks more cluttered, it does have one advantage over the six-eight version: in six-sixteen, all pulse groups can be beamed together. This is not possible in six-eight because quarter notes (such as those in mm. 3 and 4) cannot be beamed. Nine-sixteen is a compound-triple meter. Nine sixteenth notes are packaged as three dotted-eighth-note pulses per measure. Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter EBSIT E W Figure 8.10. “Beautiful Dreamer” in nine-eight and nine-sixteen. |353 Twelve-sixteen is a compound-quadruple meter. Twelve sixteenth notes are packaged as four dotted-eighth-note pulses per measure. EBSIT E W Figure 8.11. Chopin, Nocturne in E-flat Major, in twelve-eight (as originally composed) and twelvesixteen. EP L A Y R • In a sixteen-based compound meter, the dotted eighth note represents the pulse. Each dotted eighth divides into three sixteenth notes. • Six-sixteen is a compound duple meter. Each measure contains two dottedeighth-note beats and six sixteenth-note divisions. • Nine-sixteen is a compound triple meter. Each measure contains three dottedeighth-note beats and nine sixteenth-note divisions. • Twelve-sixteen is a compound quadruple meter. Each measure contains four dotted-eighth-note beats and twelve sixteenth-note divisions. Four-based Compound Meter In a four-based compound meter, the pulse is represented by the dotted half note, which divides into three quarter notes. Four-based compound meter is not very common in music because it can be difficult to read accurately. Examine the two versions of “Beautiful 354| Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter Dreamer” in Figure 8.13. In the nine-eight version, the eighth notes are beamed in groups of three in order to clearly communicate divisions within the pulse. In nine-four, however, it is very easy for a performer to get lost among the quarter notes, especially in measure 3. Six-four is a compound duple meter. Six quarter notes are packaged as two dotted-half-note pulses per measure. EBSIT E W Figure 8.12. “Silent Night” in six-eight and six-four. Nine-four is a compound-triple meter. Nine quarter notes are packaged as three dotted-halfnote pulses per measure. Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter EBSIT E W Figure 8.13. “Beautiful Dreamer” in nine-eight and nine-four. |355 Twelve-four is a compound-quadruple meter. Twelve quarter notes are packaged as four dotted-half-note pulses per measure. EBSIT E W Figure 8.14. Chopin, Nocturne in E-flat Major, in twelve-eight and twelve-four. EP L A Y R • In a four-based compound meter, the dotted half note represents the pulse. Each dotted half divides into three quarter notes. • Six-four is a compound duple meter. Each measure contains two dotted-halfnote beats and six quarter-note divisions. • Nine-four is a compound triple meter. Each measure contains three dottedhalf-note beats and nine quarter-note divisions. • Twelve-four is a compound quadruple meter. Each measure contains four dotted-half-note beats and twelve quarter-note divisions. 356| Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter SUMMARY OF COMMON METER TYPES Simple Meter G G Simple duple Pulse Pulse division G G G Simple triple Pulse Pulse division Ç Ç Ç Ç Ç G G G G Ç Ç Ç Ç Simple quadruple Pulse Pulse division Compound Meter G G Compound duple Pulse division Ç Ç G G G Ç Ç Ç Compound triple Pulse division G G G G Compound quadruple Pulse division Pulse division Ç Ç Ç Ç Pitch: Triads/Rhythm: Four- and Sixteen-based Compound Meter |357 This page intentionally left blank MEMORIZATION STRATEGIES Recognizing Triad Qualities Here is a visually oriented shortcut that may help you recognize triads quickly. Write out triads on all seven possible roots as they appear on the staff without accidentals (i.e., on the white keys of the piano). We will call these “plain” triads, and sort them into three groups on the basis of quality. Memorizing the plain triads by group will greatly reduce your time and mental labor. For example, if you see an E triad with no accidentals, you could calculate the third E-G (minor), and the fifth E-B (perfect) and arrive at the conclusion that the triad must be minor. Or you could simply know that the chord is minor because you know that all plain E triads are minor. Applying equal accidentals to all members of a triad results in the same quality. If the triad in question is E∫-G∫-B∫, it remains minor. Likewise, the triad C#-E#-G# is major, and B∫-D∫-F∫ is diminished. Group 1 triads (C, F, G). Go to a piano, play a C major triad (C-E-G), and ask yourself how you would make that triad minor. You are likely to answer, “Lower the third one half step Memorization Strategies |359 to E-flat.” That is one way; the other is to leave the third where it is and raise the root and fifth by a half step (C#-E-G#). Both actions result in a minor triad. The same is true for all the triads in Group 1. Return to the piano, play the C major triad again, and imagine how you would change its quality to augmented. The simplest way is to raise the fifth one half step (G to G-sharp). On the other hand, you could leave the G where it is and lower the root to C-flat and the third to E-flat. In both cases, the result is still an augmented triad, containing a major third and augmented fifth from its root. 7RPDNHD*URXSWULDGDXJPHQWHG« # ww w www 0 b b www 0 ww w 0 w b b ww & www 0 # www & www # www «UDLVHWKHILIWK««25ORZHUWKHURRWDQGWKLUG & www 0 0 ww w w b b ww Repeat the process with the F major and G major triads. We can change any triad in Group 1 from major to augmented by sharping the fifth or flatting the root and third. Remember that to “augment” something means, literally, to increase its size. Whether we raise the top of the chord or lower the bottom, the triad ends up larger than it began. Play the C major triad a third time, and then change its quality to diminished. You might lower the third and fifth to E-flat and G-flat respectively, but you could also leave 360| Memorization Strategies the E and G in place and raise the root from C to C-sharp. The same method may be applied to the F and G triads. Summary of Group 1 triad qualities. Use the following visual cues to help you identify Group 1 triads quickly. • Plain C, F, or G = major • C, F, or G plus or = minor • C, F, or G plus or = augmented • C, F, or G plus or = diminished Group 2 triads (D, E, A). In Group 2, all plain triads are minor. To change any of them to major quality, simply add a sharp to the third, or add flats to the root and fifth. 7RPDNHD*URXSWULDGPDMRU« & www P # www 0 w & ww ww w P w b b ww www b b www «UDLVHWKHWKLUG««25ORZHUWKHURRWDQGILIWK & www ww w 0 P # www 0 # www P w b b ww P 0 P 0 0 Memorization Strategies |361 Go to the piano, play an A minor triad, and ask yourself how you would change its quality to augmented. You would probably raise the third to create an A major triad (A-C#-E), and then raise the fifth to make it augmented (A-C#-E#). Alternatively, you could start with the plain A minor triad and simply lower the root to A-flat, creating the augmented triad A∫-C-E. The same is true for all triads in Group 2 (D, E, and A). Play the A minor triad once again. The simplest way to make it diminished is to lower the fifth, resulting in A-C-E∫. Alternatively, you could raise the root and third, creating the diminished triad (A#-C#-E). The same pattern applies to all Group 2 triads. Summary of Group 2 Triad Qualities • Plain D, E, or A = minor • D, E, or A plus or = major • D, E, or A plus or = augmented • D, E, or A plus 362| Memorization Strategies or = diminished Group 3: the B triad. Group 3 contains only the B triad, which is diminished when all of its notes are natural. If we think of music as a foreign language, then the B triad is like an irregular verb: the simplest course of action is to memorize it in all of its forms. This example shows all four qualities of the B and B-flat triads. Remember that you can always double-check your work by calculating the quality of the third and fifth. This process is time-consuming, and need not be applied to every single triad on your assignments and exams. It is, however, useful for spot checks, and particularly helpful for the B triads, since they are not consistent with the visual cues for the other groups. Factoring Accidentals If a triad contains double sharps or double flats, simplify it by removing the same number of accidentals from each chord member. Hearing Triads in Root Position 1. First, decide whether or not the triad contains a perfect fifth. To do this, find the root and then sing do-sol, or the first four pitches of “Twinkle, Twinkle, Little Star.” If the pitches fit with the triad you hear, then the triad is either major or minor. (Proceed to step 2.) If the pitches do not fit, the triad is either diminished or augmented. (Proceed to step 3.) 2. If the triad is major or minor: • If a root-position major triad is played, you should hear do-mi-sol, the tonic major triad. You can also sing the first four pitches of “Oh When the Saints Go Marching In” (do-mi-fa-sol). If it fits with the triad you hear, then the triad is major. Memorization Strategies |363 • If a root-position minor triad is played, you should hear do-me-sol, the tonic minor triad. You can also sing the first four pitches of “Greensleeves” (dome-fa-sol). If it fits with the triad, then the triad is minor. 3. If the triad is augmented or diminished: • A diminished triad is made of two stacked minor thirds. Sing any two adjacent pitches. If the interval is a minor third (do-me), the triad is diminished. • An augmented triad is made of two stacked major thirds. Sing any two adjacent pitches. If the interval is a major third (do-mi), the triad is augmented. Recognizing Triad Inversions by Sight and Sound When identifying the position of a triad, first stack the notes in simple position without changing the bass note. Then you can quickly determine the root and the inversion using these visual cues: • A root position triad contains no gaps; all notes are evenly spaced. • A first-inversion triad has a gap at the top, because it is stacked third + fourth. • A second-inversion triad has a gap at the bottom, because it is stacked fourth + third. • When the triad is inverted, the root is the top note of the gap. This information is not only helpful on paper, but also quite useful to the ear. When you hear a triad, sing its pitches from the bass upward, and find the gap created by the interval of a fourth. (If the pitches are spaced evenly, then the chord is in root position.) If the chord is inverted, find the root at the top of the gap. Then move the root to the bottom, sing the chord in root position, and find the quality. KEYBOARD AND SINGING EXERCISES 8.1. Rhythmic patterns. Tempo goal: dotted-note pulse = 52 bpm. When you practice these patterns, begin by setting your metronome to the pulse division (the sixteenth note or quarter note). As you increase your speed, use your metronome to set the dotted-note pulse. a. Choose a comfortable pitch for your voice and sing the patterns in order using the counts given. Remember to use the second measure of each pattern to prepare for the next. b. Sing the rhythms out of order, leaping from one to the next randomly. Again, use the second measure to choose and prepare. c. Gradually increase the tempo of the exercise. Remember that accuracy is more important than speed. 364| Keyboard and Singing Exercises The rhythmic patterns for this chapter are the same as for Chapters 6 and 7, but they have been rewritten in six-sixteen and six-four meter. The patterns will sound identical to the ones you learned before, so you should focus on mapping the sounds you already know to the new time signatures. Patterns in Six-sixteen Patterns in Six-four 8.2. Variation. Write out all of the patterns above, but replace the first duration of beat three with the equivalent rest. Add the new patterns to your practice sessions. 8.3. Rhythm exercises. a. Each of the following exercises is in two parts, where Part 1 is a basic rhythm and Part 2 is the same rhythm with rests and/or ties added. b. Remember that four-based compound meters are more difficult to read because it is not possible to beam the pulse units. Before you begin, draw brackets around each dotted-half-note beat. c. Set your metronome to a slow-to-medium tempo, and perform Part 1 several times while finger-counting. Keyboard and Singing Exercises |365 d. Divide the class, so that one half performs Part 1 and the other performs Part 2 simultaneously. Those singing Part 2 should listen carefully to Part 1 in order to help accurately place the rests and ties. e. If you are working on your own, find a friend to help you do the exercises, or record yourself singing Part 1 and then play back Part 1 as you sing Part 2 over it. f. When singing the two parts together, choose any two pitches, and sing on a neutral syllable. g. Once you are ready, gradually increase the tempo. 1. 2. 366| Keyboard and Singing Exercises 3. 4. 5. Keyboard and Singing Exercises |367 6. 8.4. Playing and singing triads. The next exercises are written starting on A3, but you should begin on any pitch that is low and comfortable in your voice range. Play each exercise at the piano as you sing the letter names for the notes. Repeat the exercise on each of the white keys of the piano; if the pitches become too high for your voice range, drop one octave. 1. Major 2. Minor 368| Keyboard and Singing Exercises 3. Augmented 4. Diminished 8.5. Variations. 1. Repeat Exercise 8.4 using the same rhythm, but reverse the direction of the triads: start at the highest note and then sing downward and upward. For example: 2. Repeat Exercise 8.4 using the same rhythm, but improvise the order of the notes for each triad. 3. Repeat Exercise 8.4 without using the piano. Start by singing the triads on a neutral syllable to be sure that you are singing the correct pitches. Remember that if you need to check your pitch at the piano, you should play the note after you sing it, not before. Once you are ready, add the note names. Keyboard and Singing Exercises |369 LE AL N ✪ • G-sharp/A-flat • A-sharp/B-flat • C-sharp/D-flat • D-sharp/E-flat • F-sharp/G-flat 8.7. Triad quality chains. Play the next exercises at the piano while singing the pitches on a neutral syllable. Each exercise moves up or down a half step as it repeats. Keep repeating until you have reached the limit of your voice range. 