Dr. David Hamrick
Zale Library at Paul Quinn College
16 November 2012
Sound is a mechanical wave
• It moves through a medium
• Like waves in water
• Or earthquakes through the ground
• We usually think of air as the medium
• Can travel through other gases
• Can travel through liquids
• Can travel through solids (varies
depending on material)
• Why does helium make your voice
sound higher?
• Helium is a lower-density medium
• More on this later!
Sound is a compression wave
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Vibrating body transfers energy to medium
Medium is compressed, then released
The “wave” is really a series of high and low pressure areas
It’s easier to represent this as a 2-D wave
The Speed of Sound
• Density of the medium determines how fast it can compress/decompress
• The average density of air allows a wave to travel about 768 mph
• Helium’s lower density allows sound to travel 3x faster!
Wave = Complete cycle of compression/decompression
• In a 2D representation, 2 points at same place in the cycle
• Usually measured from midpoint to midpoint
Frequency = Number of waves per second
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Measured in “Herz” (Hz), “kiloHertz” (kHz), megaHertz (mHz)
In musical terms this is called “pitch”
We call shorter waves (high frequency) “high” pitches
We call longer waves (low frequency) “low” pitches
Amplitude = Intensity of each wave (power exerted)
• In the image below, the frequency (pitch) remains the same while the
amplitude (volume) increases and decreases
• Measured in “decibels”
• Zero decibels (0 dB) is just below range of human hearing
• The decibel scale is logarithmic, not linear
• Every 10 decibels describes 10x power increase
• 20 dB is not twice as loud as 10 dB, it is 10x as loud!
• In musicals terms this is called volume or dynamics
Radio works by modulating either frequency or amplitude
• Radio waves are electromagnetic, not mechanical, but described the same
• Amplitude Modulation (AM) =
• Constant frequency
• Changing amplitude
• Frequency Modulation (FM) =
• Constant amplitude
• Changing frequency
• Also much higher frequency than AM
• Shorter waves make FM signal easier
to bounce around corners, inside buildings
• AM limited by amount of amplitude change you can force
• FM carries more complex signals (stereo & quadrophonic)
• Human hearing can detect an amazing range of amplitude
• Normal conversation (about 50 dB) has an amplitude 1,000x the hearing
threshold (0-1 dB)
• Jet engine (about 100 dB) has an amplitude 100,000x the threshold
• Human hearing can also detect a wide range of frequencies
• About 20 Hz to 20 kHz is the typical range
• Lowest note on piano (A0) is 27.5 Hz; highest (C8) is 4.2 kHz
• Animal hearing can go far beyond ours!
• Most dogs hear about 40 Hz to 60 kHz (about 3x human range)
• Bats use echolocation calls