1. 2. 4 w 3OD\ & 4 w w & 44 œ œ œ œ œ 0DMRU 6LQJ b www /RZHUWKLUG/RZHUURRWDQGILIWK Œ œ bœ œ œ œ 0LQRU 1HXWUDOV\OODEOH w & b b b ww bœ œ œ & bœ bœ 0DMRU 370| # # www 5HSHDWH[HUFLVHDKDOIVWHSORZHU HWF Œ Keyboard and Singing Exercises 0LQRU #œ œ #œ œ œ Œ Œ GE Repeat Exercise 8.4 starting on each of the black keys of the piano. Sing through each set of triads using both the flat and sharp names for each black key. CH 8.6. Perform exercises 3, 4, and 5 in the same manner, starting on a comfortable pitch in the middle of your range. 3. Minor triad (raise third) major triad (raise root and fifth) minor triad (repeat) 4. Major triad (raise root) diminished triad (raise fifth) minor triad (raise third) major triad (repeat) 5. Major triad (raise fifth) augmented triad (raise root) minor triad (raise third ) major triad (repeat) 8.8. Triads in musical contexts. All of the following excerpts are from songs that have been used as examples earlier in the book. Sing through the songs using solfège or a neutral syllable. You may also play them on the piano or your instrument. When you reach the triads marked, isolate those pitches and repeat them several times, taking care to memorize the sound of each triad. Then continue with the song. Some examples include passing tones, enclosed in parentheses. Omit these as you isolate the triad pitches. 1. “When the Saints Go Marching In” uses root position major triads with and without passing tones. 2. “Amazing Grace” uses major triads in root position and second inversion. Keyboard and Singing Exercises |371 3. The last phrase of “Silent Night” contains a diminished triad in root position and a major triad in first inversion. 4. The first phrase of “Greensleeves” contains a root-position minor triad with a passing tone, and two root-position major triads (both descending). 5. “When Johnny Comes Marching Home” begins with a second-inversion minor triad that includes a passing tone. HEARING EXERCISES Goal for Exercises 8.9–8.11: Ten consecutive correct answers before moving to the next level. 8.9. Hearing triads in root position. Your instructor or study partner will play a rootposition triad as an arpeggio up and down. Sing back the pitches on a neutral syllable and identify the triad quality. Work through the following levels in order. 1. Major and minor triads only. 2. Augmented and diminished triads only. 3. All four triad qualities in root position. ? œ #œ œ œ œ <RXULQVWUXFWRUSOD\VWKLV œ #œ œ œ œ /LVWHQDQGVLQJEDFNWKHSLWFKHV RQDQHXWUDOV\OODEOH«DQGWKHQLGHQWLI\WKHWULDGTXDOLW\ PDMRU QD QD QD QD QD 372| Hearing Exercises 8.10. Hearing inverted triads. Your instructor or study partner will play an inverted triad as an arpeggio up and down. Sing back the pitches on a neutral syllable and identify the triad quality. Work through these levels in order: 1. Practice major triads in all three positions (root, first inversion, and second inversion). 2. Practice minor triads in all three positions. 3. Combine all positions of major and minor triads. 4. Add diminished triads in root position and first inversion. 5. Add the augmented triad. 8.11. Repeat Exercises 8.9 and 8.10 with these variations: a. The instructor will play only an ascending arpeggio. b. The instructor will play only a descending arpeggio. c. The instructor will play the triad harmonically. (Separate the pitches in your mind and sing them back as an arpeggio.) INFORMED LISTENING: EXAMPLES FOR STUDY The pieces in this exercise contain a variety of triad qualities and inversions. Listen to them, and sing back the pitches that make up the triad indicated in the explanation. 8.12. The Beatles “I Will” from The Beatles (White Album) The song begins with a pick-up followed immediately by a major triad in root position: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ ti-do-sol-mi-do major triad 8.13. Muzio Clementi, “Allegretto” (Movement 1) from Sonatina in G Major, Op. 36, No. 2 The right-hand melody begins with a G major triad in first inversion (m. 1), which is soon followed by the same triad in second inversion (m. 5). Later in the piece (at about 0′48″ and again at 1′27″), the same rhythmic motive occurs, this time using the pitches of a B diminished triad: Informed Listening: Examples for Study |373 8.14. Alicia Keys, “Fallin’,” from Songs in A Minor After a short vocal introduction, a series of arpeggios are heard in the piano and continue throughout the song. The triads, listed below, all last two beats. Try to find them on the piano and play along with the song. • E minor, first inversion • D major, second inversion • E minor, first inversion • D major, first inversion 8.15. Ben Folds Five, “Boxing,” from Ben Folds Five During the piano introduction, at about 0′12″, listen for an A augmented triad on beat 3, followed by a D major triad on the next downbeat. The motive happens twice. Find the pitches at the piano and play along with the recording. 8.16. Wolfgang Amadeus Mozart, “Menuetto” from Symphony No. 40 in G Minor, K. 550 The opening melody contains a second-inversion G minor triad followed by a root-position G minor triad in measures 3–4. 8.17. Johannes Brahms, “Bitteres zu sagen denkst,” Op. 32, No. 7 The first four notes of the piano introduction form an ascending minor triad in root position. The singer echoes the triad when he enters. INFORMED LISTENING: EXAMPLES WITH QUESTIONS Listen to each example several times and circle the correct answers from the choices given in brackets. If you have trouble, try matching the pitches you hear at the piano. 8.18. Maurice Ravel, “Pavane de la Belle au bois dormant,” from Ma Mère l’Oye (Mother Goose) The first three notes of the melody form a(n) [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. 8.19. Frederic Chopin, Prelude in D-flat Major (“Raindrop”), Op. 24, No. 15 The first three notes of the melody form a(n) [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. 8.20. The Beatles, “Blue Jay Way,” from Magical Mystery Tour The singer’s first five notes form a(n) [major / minor / augmented / diminished] triad in root position. 374| Informed Listening: Examples with Questions 8.21. Franz Josef Haydn, “Allegro” (Movement III) from Cello Concerto in D Major The rhythm of the first four measures is given below. Listen for the two triads marked “A” and “B,” and then circle the correct answers from the choices given. Both triads are in root position. 1. Triad A is [major / minor / augmented / diminished]. 2. Triad B is [major / minor / augmented / diminished]. 8.22. Gabriel Fauré, “Au Cimetière,” Op. 51, No. 2 The piano introduction consists of a repeated [major / minor / augmented / diminished] triad played harmonically. 8.23. Wolfgang Amadeus Mozart, “Kyrie” from Mass in C Minor, K. 427 The first eight notes of the melody form a(n) [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. 8.24. The Beatles, “Oh! Darling!” from Abbey Road The first sound you hear is a triad played by the guitar, just before the voice enters. This triad is [major / minor / augmented / diminished]. Note: the same chord is heard at the end of the bridge, at 1′40″ and 2′46″. 8.25. Ludwig van Beethoven, “Allegretto” (Movement II) from Symphony No. 7 This piece begins and ends with a sustained chord. This chord is a(n) [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. 8.26. Beck, “The New Pollution,” from Odelay The song begins with three descending triads. 1. The first triad is [major / minor / augmented / diminished] and is in [root position / first inversion / second inversion]. 2. The next two triads are both [major / minor / augmented diminished] and in [root position / first inversion / second inversion]. 8.27. Stephen Sondheim, “It Would Have Been Wonderful,” from A Little Night Music (performed by Len Cariou and Laurence Guittard) At about 1′36″, the words “Go away” are sung on three pitches. These three pitches form a [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. Note: the same figure is sung later in the piece on the words “Simply lied” (2′56″) and “Here with him” (4′01″). 8.28. Johannes Brahms, Hungarian Dance No. 5 in G Minor The first three notes of the melody form a [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. Informed Listening: Examples with Questions |375 8.29. The Red Hot Chili Peppers, “The Adventures of Rain Dance Maggie,” from I’m with You The first three notes of the chorus (on the words “Hey now . . .”) form a descending [major / minor / augmented / diminished] triad in [root position / first inversion / second inversion]. INFORMED LISTENING: CHALLENGING EXAMPLES 8.30. John Williams, “The Raiders March,” from Raiders of the Lost Ark The first four notes of this melody make up a triad with a passing tone. 1. The triad quality is [major / minor / augmented / diminished] and it is in [root position / first inversion / second inversion]. 2. The passing tone falls between the [root / third / fifth] and the [root / third / fifth] of the triad. 8.31. The Beatles, “Yesterday,” from Help! The first five notes of the bridge (beginning about 0′39″ with the word “Why…”) form a triad with a passing tone. 1. The triad quality is [major / minor / augmented / diminished] and it is in [root position / first inversion / second inversion]. 2. The passing tone falls between the [root / third / fifth] and the [root / third / fifth] of the triad. DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 8.32. Memorize Singing Exercises 8.4 and 8.5 and sing them on a neutral syllable. As you sing, try to visualize piano keys, notes on the staff, fingerings on your instrument, or letter names for the pitches you are singing.1 8.33. Listen closely to music you hear throughout your day. Find and sing the tonic; then try to improvise triad arpeggios that fit with the music you hear. Throughout the song, try to notice when the chords change, and alter your triad arpeggio to match the new chord you hear. At this point, it is less important that you recognize the specific triad qualities that you hear, and more important that you focus on matching your triad pitches with those you hear in the song. 1 Don’t worry about singing the exact pitches that you visualize. For example, you may start on any comfortable pitch, but call it “C” for the purpose of the exercise. 376| Drills to Go CLASSROOM ACTIVITIES 8.34. Guided rhythm improvisation. 1. Choose eight rhythmic patterns, all in the same meter, from Exercises 8.1 and 8.2. 2. Write your choices on the board in two columns of four patterns each. 3. Set your metronome to a slow tempo to establish the pulse. (Use the dotted note as the pulse, not the beat division.) 4. Choose any pitch, and lead the class in singing the rhythms in order. Use a neutral syllable such as “nah” or “tah.” 5. Repeat step 3, but this time randomize the order of your choices. Start with any rhythm, and as the class reaches the landing measure, point to the next rhythm you want them to sing. (Be sure to give them enough time to anticipate where they’re going.) 6. If there are incorrect responses, repeat the pattern until the entire class sings it correctly, and then move on. 7. Continue the exercise for about one minute; then switch leaders. 8.35. Triad inversions. Sing Exercises 8.4 and 8.5 as a class. For Variation 2, each student will improvise in his or her own way, creating a “wash” of sound made up of the three triad pitches. 8.36. Triad inversions as chords. This activity is also based on Exercise 8.4. Divide the class into three groups, and have each group sing one of the exercises below on a neutral syllable. The instructor or a class leader will cue each group to enter on its assigned triad member and hold it until all three groups have entered. The leader will then have the class hold the resulting chord for a few seconds. Listen to each chord, noting its overall sound, and the position of your own pitch within it. 8.37. Triad quality chains. Sing the triad quality chains in Exercise 8.7 as a class. 8.38. Triad quality chains as chords. This activity is also based on Singing Exercise 8.7. Divide the class into three groups. Each group will sing and hold a degree of the major triad (root, third, or fifth); then the leader will cue one group at a time to shift up or down a half step to alter the triad quality. The class will sustain the sound continuously throughout the exercise; take a quick breath and reenter on pitch whenever necessary. Classroom Activities |377 WRITTEN EXERCISES Music Theory Skill Builder. For extra practice, try the Chapter 8 online drills and quizzes at www.oup.com/us/root. 8.39. Label each triad with its root (letter name) and quality (M, m, +, o). Questions 1–12 include only major and minor triads. Questions 13–25 include all four triad qualities. 8.40. Build the requested triads in root position with the given note as the root. 378| Written Exercises 8.41. Build the requested triads in root position with the given note as the third. 8.42. Build the requested triads in root position with the given note as the fifth. 8.43. Identify the root, quality, and position of each triad. All triads are in first inversion (6) or second inversion (^ ). $ Written Exercises |379 8.44. For each question: a. Build the requested triad in the position indicated. b. In the second set of blank staves, rewrite each triad, putting the odd-numbered questions in first inversion and the even-numbered questions in second inversion. Label each rewritten triad with root, quality, and inversion number. 8.45. For each excerpt, condense the triad into simple position on the staff below the music. As you do this, be sure to keep the original bass note on the bottom. Then identify the root, quality, and position of the chord. Ignore any notes in parentheses and any chords marked with an X. • For root position, do not use an inversion number. • For first inversion, use 6. • For second inversion, use ^ . $ 380| Written Exercises 1. Antonín Dvořák, “Largo” from Symphony No. 9, Op. 95 (Piano transcription by Oscar Posa), mm. 1–10 Pay close attention to the key signature. Written Exercises |381 2. Robert Schumann, Movement I from Albumblätter, Op. 99, mm. 9–12 3. Hymn Tune “Irish,“ mm. 1–8 382| Written Exercises 4. Hymn Tune “Duke Street,” mm. 5–8 8.46. Three pieces of music are given. The first is in six-sixteen, the second in nine-sixteen, and the third in twelve-sixteen. In each example, all of the notes in each measure are beamed together; this is incorrect. a. Rewrite each example, separating the beams at the appropriate spots. b. After you correct the example, rewrite it in the requested meters. Written Exercises |383 1. Trad., “Home on the Range” Rewrite with corrected beams: 384| Written Exercises Rewrite in six-four meter: Written Exercises |385 2. Trad., “A Country Wedding” (Slip-Jig) Rewrite with corrected beams: 386| Written Exercises Rewrite in nine-eight meter: Written Exercises |387 3. J. S. Bach: “Prelude No. 21” from The Well-Tempered Clavier, Book II. (mm. 1–6) Note: this excerpt is in two parts; be sure to rebeam both parts. 388| Written Exercises Rewrite with corrected beams: Rewrite in twelve-eight meter: Written Exercises |389 COMPOSITION 8.47. Compose a melody in six-eight meter, using the given instructions, template, and sample composition as a guide. Composition Template A. Overall structure and rhythm 1. Your composition will be sixteen measures long, and in six-eight meter. It will be structured in four phrases of four measures each. 2. You may choose treble or bass clef. Stay within three ledger lines above and below the staff. 3. Use the rhythms given in the template for measures 4, 8, 12, and 16. Do not use ties, and use rests only at the start of a beat. Otherwise, you may use any rhythms you wish. B. The process 1. To begin, choose a rhythm and a major or minor triad for the first beat. Compose the triad over the rhythm in any way you wish. 390| Composition 2. Proceed by a half step or whole step to the next beat. Use this new note as the root, third, or fifth of a new triad. 3. Repeat these steps for each beat until you reach measure 4. 4. On each beat, you may use any triad type in any position. 5. In measures 4, 8, 12, and 16, you may write any notes you wish. These measures must be entered by step, but you may proceed to the next phrase by any interval. C. Musical considerations (see sample composition). 1. Begin phrase 3 the same as phrase 1. Measure 9 will be identical to measure 1. 2. Where necessary, enharmonic spellings may be used to avoid double accidentals. (See m. 7, D-flat to B.) D. When you’ve finished composing: 1. Label each triad with its root, quality, and inversion. Be sure to calculate the inversion by the lowest-sounding note in the triad. No inversion label is needed for root position triads. 2. In measures 4, 8, and 12, label the intervals between the notes. E. Optional considerations The sample composition also adheres to the following guidelines. These suggestions will help to make your piece sound more musical; use them if you wish, but you are not required to do so. 1. In phrases 1 and 2, use only major and minor triads. In phrases 3 and 4, use all four triad qualities. Composition |391 2. Let your highest and lowest notes happen only once in the piece. 3. You may repeat any notes within the triad, but don’t repeat notes in succession (for example, F-F). Chapter Goals Revisited F. Sample Composition Be sure that you have achieved all Chapter 8 Goals before proceeding to Chapter 9. • Identify the root, quality, and inversion of any triad in simple position. (pages 343–349) • Spell any quality triad from a given root, third, or fifth. (pages 343–349) • Identify the root and quality of any triad in a musical context, arranged in multiple voices and octaves. (pages 350–351) • Sing triads of any quality, with and without the piano. (pages 368–372) • Hear and identify triad qualities in a piece of music. (pages 372–373, 372–375) • Perform and notate basic rhythms in six-sixteen, nine-sixteen, and twelvesixteen meter. (pages 351–353, 357, 364–368) • Perform and notate basic rhythms in six-four, nine-four, and twelve-four meter. (pages 354–357, 364–368) Once you are confident that you have achieved these goals with speed and accuracy, proceed to the next chapter. 392| Composition CHAPTER 9 Chapter Goals (POSTLUDE) PITCH: DIATONIC TRIADS RHYTHM: ADVANCED RHYTHMIC CONCEPTS After you finish this chapter, you should be able to do the following, quickly and accurately: • Identify diatonic triads by Roman numeral and quality in major and minor keys. • Spell diatonic triads in any major or minor key from a given Roman numeral. • Identify diatonic triads in a musical context, arranged in multiple voices and octaves. • Understand some basic principles of voice leading. • Sing I-IV-V-I (in minor, i-iv-V-i) in simple position using solfège and note names for each major and minor key. • Understand the basic functions of the primary triads (tonic, subdominant, and dominant). • Improvise simple patterns over music that uses the tonic, subdominant, dominant, and submediant chords. • Identify the use of some advanced rhythmic concepts in the music you hear. These include irregular meter, tuplets, supertriplets, subtriplets, hemiolas, duplets, and quadruplets. DIATONIC TRIADS IN MAJOR KEYS If we construct a triad on each degree of the scale, using only notes within that key signature, the result is a set of diatonic triads. Figure 9.1 shows all of the diatonic triads for the key of F major. EBSIT E W Figure 9.1. Diatonic triads in F major. Within the context of a key, we identify triads with Roman numerals, so that we may easily distinguish (for example) the subdominant scale degree (4) from the subdominant triad (IV). The major triads are labeled with uppercase Roman numerals, while lowercase Roman numerals are used for the minor triads. The diminished leading-tone triad is identified by a lowercase Roman numeral followed by the diminished symbol (o). Augmented triads are normally labeled with an uppercase Roman numeral and the augmented symbol (+), although they do not occur within the major scale. |393 Because the sequence of whole and half steps is constant for every major scale, the qualities of the diatonic triads also remain the same for any major key: • I, IV, and V are major. • ii, iii, and vi are minor. • viio is diminished. Memorize the triad qualities and the solfège syllables that make up each triad (do-mi-sol, re-fa-la, etc.). This will help you build and identify diatonic triads quickly and easily, in any key. DIATONIC TRIADS IN MINOR KEYS Because the minor scale has three forms, you might expect it to yield three different sets of diatonic triads. This is technically true, but some triad qualities are more common than others in minor-key music. Figure 9.2a shows the triads generated by the natural, harmonic, and ascending melodic minor scales; Figure 9.2b is a composite containing the most frequently used triad qualities for minor keys. In general, the triads shown on the 394| (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts top staff of Figure 9b are the most common in minor keys; the ones in parentheses are also used occasionally, and the remaining variants are quite rare. TT T a. Triads generated by all three minor scale forms @@@ T Natural @ TT minor i TTT i ii @@@ T Harmonic @ TT minor i L TTT L K TTT ii III K TTT III K TTT III TT T TT T TT T iv v K TTT VI TT T T K TT iv V K TTT K TTT vii K TTT V vi vii TT T K TTT IV VI L VII L EBSIT E @@@ T Melodic @ TT minor ii TTT W Figure 9.2. Diatonic triads in F minor. L b. Most frequently used triads in minor keys The composite scale used to build the triads above is almost a harmonic minor scale. The raised leading tone ti is present in the V and viio triads, but not in III, where it would create an augmented triad. Augmented mediant triads do sometimes occur in tonal music, but it is much more common for III to appear as a major triad. The mediant triad represents the relative major key (for example: in the key of A minor, the mediant is a C major triad). Recall from Chapter 5 that music in a minor key will often move to the relative major. A major-quality mediant triad allows a smooth transition between the two keys. EP L A Y • The qualities of the diatonic triads are the same for all major keys: R • Diatonic triads use only notes within the given key signature. o I, IV, and V are major. o ii, iii, and vi are minor. o viio is diminished. (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts |395 • The three forms of the minor scale yield a variety of triad qualities. In most cases: o i and iv are minor. o III, V, and VI are major. o iio and viio are diminished. • You may also encounter these triads occasionally: o The augmented mediant (III+) is sometimes used as a substitute for V, particularly in jazz and popular styles. o The major subdominant (IV) is used when a raised 6 (la) is present (usually due to the melodic minor scale). o The major subtonic (VII) and the minor dominant (v) are sometimes used when the subtonic scale degree te is present in the music. This sometimes happens in classical music, but it is more common in popular and jazz styles. HARMONY The study of harmony in music deals with the organization of chords–specifically, how chords interact with one another and with the melody they support. Once you understand the various types of triads that exist within a key, the next step is to learn how chords are organized to create a progression. The structure of harmony follows a common practice based on historical precedent and acoustics, although the conventions may vary with the style of the music and the era in which it was written. For example, the principles governing a blues progression differ from those in a Mozart symphony. As you continue your musical training, the study of harmony will occupy a great deal of your time and labor. This section is meant to be a very brief introduction to harmony and triadic functions, and it is by no means the final word on the matter. LABELING TRIADS IN MUSIC To apply Roman-numeral labels to triads in a piece of music, use a method similar to the one you learned in Chapter 8: 1. Inventory the pitches and condense them into simple position, leaving the original bass note on the bottom. 2. Find the root, quality, and inversion of the triad. 3. Instead of labeling the triad with a letter name, assign it a Roman numeral that represents the scale degree of its root. Be sure to use the root to determine the 396| (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts Roman numeral, keeping in mind that the root is not always the same as the bass note. EBSIT E W Figure 9.3. Johann Crüger, “Nun Danket All” (Second Tune). DIATONIC TRIAD FUNCTIONS Primary Triads The tonic, subdominant, and dominant are called primary triads because they can collectively generate all seven degrees of the major or harmonic minor scale. In other words, any tone in the scale can be harmonized with one of these three chords. In major keys, all three primary triads are major quality. In minor keys (as discussed above) the tonic (i) is minor, the subdominant (iv) is usually minor, and the dominant (V) is usually major (see Fig. 9.2b). I = IV = V = = do-mi-sol fa-la-do sol-ti-re do-re-mi-fa-sol-la-ti–do i = iv = V = = do-me-sol fa-le-do sol-ti-re do-re-me-fa-sol-le-ti-do *When is a tonic six-four not a tonic six-four? Some musical analysis systems avoid assigning Roman numerals to second-inversion triads because they function very differently from those in root position and first inversion. If you are continuing your music studies after this term, you will study six-four functions in much more detail later on; be prepared to abide by whatever system your teacher recommends. (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts |397 In general, the primary triads function as follows: • The tonic triad (I) defines the key and provides a stable home base. • The dominant (V) leads to the tonic, supporting the ti to do resolution (V to I). • The subdominant (IV) normally progresses to the V chord (IV to V). For this reason, it is sometimes is called a pre-dominant chord. • The subdominant may also progress to the tonic. This is sometimes called a plagal progression (IV to I). The guidelines result in these progressions: I-IV-I I-V-I I-IV-V-I The progression V-IV is not typical in common-practice music, though it does appear in some popular styles, especially rock and blues. Introduction to Voice Leading The subdominant (IV) is spelled fa-la-do, and the dominant (V) is spelled sol-ti-re. Each triad shares one common tone with the tonic triad. If we notate either one next to the tonic triad with the common tone kept in the same position, we discover that the remaining two voices are separated by only a step. This means that the chords can be arranged to move very smoothly from one to the next. This process is called voice leading. EBSIT E W Figure 9.4. Voice leading with tonic, subdominant, and dominant triads. Good voice leading also sets up tendency tones so that they can resolve properly. In the progression from IV to I: • do is the common tone • fa resolves to mi • la resolves to sol When proceeding from V to I: • sol is the common tone • ti resolves to do • re resolves to mi* * In some cases, re may also resolve to do. 398| (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts Figure 9.5 contains three basic chord progressions using the primary triads. On the top staff, the triads are written in simple root position or block chords; on the lower staves, they are written to be played on the piano. 1. Play the top staff only, and sing each triad arpeggio up and down as you play. You will find that the triads sound disconnected and choppy when arranged this way. 2. Play only the right hand of the piano part. Notice that all three pitches of each triad are present, but they are ordered so as to create smooth voice leading between the chord members. This version is easier to play because the hand does not have to move as much, and it’s easier to sing because the voice doesn’t jump around needlessly. 3. If you can, play both hands of the piano part. (If you cannot, then listen to the progressions online.) The left hand or bass voice plays the root of each triad in order to keep all chords in root position, and to provide a strong foundation for the pitches above. Although common tones are kept in the upper voices, strong root motion typically progresses by fourth or fifth, or upward by step. Figure 9.5. a. Progressions in C major. œœœ œœ œ , ,9 œœœ Ç œ &KRUGVZLWKSURSHUYRLFHOHDGLQJ ?4 œ 4 ÇÇ Ç œ , œœ œ œœ œ œœ œ œ , 9 ÇÇÇ œœœ œœœ œœ œ Ç œ œœ œ œ œ œœ œ œœ œ , , ,9 9 , ÇÇ Ç œœ œ œœœ œ EBSIT E & 44 œœœ ÇÇÇ W & 44 œœœ %ORFNFKRUGV b. Progressions in C minor. b & b b 44 œœœ œœœ ÇÇÇ œ œœœ n œœ ÇÇÇ ? b 4 œ œ Ç bb 4 œ %ORFNFKRUGV b & b b 44 œœœ œœœ ÇÇÇ &KRUGVZLWKSURSHUYRLFHOHDGLQJ , ,9 , Ç œœ œœ œœ œœ œ œ nœ œ œ œ œ œ , , œœ œœ ÇÇ œ nœ Ç , œ 9 œ œœœ œœœ n œœ œœœ ,9 9 , (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts |399 Secondary Triads The remaining triads in the scale, called secondary triads, are generally used to embellish or substitute for the primary triads. Each secondary triad shares two common tones with one of the primary triads. The mediant (iii) is spelled mi-sol-ti and the submediant (vi) is spelled la-do-mi. Each triad shares two common tones with the tonic. Either can be used to lead away from the tonic, often continuing to the subdominant. Figure 9.6. a. Voice leading from tonic to submediant. b. Voice leading from tonic to mediant. 400| (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts EBSIT E Figure 9.7. Progressions with subdominant and supertonic triads. W The supertonic (ii) often substitutes for the subdominant (IV), because the chords share two tones. When functioning this way, the supertonic often appears in first inversion (ii6) so that the bass line is unchanged. EBSIT E W The leading tone triad (viio) is a weaker substitute for the dominant (V), because the chords share two tones, ti and re. It often appears in first inversion, connecting I and I6. Figure 9.8. Progressions with the leading tone triad. (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts |401 • When identifying triads in music, use the root to find the Roman-numeral designation and the lowest-sounding note or bass note to find the inversion. • The primary triads are I, IV, and V (in minor, i, iv, and V). All scale tones are represented in the primary triads. • Each primary triad has a function: Y R o The tonic triad (I) establishes the key and provides a home base for the music. EP L A o The dominant triad (V) supports the leading tone and resolves to the tonic. o The subdominant triad (IV) leads to the dominant (V) or back to the tonic (I). • Voice leading is the arrangement of chord tones to produce smooth, singable lines. Proper voice leading maintains common tones and stepwise motion between chord members in the upper voices. • The secondary triads are the superonic (ii), the mediant (iii), the submediant (vi), and the leading-tone triad (viio) (in minor, iio, III, VI, and viio). • A secondary triad may embellish or substitute for a primary triad with which it shares common tones. ADVANCED RHYTHMIC CONCEPTS Irregular Meter Any meter that is not duple, triple, or quadruple is considered irregular or asymmetrical. Irregular meters often contain an odd number of beats, such as five, seven, or eleven. Because metric accents are not always obvious in irregular meters, a composer will often specify how notes are to be grouped within the measure: Figure 9.9. a. Five-four grouped as 3+2 EBSIT E W b. Five-four grouped as 2+3 b & b 45 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ Ç ? 74 œ œ œ. œ. œ œ œ œ œ œ c. Seven-four grouped as 3+2+2 ?œ HWF 402| œ. œ. œ œ œ bœ œ Ç HWF Ç. œ. œ. b œ œ œ œ œ œ œ œ Ç. (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts Ç Ç When an irregular meter uses a denominator of eight (or even sixteen), the metric groupings are normally shown with beams. At a fast enough tempo, a series of beats of differing lengths will emerge. In Figure 9.10, the grouping of eighth notes into twos and threes creates an alternation of quarter-note and dotted-quarter-note beats. Divide the class in half and perform the examples: Group 1 will sing the melody on solfège while Group 2 claps and sings the beats on the tonic pitch. Note that in example B, the arrangement of groupings changes in measure 5. Figure 9.10. Irregular meters with uneven beats. Subtriplets and Supertriplets When three equal sounds occupy a duration shorter than one beat, the figure is called a subtriplet. In Figure 9.11, three sixteenth notes occupy the time of one eighth note (or one-half beat in four-four). In a beat containing a subtriplet, beam the entire beat together, but break the secondary beam for clarity (m. 3, b. 4). Divide the class in half and perform (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts |403 Figure 9.11. Group 1 will sing the rhythm on a neutral syllable, and Group 2 will speak or sing the counts. EBSIT E W Figure 9.11. Subtriplets. When three equal sounds occupy a duration longer than one beat, the figure is called a supertriplet. In Figure 9.12, three quarter notes occupy the time of one half note. Because quarter notes do not have beams, a bracket is needed to group the three notes together. Perform Fig. 9.12 in the same manner as the previous examples. EBSIT E W Figure 9.12. Supertriplets. You may wish to think of the supertriplet as a syncopation of two one-beat triplets whose eighth notes are tied together in pairs. To hear how the durations combine, perform all 404| (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts three parts of Figure 9.13 individually, and then simultaneously. Parts 2 and 3 should sound identical. EBSIT E W Figure 9.13. Supertriplets as syncopated one-beat triplets. Irregular Tuplets A tuplet is any irregular division of the beat in simple or compound meter. Among the most common are the quintuplet, which divides the beat into five equal parts, and the septuplet, which divides the beat into seven equal parts. Other combinations are possible. EBSIT E W Figure 9.14. Tuplets. Duplets and Quadruplets A duplet or quadruplet is a two- or four-part division of the beat (respectively) in compound meter. Recall that compound meter normally divides the beat into three equal parts, so a division of two or four is considered irregular. These figures may be notated with a numeral 2 or 4 above the figure, or with dotted notes: a dotted-quarter note beat may contain two dotted-eighth notes or four dotted-sixteenth notes. (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts EBSIT E W Figure 9.15. Duplets and quadruplets. |405 Hemiola A hemiola is a specific type of syncopation that plays on the contrasting metric accents between simple and compound meters. The most common type of hemiola occurs when a composer writes a piece in six-eight and inserts a short passage of three-four. The overall length of each measure does not change, but the eighth-note grouping temporarily shifts from three groups of two to two groups of three. The result is a slight feeling of imbalance, which can sound delightful when used in moderation. Perform Figure 9.16, singing and clapping as indicated. Be sure to observe the notated accents. Notice that the meter signature does not change; the three-four grouping is simply imposed on the six-eight meter. EBSIT E W Figure 9.16. Hemiola in six-eight. The hemiola may also work in reverse: six-eight groupings may appear in a work otherwise written in three-four. Although three-four and six-eight are the most common meters in which to find hemiolas, they may occur in any meter. In Figure 9.17, a passage of twelve-sixteen appears in a piece in four-four meter. 44 œ EBSIT E W Figure 9.17. Hemiola in four-four. œ. œ œ œ œ œ œ +HPLROD WZHOYHVL[WHHQLQIRXUIRXU œ œ œ œ œ œ œ œ œ œ œ œ œ > > > > 406| œ œ œ œ œ œ œ œ œ œ œ œ œœœœœœœ (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts • Irregular or asymmetrical meters have an unusual number of beats, such as five, seven, or eleven. EP L A Y • A subtriplet occurs when three notes of equal length occupy a duration shorter than one beat. (For example, three sixteenth notes may occupy the time of one eighth note in four-four meter.) R • A supertriplet occurs when three notes of equal length occupy a span of time longer than one beat. (For example, three quarter notes may occupy the time of a half note in four-four meter.) • An tuplet is any irregular division of the beat in simple or compound meter. Quintuplets (five equal durations) and septuplets (seven equal durations) are common examples. • Duplets divide the compound-meter beat into two parts, instead of the typical three parts. • Quadruplets divide the compound-meter beat into four parts instead of three. • A hemiola imposes compound-meter groupings onto simple meter, or vice versa. (Postlude) Pitch: Diatonic Triads/Rhythm: Advanced Rhythmic Concepts |407 This page intentionally left blank SINGING EXERCISES 9.1. Diatonic triads in the major and minor scales. Tempo goal: 𝅘𝅥 = 66 bpm. These exercises are written in the key of A, but you should start on any pitch that is low and comfortable in your voice range. Sing each triad in the scale as an arpeggio, using the rhythm and solfège given. After you sing the solfège for the triad, sing its name, as shown in the example. Practice the exercise with and without the piano. 1. Diatonic triads in major Singing Exercises |409 2. Diatonic triads in minor 9.2. Variation. Choose a key for your practice session and repeat Exercise 9.1, singing note names instead of solfège. You do not have to sing the exercise in the actual key for which you name the notes; instead, use any key that is low and comfortable. 410| Singing Exercises 9.3. Chord progressions. Tempo goal: 𝅘𝅥 = 66 bpm. Select a comfortable pitch near the middle of your voice range, and sing these two chord progressions as arpeggios. Using solfège, sing the chord up and down using the given rhythm. 1. I-IV-V-I (major) 2. i-iv-V-i (minor) Singing Exercises |411 9.4. Variations. a. Using the rhythm above, sing each chord down, and then up. For example: solmi-do-mi-sol, la-fa-do-fa-la, etc. b. Using the rhythm above, improvise the order of the pitches in each chord. HEARING EXERCISES Goal for Exercises 9.5–9.7: ten consecutive correct answers. 9.5. Your instructor or study partner will play a major scale, and then a diatonic triad as a simple root-position arpeggio. Sing back the pitches, and name the triad and its quality. 9.6. Variation. Repeat Exercise 9.5 using the harmonic minor scale. Use a major mediant triad (III), a major dominant triad (V), and a diminished leading tone triad (viio). 9.7. Variation. Repeat Exercises 9.5 and 9.6, but this time your instructor will play each triad harmonically. Separate the pitches in your mind, sing them back as an arpeggio, and name the triad and its quality. INFORMED LISTENING: EXAMPLES FOR RHYTHM STUDY 9.8. Dave Brubeck, “Unsquare Dance,” from Time Further Out This work is in seven-four meter, grouped as two plus two plus three. As you listen, follow the bass and hand claps throughout the piece as you count the groupings aloud: 412| Informed Listening: Examples for Rhythm Study 9.9. Smokey Robinson and the Miracles, “It’s Christmas Time,” from Our Very Best Christmas The verse of this song alternates measures of three-four and five-four meter. Since three and five add up to eight, you might wonder why it is not in four-four, with different bar lines. The answer is in the metric accents. Count with the piano part as you listen to the introduction and verse: Listen to the passage again, but this time try counting measures of four-four. You will find that even though it is possible, it feels awkward to do so. At the chorus (beginning about 1′00″), the meter changes to regular four-four time. 9.10. The Allman Brothers Band, “Whipping Post,” from A Decade of Hits, 1969–1979 The introduction consists of seven measures in eleven-eight meter, grouped as 3+3+3+2. As you listen, count aloud: When the voice enters, the meter changes to a standard twelve-eight (four groups of three). The eleven-eight meter returns during the instrumental break that follows every chorus. 9.11. Frederic Chopin, Prelude in D-flat Major (“Raindrop”), Op. 24, No. 15 A septuplet is played in the melody on measure 4, beat 4. Notice that the performer takes some liberty with the tempo at this point. Informed Listening: Examples for Rhythm Study |413 A bit later in the piece, you will hear a figure containing subtriplets, played at about 0′34″ and again at about 0′46″ and 0′53″. Chopin chose to notate the figure using grace notes, which are small ornamental notes that are usually played just before the beat they are to embellish. In this piece, the performer usually plays the figure as a subtriplet on the “and” of beat 3. 9.12. The Association, “Along Comes Mary,” from Cherish: The Best of the Association The song proceeds with a typical four-four rock beat throughout. From 2′38″ to the end, a repeated supertriplet occurs in the vocal line. This rhythmic figure continues until the very last repetition, which is sung on four eighth notes. Listen carefully, and compare the two rhythms, notated below: 9.13. The Police, “Driven to Tears,” from Zenyatta Mondatta Listen for supertriplets in the instruments during the chorus. After the title of the song is sung twice, this rhythm is played prominently in the bass: 9.14. Frank Zappa and the Mothers of Invention, “Zomby Woof,” from Over-nite Sensation Listen for prominent quintuplets at 0′05″, 0′33″, and 0′58″. 9.15. The Beatles, “Girl,” from Rubber Soul This song may be felt in a quick twelve-eight. During the bridge 1′00″, duplets are prominent in the backing voices. The duplets recur in the same fashion during the guitar solo at 2′00″. 414| Informed Listening: Examples for Rhythm Study 9.16. The Jimi Hendrix Experience, “Manic Depression,” from Are You Experienced? This song can be felt in a very fast nine-eight meter. Beginning at about 2′29″, there is a call-and-response section between the drums and guitar. At 2′32″, the drummer plays a measure with duplets. This moment goes by very quickly; be sure to listen to the passage several times to hear the context of the duplets in the compound meter. 9.17. Wolfgang Amadeus Mozart, “Menuetto” from Symphony No. 40 in G Minor, K. 550 The recurring melody, shown below, forms a hemiola by imposing a feeling of three-two on the overall three-four meter of the piece. 9.18. Stevie Wonder, “Isn’t She Lovely,” from Songs in the Key of Life This song can be felt in a very fast twelve-eight. The singer’s first three pitches (“Isn’t she . . .”) are sung as quarter notes, forming a hemiola over the prevailing compoundquadruple meter. 9.19. The Eagles, “Hotel California,” from Hotel California This song ends with an extended call-and-response passage between the two guitars, beginning at about 4′20″. (This is commonly called a “guitar duel.”) Eventually, the guitars begin playing together, and there is a very prominent hemiola that begins at 5′39″ and repeats Informed Listening: Examples for Rhythm Study |415 until the end of the song. In this case, the hemiola consists of a six-eight grouping inside a measure of four-four. The verse of this song alternates between bars of four and three beats, creating an overall feeling of seven. As you listen, count aloud, beginning just after the brass introduction (about 0′08″). Listen carefully to the beat divisions, and you will hear that the song is actually in compound meter. (The measures above could be notated in twelve-eight and nine-eight.) The pulse regularly divides into three parts (count “TA-ka-da, TA-ka-da . . .”), but quadruplets appear in several places: • The lyric “nothing you can . . .” is sung on a quadruplet each time it appears. • The strings play repeated quadruplets just before the second chorus (about 1′31″). • At 2′53 ″, two trumpets begin playing a melody comprising duplets and quadruplets. (The melody is a quote from J. S. Bach’s “Invention No. 8 in F major.”) 416| Informed Listening: Examples for Rhythm Study LE AL N CH ✪ GE 9.21. The Beatles, “All You Need Is Love,” from Magical Mystery Tour ✪ CH The bass and drums set up a very fast four-four in the introduction to this song. At about 0′15″, the guitar enters with a hemiola created by playing a series of dotted eighth notes. This effectively creates measures of nine-sixteen over four-four. LE AL N GE 9.20. Phish, “First Tube,” from Farmhouse INFORMED LISTENING: CLASSROOM ACTIVITY All of the songs presented here use only tonic, subdominant, dominant, and submediant chords. Divide the class into three or four parts. (The bass part is optional.) For each song, play the recording and sing along with the chords, using the instructions and charts below. Basic exercise: for parts 1, 2, and 3, sing your line in solfège as the song plays, repeating your note on each beat. For example, Part 2 of “Cat in the Bag” (9′21″) will perform two quarter notes per measure: “mi-mi | fa-fa | mi-mi | re-re,” until you reach measure 8, which will be sung as a half note. You might find your part a bit boring because it contains only two or three pitches, and it doesn’t move very much. As you sing, focus on the changing chords around you, and your own position within each chord. When you repeat a passage, choose another starting note. Improvisation exercise: choose a starting note (do, mi, or sol), and as you sing, leap among the chord tones within each measure. For example, if you are singing “Cat in the Bag,” your improvisation might sound like this: “do-mi | fa-la | sol-do | re-re,” etc. The optional bass part provides the root of each chord throughout the song. If you choose to include this part, try to ensure that it is the lowest-sounding voice. If your class is large enough, choose a few low-voiced male students to sing the bass on solfège syllables. 9.22. Mark O’Connor, “Cat in the Bag,” from The New Nashville Cats • Wait for a two-beat introduction, and then begin. • Sing each repeated section twice; then repeat the whole piece. Informed Listening: Classroom Activity |417 9.23. BeauSoleil, “Chanson Pour Tommy,” from Cajunization • There is a three-note pickup; start on the first downbeat. • Repeat as desired until the end of the piece. 9.24. Creedence Clearwater Revival, “I Put a Spell on You,” from Creedence Clearwater Revival After the drum introduction, wait two full measures, and then begin on the downbeat just after the voice enters. • Sing four pitches per measure, and be aware that measure 15 contains two different chords. • Sing the song twice, and wait about ten seconds for an interlude. Then, sing it one more time. 418| Informed Listening: Classroom Activity • Since this song is in a minor key, be sure that you are singing the correct pitches for me and le. DRILLS TO GO Practice these drills away from the piano and away from the book, as you go about your day. 9.25. Memorize Exercises 9.1 through 9.4, and sing them in solfège where appropriate. 9.26. Try this exercise with a song you hear during the course of your day. It will work best if the song is very simple and has a repeating chord progression. a. Sing the tonic pitch, and decide whether the piece is in a major or minor key. b. Sing the tonic triad (do-mi-sol or do-me-sol) up and down. c. When you hear the tonic triad in the music, sing do, and hold it for as long as it is present in the music. (You will know it is present if you hear it “fit” with the music.) Once do is no longer present, move to the closest pitch that is present– likely re or ti. Then move back to do when you hear it again. Drills to Go |419 d. Repeat the process starting from mi (or me), and then from sol. e. As you create melodic lines using solfège, try to determine the chord structure of the song. WRITTEN EXERCISES 9.27. For each question: a. Name the major or minor key indicated by the given key signature. b. Label each triad with the correct Roman numeral for that key. Questions 1–10 are in major keys. Questions 11–20 are in minor keys. 420| Written Exercises 9.28. For each question, write the requested key signature and triad. Questions 1–10 are in major keys. Questions 11–20 are in minor keys. 9.29. For each question: a. Identify the key of the example. b. Condense each triad into simple position on the staff below the music. When you do this, be sure to keep the original bass note on the bottom. Ignore all notes in parentheses. c. Label each triad with the correct Roman numeral and inversion symbol. Whenever a chord is repeated in succession, label only the first occurrence. • For root position, do not use an inversion number. • For first inversion, use 6. 6 • For second inversion, use 4. Written Exercises |421 1. W. H. Monk, adapted from Palestrina, “Victory” 422| Written Exercises 2. Trad. English, “God Rest You Merry, Gentlemen” (mm. 1–4) Written Exercises |423 3. Rowland Prichard, “Hyfrydol” (mm. 1–4). Some answers are given. 424| Written Exercises 4. Solemnis Haec Festivas Written Exercises |425 Chapter Goals Revisited 5. Trad. English, “Greensleeves,” mm. 1–4 Once you have finished this chapter, you should be able to do the following, quickly and accurately: • Identify diatonic triads by Roman numeral and quality in major and minor keys. (pages 393–396) • Spell diatonic triads in any major or minor key from a given Roman numeral. (pages 393–396) • Identify diatonic triads in a musical context, arranged in multiple voices and octaves. (pages 396–397) • Understand some basic principles of voice leading. (pages 398–399) • Sing I-IV-V-I (in minor, i-iv-V-i) in simple position using solfège and note names for each major and minor key. (pages 409–412) • Understand the basic functions of the primary triads (tonic, subdominant, and dominant). (pages 397–398) • Improvise simple patterns over music that uses the tonic, subdominant, dominant, and submediant chords. (pages 417–419) • Identify the use of some advanced rhythmic concepts in the music you hear. These include irregular meter, tuplets, supertriplets, subtriplets, hemiolas, duplets, and quadruplets. (pages 402–407) 426| Written Exercises CODA At this point, it might be appropriate to say: “Be sure you have achieved all Chapter 9 Goals before proceeding with further music study.” In fact, if you have reached the end of this book feeling better-prepared to continue in your studies as a musician, then I am confident that Chapter 9 has served its essential purpose—as have the other eight. If you have chosen not to major in music or to pursue it professionally—even if you never take another music course—it is my sincere hope that Applied Music Fundamentals has made you a more astute listener and has raised your curiosity about the music you encounter in your everyday life. There is a common misconception among beginning musicians: “If I learn too much about music, it will lose its magic.” Those who think this miss the point of how deep and complex that magic can be. We will never be able to decode every mystery about the music that moves us, but our first step must be to understand the tools with which the composer crafted it. I wish you all the best as you continue this amazing journey. Jena Root Coda |427 APPENDIX A Alto Clef and Tenor Clef When a movable C clef appears at the beginning of a line of music, the middle of the symbol indicates the position of middle C (C4). Although the C clef may be placed on any staff line, it is most often found on the third line, where it is called the alto clef, or the fourth line, where it is called the tenor clef. The alto clef is the primary clef used by the viola, whose range spans both treble and bass staves. This clef is a convenient way to notate music without the need for constant clef changes or an overwhelming number of ledger lines. a. Music written on the grand staff 428| Appendix A b. The same music written in the alto clef The tenor clef is used occasionally by the trombone, bassoon, cello, and bass. All of these instruments normally read bass clef, but the tenor clef may be used to avoid excessive ledger lines during higher passages of music. a. Music written in the bass clef b. The same music, beginning in bass clef, then changing to tenor clef to avoid ledger lines Appendix A |429 APPENDIX B Singing Pitch Names Singing melodies on pitch names is a wonderful way to learn the content of scales, but it can be awkward, especially in keys with many sharps or flats. For example: This melody . . . . . . would be sung something like this: One solution is to use a system based on German key names. Natural notes are sung using normal letter names: 430| Appendix B Sharp notes are sung using the initial sound with the suffix “is” (pronounced “eese”). ? #### ## # œ 3URQRXQFHG $LV $FH œ œ œ œ œ œ œ %LV &LV 'LV (LV )LV *LV $LV %HHVH &HHVH 'HHVH (HVH )HHVH -HHVH $FH RU*HHVH Flat notes are sung using the initial sound with the suffix “ess.” The example above, in E-flat major, is sung: Appendix B |431 APPENDIX C Chromatic Solfège Syllables Solfège for raised scale tones Solfège for lowered scale tones Example: “The Mexican Hat Dance” 432| Appendix C APPENDIX D Modes Recall from Chapter 5 that the minor scale can be derived by rotating the major scale to begin on scale degree 6. Rotating the major scale to start on each of its degrees results in seven diatonic modes. & œ œ œ œ œ œ œ œ ,RQLDQ LGHQWLFDOWRPDMRU 1 & & & & & & 2 3 4 5 6 7 1 4 5 6 7 1 2 5 6 7 1 2 3 6 7 1 2 3 4 1 2 3 4 œ œ œ œ œ œ œ œ 'RULDQ 2 3 œ œ œ œ œ œ œ œ 3KU\JLDQ 3 4 œ œ œ œ œ œ œ œ /\GLDQ 4 5 œ œ œ œ œ œ œ œ 0L[RO\GLDQ 5 6 7 5 œ œ œ œ œ œ œ œ $HROLDQ LGHQWLFDOWRQDWXUDOPLQRU 6 œ œ œ œ œ œ œ œ 7 1 2 3 4 5 6 2 3 4 5 6 /RFULDQ 7 1 7 Appendix D |433 Another way to memorize modes is to compare each one to the major or minor scale with the same tonic. For example, compare the D minor scale with the D Dorian mode shown above. The natural minor scale contains a B-flat as its sixth degree, while the Dorian scale contains a B-natural. We can then generalize this comparison to all Dorian scales, and say that the Dorian mode is a natural minor scale with a raised sixth degree. Comparisons and solfège for all seven modes are given in the chart below. 434| Mode Scale Comparison Solfège Ionian Identical to major drmfsltd Dorian Natural minor with raised 6 d r me f s la te d Phrygian Natural minor with lowered 2 d rah me f s le te d Lydian Major with raised 4 drmfisltd Mixolydian Major with lowered 7 d r m f s l te d Locrian Natural minor with lowered 2 and 5 d r me f se le te d Appendix D APPENDIX E Seventh Chords When four notes are stacked in thirds, the result is a seventh chord. The added note forms the interval of a seventh with the root of the chord. The four chord members are called the root, third, fifth, and seventh. The quality of a seventh chord is found by combining the type of the triad (formed by the bottom three notes) and the type of the seventh (measured from the root). The chord shown below is called a major-major seventh chord, or more simply, a major seventh chord, because both the triad and the seventh are major-quality. There are four triad qualities and three possible seventh qualities (excluding the augmented seventh, which is enharmonic to an octave), resulting in twelve possible seventh chord qualities. Only five of the qualities are in common use in tonal music: Appendix E |435 A root-position seventh chord is labeled with the numeral 7; the three inversions are labeled with numerals derived from the intervals present above the bass note. 436| Appendix E GLOSSARY Accidental Agogic accent Anacrusis Articulation Asymmetrical meter Augmentation dot Augmented triad Bar line Bars Bass clef Beats Chord Chromatic half step Clef Closing bar line Common practice Compound interval Compound meter Diatonic half step Diatonic scale Diatonic triads Diminished triad A symbol that alters the pitch of a note. Accidentals include sharp, flat, and natural signs. A type of syncopation in which a sound that begins on a weak part of the beat is held longer than those around it. A partial measure used to begin a piece of music on a beat other than beat 1. Often, the final bar of music is shortened by the length of the anacrusis. How a sound is shaped at its beginning and end, and how it connects to the sounds around it. See irregular meter. When placed after a note, it adds one-half of the note’s duration to itself (e.g., the duration of a dotted quarter note equals a quarter note plus an eighth note). A triad that contains a major third and an augmented fifth above its root. The symbol “+” is used to indicate an augmented triad. A vertical line used to divide groups of beats into measures. See measures. A symbol indicating that F3 occupies the fourth line of the staff. Evenly spaced units of time that make up the pulse. A group of pitches sounding together. Two notes a half step apart with the same letter name (e.g., D and D-sharp). A symbol used to map pitch names to the lines and spaces of the staff. A normal bar line followed immediately by a thicker one. Used to signal the end of a piece. A style that governed the composition of Western music from about 1600–1900, and is the basis for many popular and jazz styles today. The common practice style is based on historical precedent and acoustics. An interval larger than one octave. Describes music in which the pulse divides into three equal parts. The pulse unit is always a dotted note. Two notes a half step apart with different letter names (e.g., D and E-flat). A scale in which all seven letter names are used, and each letter is only used once. Triads constructed on each scale degree using only the notes within that key signature. Diatonic triads are normally labeled with Roman numerals according to the scale degree on which each one is built. A triad that contains a minor third and a diminished fifth above its root. Glossary |437 Do-based minor A solfège system that maps do to the tonic of the minor scale. It is useful for understanding the link between a minor key and its parallel major. Dotted eighth note A note worth the value of three sixteenth notes. It is written as a filled notehead with a stem and an augmentation dot. Dotted half note A note worth the value of three quarter notes. It is written as an open notehead with a stem and an augmentation dot. Dotted quarter note A note worth the value of three eighth notes. It is drawn as a filled notehead with a stem and an augmentation dot. Double flat Lowers the pitch of a note by two half steps (one whole step). Double sharp Raises the pitch of a note by two half steps (one whole step). Downbeat The first beat of a measure. See also metric accent. Duple meter A meter containing two beats per measure. Duplet A rhythm that divides the compound-meter beat into two parts, instead of its typical three parts. Duration The length of time that a pitch sounds. Dynamic The loudness or softness of a sound. Dynamic accent A type of syncopation in which the accented note is performed more loudly than the notes around it. Eight-based compound meters Time signatures in which a dotted quarter note is used to represent the pulse, and an eighth note is used to represent the pulse division. Examples are six-eight, nine-eight, and twelve-eight. Eight-based simple meters Time signatures in which an eighth note is used to represent the pulse. Examples are two-eight, three-eight, and four-eight. Eighth note A note that is worth half of one quarter note. It is written as a filled notehead with a stem and a flag. Eighth notes within a beat are joined using a beam. Enharmonic interval Two intervals that sound the same but are notated differently (e.g., an augmented second [C to D-sharp] and a minor third [C to E-flat]). Enharmonic keys Two scales that sound the same but are spelled differently (e.g., C-sharp major and D-flat major). Enharmonic notes Two notes that sound the same but are spelled differently (e.g., F-sharp and Gflat). F clef See bass clef. First inversion Describes a triad in which the third is the lowest-sounding chord tone. Flat Lowers the pitch of a note by one half step. Four-based compound meters Time signatures in which a dotted half note is used to represent the pulse, and a quarter note represents the pulse division. Examples are six-four, nine-four, and twelve-four. Four-based simple meters Time signatures in which a quarter note is used to represent the pulse. Examples are two-four, three-four, and four-four. G clef See treble clef. Grand staff A treble staff and a bass staff that are used together and joined with a brace. Half note A note worth the value of two quarter notes. It is written as an open notehead with a stem. Half step The distance between any two adjacent piano keys. Harmonic interval The distance between two pitches played at the same time. Harmonic minor scale A minor scale that raises the seventh scale degree a half step, changing te to ti. Harmony Describes how chords interact with one another and with the melody they support. Hemiola The use of compound-meter groupings within simple meter, and vice versa. Interval The distance between two notes. Every interval consists of a number and a quality. 438| Glossary Interval number Interval quality Irregular meter Key signature La-based minor Ledger lines Major scale Major triad Mapping Measures Melodic interval Melodic minor scale Meter Meter signature Metric accent Middle C Minor triad Natural Natural minor scale Notation Note Note value Octave Octave designation Ottava bassa sign Ottava sign Parallel keys Passing tone Pickup Pitch Primary triads A representation of the visual space between two notes as they appear on the staff. A label used to define the exact distance between two notes. Interval quality types include perfect, major, minor, augmented, and diminished. Describes music in which the pulse groupings may vary. A pattern of sharps or flats placed immediately after the clef at the beginning of each line of music in order to indicate which notes are to be played sharp or flat in that piece or passage. A solfège system that maps the syllable la to the tonic of the minor scale. It is useful for understanding the link between a minor key and its relative major. Lines added above and below the staff to extend its range. A collection of seven notes (plus the repeated tonic) in the stepwise pattern: tonic-whole-whole-half-whole-whole-whole-half. A triad that contains a major third and a perfect fifth above its root. Assigning a set of variable elements to a fixed structure, such as assigning letter names to the staff, based on the clef given. Groups of beats that are separated by bar lines. The distance between two pitches played one after another. A minor scale that raises the sixth and seventh scale degrees a half step when ascending and reverts to the natural minor scale when descending. The organization of the pulse into groups (called measures) based on the placement of accents. Most meters divide the pulse into groups of two, three, or four. (See duple, triple, and quadruple meter.) See time signature. A name for the natural emphasis on the first beat of a measure. The note on the ledger line in between the treble clef and the bass clef. It is also near the center of the piano and is identified as C4. A triad that contains a minor third and a perfect fifth above its root. Clears a previous accidental, usually within the same measure. A courtesy natural may be used in a subsequent measure after an accidental to remind the performer that the note has returned to its unaltered state. A minor scale that only uses notes in the key signature. Written music. A written symbol representing a pitch and/or a duration. See duration. The distance between two notes of the same name. A number appended to a pitch name that describes the exact location of that pitch. For example, C4 is middle C, and C5 is one octave higher. Indicates that a note or passage of notes is to be played one octave lower than written. Indicates that a note or passage of notes is to be played one octave higher than written. Keys that share the same tonic but have different note content and key signatures, such as C major and C minor. A tone that does not belong to a chord, but is used to connect two chord tones in stepwise motion. For example, in the melodic line C-E-F-G, the F is a passing tone connecting two members of the C major triad. See anacrusis. A musical sound. The I, IV, and V chords (i, iv, and v in a minor key). These three triads represent every tone in a diatonic scale. Glossary |439 Progression Pulse Quadruple meter Quadruplets Quarter note Relative keys Repeat sign Resolution Rest Rhythm Root position Scale Scale degree names Scale degree numbers Second inversion Sharp Simple meter Sixteen-based compound meters Sixteenth note Solfège Staff Subtriplet Supertriplet Syncopation Tempo Tendency tones Tetrachord Tie Timbre 440| Glossary A series of chords arranged in a logical order. A progression (or chord progression) normally sets up musical expectations that may or may not be fulfilled. Made up of evenly spaced beats. A meter containing four beats per measure. A rhythmic figure that divides the compound-meter beat into four parts instead of its typical three parts. A common durational symbol that is written as a filled notehead and a stem. In four-based simple meters (such as two-four, three-four, and four-four), the quarter note is worth one beat. Keys that share the same key signature and pitch content but start on different tonics (e.g., C major and A minor). Used in written music to indicate that a passage should be played twice. The movement of an unstable scale tone to a stable one. For example, the scale tone ti resolves to do. A symbol that represents a definite length of silence. The interaction between note durations and the underlying pulse. A triad in which the root is the lowest-sounding chord tone. A collection of the notes used in a piece of music, condensed into one octave and arranged in stepwise order. A system of describing scale degrees in which a unique name corresponds to each scale degree (tonic, supertonic, mediant, etc.). A system of describing scale degrees in which a sequential number corresponds to each scale degree (1, 2, 3, etc.). Describes a triad in which the fifth is the lowest-sounding chord tone. Raises the pitch of a note by one half step. Describes music in which the pulse divides into two equal parts. Time signatures in which a dotted eighth note is used to represent the pulse, and a sixteenth note is used to represent the pulse division. Examples include six-sixteen, nine-sixteen, and twelve sixteen. A note worth one half of an eighth note. It is written as a filled-in notehead with a stem and two flags or beams. A system of scale-degree identification in which a unique syllable corresponds to each scale degree (do, re, mi, etc.). A set of five horizontal and parallel lines on which musical notes are arranged. (Plural: staves.) Three notes of equal length that occupy a duration shorter than one beat. (For example, three sixteenth notes may occupy the time of one eighth note in fourfour meter.) Three notes of equal length that occupy a duration longer than one beat. (For example, three quarter notes may occupy the time of a half note in four-four meter.) A disturbance of the normal system of metric accents that occurs when an otherwise weak part of a measure or beat is emphasized. The speed of the music. It is determined by the number of beats per minute. Unstable tones of a scale that have a tendency to resolve to tones within the tonic triad. Tendency tones are found on scale degrees 2, 4, 6, and 7. A four-note segment of a scale with a particular pattern of whole steps and half steps. Two tetrachords can be combined to make a complete scale. Combines two or more written durations into a single sound. For example, two quarter notes tied together will sound for the duration of a half note. The tone color of the instrument or voice producing the pitch. Time signature Tonic A symbol describing the grouping of pulses into measures or bars. A musical point of stability in a key or scale; very often the last note in a piece of music. The tonic is normally written as the highest and lowest notes of the scale. Tonic triad The chord formed by the three stablest tones of a scale. It consists of the first, third and fifth degrees of a scale (scale degrees 1, 3, and 5). Treble clef A symbol indicating that G4 occupies the second line of the staff. Triad Three simultaneously sounding pitches that can be stacked as two thirds and a fifth on the outside. The three members of the triad are called the root, third, and fifth. Triad quality A designation given to a triad according to the type of third and fifth it contains above its root. The four triad qualities are: major, minor, augmented, and diminished. Triple meter Three beats per measure. Triplet A rhythm that divides the beat into three equal parts. Eighth note triplets are written as three beamed eighth notes with a 3 written just outside of the beam. Tuplet Any irregular division of the beat in simple or compound meter. Quintuplets (five equal durations) and septuplets (seven equal durations) are common examples. Two-based simple meters Time signatures in which a half note is used to represent the pulse. Examples include two-two, three-two, and four-two. Voice leading The arrangement of chord tones to produce smooth, singable lines. Proper voice leading maintains common tones and stepwise motion between chord members in the upper voices. Whole note A note worth the value of four quarter notes. It is written as an open notehead with no stem. Whole step The distance between two piano keys that have a single key in between them. The intervening key may be black or white. Glossary |441 INDEX “25 or 6 to 4,” Chicago, 27, 71, 208, 260 accidental, 43, 437 diatonic and chromatic steps, 47–48 double sharps and double flats, 46 enharmonic notes, 44–45 enharmonics, 45–46 factoring, 363 notation, 57 sharps, flats and naturals, 43–44 “The Adventures of Rain Dance Maggie,” The Red Hot Chili Peppers, 212, 376 Aeolian mode, 433, 434 A-flat major scale, 99, 143, 182f, 183 A-flat minor scale, 188 harmonic, 240 melodic, 243 agogic accent, 54, 437 “A la musique,” Chabrier, 273 Albumblatter, Op. 99, Schumann, 382 “Allegretto” Beethoven, 23, 160, 375 Clementi, 23, 27, 115, 159, 373 “Allegro” Bach, 259 Haydn, 209, 261, 375 Mozart, 73, 314 “Allegro moderato,” Schumann, 26, 209 The Allman Brothers Band, 413 “All My Loving,” Beatles, 163 “All You Need is Love,” Beatles, 416 “Along Comes Mary,” The Association, 414 alto clef, 428–429 A major scale, 99, 143 “Amazing Grace,” 55f, 371 “America,” 224 “America the Beautiful,” Bates and Ward, 334 A minor scale, 188 harmonic, 240 melodic, 243 anacrusis, 55–56, 437 “Andante,” Schumann, 262 “Annie Laurie,” 83 “Ariette,” Mozart, 176 arpeggio, 345, 351 articulation, 1, 437 A-sharp minor scale, 188 harmonic, 240 melodic, 243 The Association, 414 asymmetrical meter, 402–403, 407, 437 “At the End of the Day,” Schönberg/ Kretzmer, 212, 259 “Aubade,” Fauré, 276, 332 “Au Cimetíere,” Fauré, 70, 375 442| Index augmentation dot, 9, 12, 437 notation, 17 augmented intervals, 290–293 augmented triads, 347, 349, 437 “Auld Lang Syne,” 75–76 “Aura Lee,” 7f, 95, 96f, 97f Bach, Johann Sebastian, 27 “Allegro,” 259 Chorale No. 16, 242f, 343f, 350f Invention No. 1 in C major, 295f Invention No. 4 in D minor, 196 “Jesus, Joy of Man’s Desiring,” 257 “Minuet I” and “Minuet II,” 208 Minuet in A minor, 328 “Minuet in G Minor,” 260 “Prelude No. 21,” 388 Toccata and Fugue in D Minor, 239f written exercise, 35–36 bar line, 16, 437 bar lines and repeats, notation, 16–17 bars, 7, 437 bass clef, 2, 3, 6, 429, 437 ledge lines in, 5–6 notations, 14 note names in, 4–5 bass tone, 349 Bates, Katherine, 334 beam, 9 beamed eighth notes, notation, 17 beaming, notation, 103, 104, 246 The Beatles “All My Loving,” 163 “All You Need is Love,” 416 “Blue Jay Way,” 374 “Day Tripper,” 163 “Dear Prudence,” 163 “Do You Want to Know a Secret?,” 163 “Girl,” 414 “I Will,” 163, 373 “The Long and Winding Road,” 164 “Lucy in the Sky with Diamonds,” 26 “Oh! Darling,” 164, 260, 315, 375 tendency tones in music of, 163–164 “Tomorrow Never Knows,” 118 “We Can Work It Out,” 159–160, 211 “While My Guitar Gently Weeps,” 210 “Yesterday,” 163, 376 beats, 437 BeauSoleil, 25, 210, 260, 418 “Beautiful Dreamer,” 236f, 353f, 355f Beck, “The New Pollution,” 25, 375 Beethoven, Ludwig van, 23, 160, 375 Bela Fleck and the Flecktones, 26, 259 Ben Folds Five, 24, 313, 372 “Berceuse,” Faure, 22, 115, 211 “Berceuse (Cradle Song),” Grieg, 116, 161, 211 Berlioz, Hector, 273, 330–331 B-flat major scale, 99, 143 B-flat minor scale, 188 harmonic, 240 melodic, 243 “Billie Jean,” Jackson, 70, 210 “Bitteres zu sagen denkst,” Brahms, 74, 374 Bizet, Georges, 27, 162, 208, 257, 260 block chords, 399 “Blue Bells of Scotland,” 90f “Blue Jay Way,” Beatles, 374 B major scale, 140, 143 B minor scale, 188 harmonic, 240 melodic, 243 “Bonner,” 11f, 13f Bonner, Carey, 11f Booker T. & the MG’s, 24, 210, 314 Boulanger, Lili, 104f, 175 “Boxing,” Ben Folds Five, 24, 313, 374 brace, 5, 6 Brahms, Johannes “Bitteres zu sagen denkst,” 74, 374 Hungarian Dance No. 5 in G Minor, 22, 212, 375 “Liebe und Frühling II,” 176 Waltz, Op. 39, No. 15, 71, 158, 313 “Wiegenlied,” 334 “The British Grenadiers,” 100f “Brouillardes,” Debussy, 48f Brubeck, Dave, 412 Cafe Accordion Orchestra, 26, 211 Cajunization, BeauSoleil, 25, 260 call-and-response pitch improvisation, 122, 213 “Camptown Races,” Foster, 102f “Can’t Hide Love,” Earth, Wind, and Fire, 26, 69 “Carillon,” Bizet, 162, 208, 257, 260–261 “The Cascades,” Joplin, 45f “Cat in the Bag,” O’Connor, 210, 417 Cello Concerto in D Major, Haydn, 209 C-flat major scale, 140, 143 Chabrier, Emmanuel, 273 “Chanson Pour Tommy,” BeauSoleil, 260, 418 Chicago, 27, 71, 208, 260 Chopin, Frederic Nocturne in E-flat Major, Op. 9, No. 2, 236f, 354f, 356f Prelude in C minor, Op. 25, No. 20, 27, 116, 314 Prelude in D-flat Major, Op. 24, No. 15, 211, 374, 413–414 Chorale No. 16, Bach, 242f, 343f, 350f chord, 341, 349, 437 progressions, 411 seventh, 435–436 triad inversions as, 377 chromatic, 47 chromatic half step, 47–48, 437 chromatic inversion, 295, 296 chromatic melody inversion, 296 chromatic solfège syllables, 432 “The Chrysanthemum,” Joplin, 295f circle of fifths, 141, 142, 143 minor keys, 184 “Clair de Lune,” Debussy, 274 classroom activities compound meter, 264–267 diatonic triads, 417–419 intervals, 316–318 minor scales, 213–214 musical notation, 29–31 rhythm, 75–76, 121–123, 164–167 triads, 377 clave scales, 165–167, 214 clef, 3, 4, 437 notation, 14–15 Clementi, Muzio, “Allegretto,” 23, 27, 115, 159, 373 closing bar line, 9, 437 C major scale, 92–93, 99, 143 C minor scale, 188 harmonic, 240 melodic, 243 common practice, 437 harmony, 396 composition, 38–39, 87–89, 134–136, 177–179, 227–229, 276–279 intervals, 336–341 triad, 390–392 compound duple, six-sixteen, 353 compound interval, 301, 437 compound meter, 11, 230–232, 306–307, 330–332, 351–356, 357, 437 counting, 233–234 four-based, 354–356 notation, 245–246 patterns, 310–311 pulse division, 230 rhythmic patterns, 247–248 sixteen-based, 352–354 songs in, 235–237 three-four vs. six-eight meter, 234 vs. triplets, 232 Contra Music: The Sound of New England, Wild Asparagus, 22, 69, 115 “Corcovado,” Milhaud, 26, 119 “A Country Wedding,” 386 courtesy natural, 43, 44, 47 Creedence Clearwater Revival, “I Put a Spell on You,” 258, 418–419 Crüger, Johann, 350f, 397f C-sharp major scale, 140 C-sharp minor scale, 188 harmonic, 240 melodic, 243 “Day Tripper,” Beatles, 163 “Dear Prudence,” Beatles, 163 Debussy, Claude, 48f, 274 degrees, 92 descending major scale, intervals in, 298–300 D-flat major scale, 140, 143, 149 diatonic, 47 diatonic half step, 47–48, 437 diatonic inversion, 295 diatonic modes, 433, 434 diatonic scale, 95, 138, 437 diatonic triads, 437 F major, 393 F minor, 395 functions, 397–402 major and minor scales, 409–410 major keys, 393–394 minor keys, 394–396 primary triads, 397–398 secondary triads, 400–402 voice leading, 398–399, 402 “Die betrogene Welt,” Mozart, 129 diminished intervals, 290–293 diminished triad, 348, 349, 437 D major scale, 94, 99, 143, 149 D minor scale, 188 harmonic, 240 melodic, 243 do-based minor, 189–191, 438 Dolly Suite, Op. 56, “Berceuse” from, 22, 115, 211 “Don’t Ask Me Why,” Joel, 72, 210 Dorian mode, 433, 434 dotted eighth notes, 100, 101–103, 438 dotted half note, 9–10, 12, 438 dotted quarter notes, 53–54, 56, 59, 438 double flats, 46, 48, 438 double sharps, 46, 47, 438 doubly augmented intervals, 294–295 doubly diminished intervals, 294–295 downbeat, 8, 11, 12, 438 “Do You Want to Know a Secret?,” Beatles, 163 drills to go, 28–29, 75, 121, 164, 212–213, 262–263, 316, 376, 419–420 “Driven to Tears,” The Police, 25, 211, 414 D-sharp minor scale, 188 harmonic, 240 melodic, 243 “Duke Street,” 383 Duparc, Henri, 275 duple meter, 11, 12, 438 informed listening, 22–23 patterns, 20 duplets, 405, 407, 438 duration, 1, 4, 6, 438 basic, 6–8 rests, 49 ties, 52 Dvorak, Antonin, 381 dynamic, 1, 438 dynamic accent, 54, 438 The Eagles, “Hotel California,” 415–416 Earth, Wind, and Fire, 26, 69 “Ecco II Messia,” 285f, 299f E-flat major scale, 99, 143 E-flat minor scale, 188 harmonic, 240 melodic, 243 eight-based compound meters, 438 eight-based meters, 195 eight-based simple meters, 438 rhythm, 191–194 eighth note, 9–10, 12, 56, 438 notation, 17, 59 eighth rest, 49, 51, 56 notation, 58 Eine Kleine Nachtmusik, Mozart, 73, 211, 314 “Elle était descendue,” Boulanger, 175 E major scale, 99, 143 E minor scale, 181, 188 harmonic, 240 melodic, 243 relative keys, 182f English Suite No. 4 in F major, Bach, 208 enharmonic intervals, 299–300, 438 enharmonic keys, 143, 438 major scales, 139–140 minor keys, 183 enharmonic notes, 44–45, 438 necessity of, 45–46 enharmonic parallel major, 187 enharmonic parallel minor, 186 “Fallin’,” Keys, 259, 374 Fauré, Gabriel, 22, 70, 115, 211, 275, 276, 331, 332, 375 F clef, 4, 6, 438 fifth, 349 first inversion, 349, 364, 436, 438 seventh chord, 436 “First Tube,” Phish, 416 Fitzgerald, Ella, 27, 159 flag, 9, 59 flagged vocal notation, 104 flashcards, 150–151, 198 flats, 43–44, 438 double, 46 key-signature order, 98, 150 major scales with more than four, 137–139 names, 431 flat sign, 47 Flight of the Cosmic Hippo, Bela Fleck and the Flecktones, 26 F major scale, 99, 143 F minor scale, 182f, 183, 188 harmonic, 240 melodic, 243 Foster, Stephen “Beautiful Dreamer,” 236f “Camptown Races,” 102f four-based compound meters, 354–356, 438 four-based simple meters, 438 four-eight meter, 191, 192f four-four meter, 8 Frank Zappa and the Mothers of Invention, 414 F-sharp minor scale, 188 harmonic, 240 melodic, 243 Gabriel, Peter, “I Have the Touch,” 162, 315 “Gaye’s Steps,” Unger and Snowe, 24, 73–74, 210 Index |443 G clef, 4, 438 German key names, 430–431 G-flat major scale, 143 “Girl,” Beatles, 414 G major scale, 93, 99, 143 relative keys, 182f G minor scale, 188 harmonic, 240 melodic, 243 “God Rest You Merry, Gentlemen,” 423 “Goodman’s Slip Jig,” Nolan, 259, 313 grand staff, 5, 428, 438 Green Onions, Booker T. & the MG’s, 24 “Greensleeves,” 244f, 266–267, 372, 426 Grieg, Edvard, “Berceuse,” 116, 161, 211 Groovin’, The Young Rascals, 25 group 1 triads, 359–361 group 2 triads, 361–362 group 3 triads, 363 G-sharp minor scale, 188 harmonic, 240 melodic, 243 guided rhythm improvisation, 30, 122– 123, 214, 264, 377 half note, 12, 438 half rest, 49, 51 notation, 58 half step, 42, 438 Hall, Daryl, 23, 69, 211 “Hallelujah,” Handel, 117–118, 210 Handel, George Frederic, “Hallelujah” from Messiah, 117–118, 210 harmonic intervals, 285, 438 hearing, 112–113, 207, 310 notation, 301 harmonic minor scale, 238, 438 intervals, 252 playing and singing, 251 purpose, 238–239 summary of, 240 harmony, 396, 438 “Hatikvah” (Israeli National Anthem), 181f “Hava Nashira,” 91f, 97f Haydn, Franz Josef, 24 “Allegro” from Cello Concerto in D major, 209, 261, 375 “Kyrie” from Mass No. 11 in D Minor, 24, 120–121, 315 “Minuet,” 212 hearing exercises ascending intervals, 311 compound meter patterns, 310–311 descending intervals, 311–312 harmonic intervals, 112–113 minor scales, 206–207, 254–256 rhythm, 20–21, 66–68 tendency row, 158 tendency tones in minor, 254 transcription, 113–114 triads, 372–373, 410 hemiola, 406, 407, 438 “Hey Ho, Nobody Home,” 190f, 191, 192f, 195f higher octave, 3 “Home on the Range,” 384 “Hotel California,” Eagles, 415–416 “How Can I Be Sure?” Lynne, 25, 315 The Young Rascals, 25, 109 444| Index Hungarian Dance No. 5 in G minor, Brahms, 22, 212, 375 “Hyfrydol,” 10f, 13f, 424 “I Have the Touch,” Gabriel, 162, 315 impromptu rhythm composition, 318 improvisation call-and-response pitch, 122, 213 guided rhythm, 30, 122–123, 214, 264, 377 rhythm, with note names, 31 rhythm, with solfège, 264 tendency row and guided, 164–165 inside-out scales, minor, 206 “Intermezzo,” Schumann, 131 interval, 438 interval inversion, 295, 297 interval number, 297, 439 interval quality, 297, 439 intervals, 111 augmented, 290–293 building, above a given note, 288–289 building, below a given note, 289–290 building major, minor and perfect, 288–289 compound, 298–299 descending major scale, 299–300 diminished, 290–293 doubling augmented and doubly diminished, 294–295 enharmonic, 297–298 harmonic minor scales, 252 hearing ascending, 206–207, 311 hearing descending, 207, 311–312 hearing exercises, 112–113, 310–312 hearing harmonic, 207, 310 identifying, in music, 305–306 inversion, 295, 309–310, 317 with letter names, 111, 156, 206 major, minor, and perfect, 281–285 major scale, 305, 307 melodic and harmonic, 285 melodic minor scales, 253 memorization strategies, 303–305 minor scale, 308, 310 natural minor scale, 205, 298–299 number and quality, 280–281, 297, 439 qualities, 293–294, 439 recognizing major, minor and perfect, 286–287 in scale, 316–317 shapes, 303 written exercises, 318–336 intervals with letter names, 111 Invention No. 1 in C major, Bach, 295f Invention No. 4 in D minor, Bach, 196 inversions, 295 chromatic melody inversion, 296 diatonic melody inversion, 295 interval, 317 interval inversion, 297 intervals with, 309–310 triad, 349, 364, 377 Ionian mode, 433, 434 “I Put a Spell on You,” Creedence Clearwater Revival, 258, 418–419 “Irish,” 382 The Irish Rovers, 26 irregular meter, 11, 29, 402–403, 407, 439 irregular tuplets, 405, 407 “Isn’t She Lovely,” Wonder, 415 “It’s Christmas Time,” Smokey Robinson and the Miracles, 413 “It Would Have Been Wonderful,” Sondheim, 259, 375 “I Will,” Beatles, 163, 373 Jackson, Michael, “Billie Jean,” 70, 210 Jaye, Rufus, 341 “Jesus, Joy of Man’s Desiring,” Bach, 257 Jimi Hendrix Experience, “Manic Depression,” 258, 415 Joel, Billy, “Don’t Ask Me Why,” 72, 210 John, Elton, “Your Song,” 116–117 Joplin, Scott, 22, 45, 211, 295f “Joy to the World,” 226 Just a Little Lovin’, Lynne, 25, 315 Key, Francis Scott, 336 keyboard, 41–43, 50 exercises, 107–111, 199–206, 247–254, 306–310 half steps and whole steps, 42–43 memorization strategies, 61 notes, 50 white keys of the, 41–42 Keys, Alicia, “Fallin’,” 259, 374 key signatures, 439 major, and scales, 99, 143 major scales, 95–98, 141 order, 97, 98, 150 shortcuts to identify, 149–150 visual way to memorize, 150 writing, 147 King, Carole, “(You Make Me Feel Like a) Natural Woman,” 259, 313 Kretzmer, Herbert, 212, 259 “Kyrie” Haydn, 24, 120–121, 315 Mozart, 25, 375 la-based minor, 189, 191, 439 “Lafferty’s,” Wild Asparagus, 22, 69, 115, 210 “Largo” from Symphony No. 9, Op. 95, Dvorak, 381 L’Arlésienne Suite No. 1, Op. 23, Bizet, 162, 208, 257, 260–261 ledger lines, 3, 4, 439 above and below bass staff, 6f bass clef, 5–6 notation, 15 treble clef, 3–4 “Les lilas qui avaient fleuri,” 104f “Le spectre de la rose,” Berlioz, 273 Liebesfruhling, Op. 37, Schumann, 130 “Liebe und Frühling II,” Brahms, 176 “Lied der Freiheit,” Mozart, 130–131 Liederkreis, Op. 39, Schumann, 131 “Loch Lomond,” 102f Locrian mode, 433, 434 “The Long and Winding Road,” The Beatles, 164 “Love You Madly,” Fitzgerald, 27, 159 “Lucy in the Sky with Diamonds,” The Beatles, 26 Lydian mode, 433, 434 Lynne, Shelby, 25, 315 major intervals, 281–285 building, 288–290 expansion to augmented intervals, 292f recognizing, 286–287 major-major seventh chord, 435–436 major scales, 90–92, 439 building, 92–95 circle of fifths, 141, 142 diatonic triads in, 393–394, 407 enharmonic keys, 139–140 intervals in, 307, 309 intervals in descending, 299–300 intervals with letter names, 111, 156 key signatures, 141, 143 more than four sharps or flats, 137–139 playing, 108, 155 playing and singing, 109, 156 singing, without the piano, 110 singing tendency row without the piano, 157 structure and scale degree names, 89–91 tendency row with solfège and note names, 157 variation in practicing, 155–156 written exercises, 123–133, 167–176 major seventh cord, 435–436 major triads, 345–346, 439 “Manic Depression,” Jimi Hendrix Experience, 258, 415 “MaNouche,” Cafe Accordion, 211 mapping, 2–3, 439 scales to solfège, 105–106 Mass in C Minor, K. 427, Mozart, 25 Mass No. 11 in D Minor, Haydn, 24, 120– 121, 315 measures, 7, 18, 439 melodic intervals, 285, 439 melodic minor scales, 241–243, 439 intervals, 252 playing and singing, 252 memorization strategies flashcards, 150–151, 198 hearing triads in root position, 363–364 intervals, 303–305 interval shapes, 303 keyboard, 61 letter-name distances, 303 mapping scales to solfège, 105–106 minor keys, 247 parallel and relative keys, 197 pitch name fluency, 19–20 plain interval qualities, 303–305 scale content, 105 shortcuts for identifying key signatures, 149–150 triad qualities, 359–363 visual way to memorize key signatures, 150 visual way to memorize scales, 149 “Menuetto,” Mozart, 72, 209–210, 374, 415 Messiah, “Hallelujah” from Handel’s, 117– 118, 210 meter, 12 categories, 11 compound, 230–237 duple, 11 quadruple, 6–8 triple, 10–11 meter signature, 12, 439 metric accent, 8, 11, 12, 439 “The Mexican Hat Dance,” 432 middle C, 5, 6, 41, 439 alto and tenor clef, 428 Milhaud, Darius, “Corcovado,” 26, 119 minor intervals, 281–285 building, 288–290 recognizing, 286–287 reduction to diminished intervals, 292f minor keys tendency tones, 245 tonic triad, 245 minor scales, 181 diatonic triads, 394–396, 410 do-based minor, 189–191 flash cards, 198 harmonic, 238–240 inside-out scales, 206 intervals in, 308, 310 intervals in the natural, 300–301 intervals with letter names, 206 la-based minor, 189 melodic, 241–243 memorization strategies, 197–198 minor key signatures and, 188–189 in music, 244–245 parallel and relative keys, 197 parallel keys, 185–187 playing, 203, 251–252 playing and singing, 203–204 scale degree names in, 244 scale segments, 204–205 singing, without the piano, 204 and solfège, 189–191 structure and relative keys, 181–185 written exercises, 214–227 minor triads, 344, 349, 439 “Minuet,” Haydn, 212 Minuet in A minor, Bach, 328 “Minuet in G Minor,” Bach, 27, 260 Mixolydian mode, 433, 434 modes, 433, 434 The Moldau, Smetana, 187f Monk, W. H., “Victory,” 422 Mozart, Wolfgang Amadeus, 72, 211 “Allegro,” 73, 314 “Ariette,” 176 “Die betrogene Welt,” 129 “Kyrie,” 25, 375 “Lied der Freiheit,” 130–131 “Menuetto” from Symphony No. 40 in G Minor, 209–210, 374, 415 Piano Sonata No. 16 in C major, 351f music elements of, 1 identifying intervals, 305–306 identifying triads, 350–351 labeling triads in, 396–397 minor scales in, 244–245 musical sound, properties of, 1 “My Favorite Things,” Rodgers and Hammerstein, 23, 210 natural, 43–44, 439 natural minor scale, 237–238, 433, 434, 439 intervals in, 205, 300–301 minor scale structure and relative keys, 181–185 parallel keys, 185–187 playing, 203 playing and singing, 203–204 natural sign, 43, 47 “The New Pollution,” Beck, 25, 375 nine-eight meter, compound triple, 231 nine-four, compound-triple meter, 355 nine-sixteen, compound-triple meter, 353 Nocturne in E-flat Major, Op. 9, No. 2, Chopin, 236f, 354f, 356f “Noisy Night,” Jaye, 341 “Noisy Night 2,” Jaye, 341 Nolan, Martin, “Goodman’s Slip Jig,” 259, 313 Norworth, Jack, 335 notation, 1, 439 accidentals, 57 augmentation dot, 17 bar lines and repeats, 16–17 beamed eighth notes, 17 beaming, 104 clefs, 14–15 compound meter, 245–246 dotted quarter note, 59 eight-based meters, 196 flagged vocal notation, 104 harmonic interval, 301 ledger lines, 15 metric hierarchy, 60 noteheads, 15 notes, rests and beaming, 104 note-spacing within the measure, 18 rests, 58 single eighth note, 59 stems, 15–16 ties, 59 time signatures, 18 writing key signatures, 147 writing triplets, 147 note, 2, 4, 439 note heads, 7, 12, 15 note names rhythm improvisation with, 31 staff, 2 tendency row with solfège and, 157 variation, 165 notes bass clef, 5f keyboard, 50 notation, 103 treble clef, 3 note-spacing within measure, notation, 18 note value, 439 “Notre Amour,” Faure, 275 number, interval, 280–281, 297 “Nun Danket All,” Crüger, 350f, 397f Oates, John, 23, 69, 211 O’Connor, Mark, “Cat in the Bag,” 27, 210, 417 octave, 3, 4, 439 octave designation, 48–49, 439 numbers, 49 ottava sign, 48 Odelay, Beck, 25 “Oh! Darling,” Beatles, 164, 260, 315, 375 “Oh Susannah,” 194f “O Ihr Herren,” Schumann, 130 “Old McDonald,” 9f “O Little Town of Bethlehem,” 44f, 305f Index |445 “One Who Really Loves You,” Booker T. & the MG’s, 24, 210, 314 ottava bassa sign, 49, 439 ottava sign, 48, 49, 439 parallel keys, 185–187, 188–189, 197, 237, 439 parallel major scale, 238 passing tones, 343, 439 patterns rhythmic, 61–66 singing exercises, 20–21, 61–66 “Pavane de la Belle au bois dormant,” Ravel, 69–70, 374 perfect intervals, 281–285 building, 288–290 expansion to augmented intervals, 291f recognizing, 286–287 reduction to diminished intervals, 291f Phish, “First Tube,” 416 Phrygian mode, 433, 434 piano, singing major scales without, 110 Piano Sonata No. 16 in C major, Mozart, 351f Piano Trio in G Minor, Op. 17, Schumann, 114, 209, 262 pickup, 439 pickup measure, 55–56 pitch, 1, 4, 439 pitches, 1, 6 pitch improvisation, call-and-response, 122, 213 pitch names fluency, 19–20 singing, 430–431 The Police, 25, 211, 414 practice strategies, 151, 198 Prelude in C minor, Op. 24, No. 20, Chopin, 27, 116, 314 Prelude in D-flat Major, Chopin, 211, 374, 413–414 “Prelude No. 21,” Bach, 388 Prichard, Rowland, 10f, 424 primary triads, 397–398, 439 progression, 396, 440 chord, 411 C major, 399f C minor, 399f leading tone triad, 401f subdominant and supertonic triads, 401f voice leading, 398 pulse, 6, 12, 440 pulse division compound meter, 351–352 simple and compound meter, 230 quadruple meter, 6–8, 8, 12, 440 informed listening, 24–25 patterns, 21 quadruplets, 405, 407, 440 quality, interval, 280–281, 297, 303–305 quarter note, 12, 440 quarter rest, 49, 51 notation, 58 “The Raiders March” Williams, 120, 376 Raiders of the Lost Ark, Williams, 120 Ravel, Maurice, 69–70, 374 The Red Hot Chili Peppers, “The Adventures of Rain Dance Maggie,” 212, 376 446| Index relative keys, 185, 186, 197, 237, 440 minor scale structure and, 181–185 repeat signs, 13, 440 resolution, 144, 145, 440 rests, 56, 440 compound meter patterns with leading, 248 notation, 58, 103 rhythm, 49, 51 sixteenth note combinations and triplet with leading, 152 sixteenth note combinations with leading, 108 retrograde, 340 retrograde inversion, 340 rhythm, 6, 12, 440 anacrusis (pickup measure), 55–56 dotted eighth notes, 101–103 dotted quarter notes and syncopation, 53–54 duplets and quadruplets, 405 eight-based simple meter, 191–194 elements of, 6 hemiola, 406–407 irregular meter, 402–403 irregular tuplets, 405 rests, 49, 51 sixteenth notes, 100–101 and solfège transcription, 256 subtriplets and supertriplets, 403–405 ties, 52 transcription, 255–256 triplets, 145–146 two-based simple meter, 194–195 rhythm exercises keyboard and singing, 152–155, 200– 202, 248–250 singing exercises, 63–65 triads, 365–368 rhythmic patterns, 20–21 compound meter, 247 hearing, 21 keyboard exercises, 107–108, 151 patterns in three-eight, 199 patterns in three-two, 200 singing exercises, 61–66, 107–108, 151 triads, 364–365 Rodgers and Hammerstein, 23, 210 root, 349 Root, Jena, “Variations on a Southern Harmony Tune,” 296f root position, 344, 349, 364, 440 hearing triads in, 363–364 seventh chord, 436 “Row, Row, Row Your Boat,” transcription, 256 “St. Columba,” 145f “St. Louis,” 305f Saudades do Brasil, Op. 67, Milhaud, 26, 119 scale degree, 90 scale degree names, 244, 440 scale degree numbers, 440 scales, 89–91, 440 ascending, 135 clave, 165–167 descending, 135 distinguishing major and minor, 210– 211 major key signatures and, 99 major moving to minor, 211–212 major to parallel minor, 209 major to relative minor, 208 memorizing scale content, 105 minor moving to major, 212 minor to parallel major, 209–210 minor to relative major, 208–209 practice strategies, 106–107 visual way to memorize, 149 written exercises, 123–133, 167–176 scale segments, 108, 110 scale tone, 90 “Scherzo,” Schumann, 114 Schönberg, Claude-Michel, 212, 259 Schumann, Clara, 26 “Allegro moderato,” 26, 209 “Andante,” 262 “Scherzo,” 114 Schumann, Robert Albumblätter, Op. 99, 382 “Intermezzo,” 131 “O Ihr Herren,” 130 “Scotch Snap,” 102f, 114 “Scott Joplin’s New Rag,” 22, 211 “Sérénade,” Duparc, 275 secondary triads, 400–402 second inversion, 349, 364, 436, 440 seventh chords, 435–436 Sgt. Pepper’s Lonely Hearts Club Band, The Beatles, 26 sharps, 43–44, 440 double, 46 key-signature order, 98, 150 major scales with more than four, 137–139 names, 431 sharp sign, 47 “Silent Night,” 337, 353f, 355f, 372 transcription, 255–256 simple intervals, 298, 299f simple meter, 11, 12, 230, 357, 440 pulse division, 230 simple position, 349 singing exercises, 20–21, 61–66, 199–206, 247–254, 306–310 diatonic triads, 409–412 six-eight meter compound duple, 231 three-four vs., 234 six-four, compound duple meter, 355 six-four patterns, 365 six-sixteen patterns, 365 sixteen-based compound meters, 352–354, 440 sixteenth note, 440 sixteenth note combinations, 108 sixteenth note combinations and triplet, 152 sixteenth note combinations and triplet with leading rests, 152 sixteenth note combinations with leading rests, 108 sixteenth notes, 100–101 sixth scale degree, 181 Smetana, Bedrĭch, The Moldau, 187f Smith, John Stafford, 336 Smokey Robinson and the Miracles, 413 Snowe, Ginny, 24, 73–74, 210 Solemnis Haec Festivas, 425 solfège, 127, 440 chromatic syllables, 432 composition, 276–279 harmonic and melodic minor scales, 251–252 mapping scales to, 105–106 minor scales and, 189–191 minor tendency row with, 253 rhythm improvisation with, 264 sample composition, 178, 179 tendency row with, 157 transcription, 255–256 Sonatina in G Major, Op. 36, No. 2, Clementi, 23, 27, 115, 159 Sondheim, Stephen, “It Would Have Been Wonderful,” 259, 375 The Sound of Music, Rodgers and Hammerstein, 23 Sousa, John Philip, “The Thunderer,” 27, 315 staff, 2, 4, 440 mapping notes to, 2–3 note names in, 2 “Star of the County Down” Bela Fleck and the Flecktones, 26, 259 The Irish Rovers, 26 “The Star-Spangled Banner,” 193f, 195f, 336 staves, 2 stem, 7 notation, 15–16 subtriplets, 403–404, 407, 440 supertriplets, 404–405, 407, 440 “Sur les lagunes (Lamento),” Berlioz, 330–331 Symphony No. 40 in G Minor, K. 550, Mozart, 72 Symphony No. 7, Beethoven, 23, 160 syncopation, 53–54, 56, 440 “Take Me out to the Ball Game,” 44f Norworth and Von Tilzer, 335 two versions, 264–266 tempo, 440 tendency row, 144 guided improvisation, 164–165 hearing the basic, 158 minor, with solfège and note names, 253 minor keys, 245 singing, without the piano, 157, 254 with solfège and note names, 157 tendency tones, 144–145, 440 minor keys, 245 music of The Beatles, 163–164 tenor clef, 428–429 tetrachord position, playing scales in, 106–107 tetrachords, 93, 94, 95, 440 flat keys, 95 sharp keys, 94 third, 349 third inversion, seventh chord, 436 “This Old Man,” 82 three-beat patterns, 62–66 Thriller, Jackson, 70 “The Thunderer,” Sousa, 27, 315 ties, 56, 440 notation, 59 rhythm, 52 timbre, 1, 440 time signature, 12, 441 notation, 18 Toccata and Fugue in D Minor, Bach, 239f “Tomorrow Never Knows” Beatles, 118 tones, 92 tonic, 441 tonic detection, 123 tonic pitch, 92 tonic triad, 144–145, 441 minor keys, 245 transcription, 113–114 rhythm, 255–256 “Row, Row, Row Your Boat,” 256 transformations, 339 treble clef, 2, 3, 6, 441 notations, 14 ledger lines in, 3–4 triad, 343, 349, 441 augmented triads, 349 compound meter, 351–352, 357 diatonic, in major keys, 393–394 diatonic, in minor keys, 394–396 diminished triads, 348, 349 four-based compound meter, 354–356, 365 hearing, in root position, 363–364, 372 hearing inverted, 373 identifying, in musical context, 350–351 inversions, 349, 377 labeling, in music, 396–397 major triads, 345–346, 349 minor triads, 346, 349 musical contexts, 371–372 playing and singing, 370–371 qualities, 344–345, 348–349, 441 quality chains, 370–371, 377 recognizing, qualities, 359–363 rhythm exercises, 365–368 rhythmic patterns, 364–365 sixteen-based compound meter, 352– 354, 365 structure and quality, 343–349 triad quality, 344–345, 348–349, 441 triple meter, 10–11, 12, 441 informed listening, 23–24 patterns, 21 triplets, 441 compound meter vs., 232 counting, 146f rhythm, 145–146 writing, 147 “Tristesse,” Fauré, 331 tuplets, 441 irregular, 405, 407 twelve-eight, compound quadruple meter, 231, 232 twelve-four, compound-quadruple meter, 356 twelve-sixteen, compound-quadruple meter, 354 “Twinkle, Twinkle Little Star,” 44f two-based meters, 195 two-based simple meter, 441 rhythm, 194–195 two-beat patterns, 62 two-four meter, 11 Unger, Larry, 24, 73–74, 210 “Unsquare Dance,” Brubeck, 412 value, 6 “Variations on a Southern Harmony Tune,” Root, 296f The Ventures, “Walk Don’t Run,” 212, 259 “Victory,” Monk, 422 voice leading, 441 diatonic triads, 398–399, 402 Von Tilzer, Albert, 335 “Walk Don’t Run,” The Ventures, 212, 259 Waltz, Op. 39, No. 15, Brahms, 71, 158, 315 Waltz Time II, Unger and Snowe, 24 Ward, Samuel, 334 “Wayfaring Stranger,” 55, 56f, 226–227 “We Can Work It Out,” Beatles, 159–160, 211 “When Johnny Comes Marching Home,” 235f, 239, 372 “When the Saints Go Marching In,” 371 “While My Guitar Gently Weeps,” Beatles, 210 “Whipping Post,” The Allman Brothers Band, 413 whole note, 12, 441 whole rest, 49, 51 notation, 58 whole step, 42, 441 “Wiegenlied,” Brahms, 334 Wild Asparagus, 22, 69, 115, 210 Williams, John, “The Raiders March,” 120, 376 Wonder, Stevie, 415 written exercises diatonic triads, 420–426 intervals, 318–336 keyboard, 76–87 minor scales, 214–227, 267–276 music notation, 32–38 scales, 123–133, 167–176 triad, 378–389 “Yesterday” Beatles, 163, 376 “You Make Me Feel Like a Natural Woman,” King, 259, 313 “You Make My Dream,” Hall and Oates, 23, 69, 211 “Your Song,” Elton John, 116–117 “Zarico Boogie,” BeauSoleil, 25, 210 Zenyatta Mondatta, The Police, 25 “Zomby Woof,” Frank Zappa and the Mothers of Invention, 414 Index |447
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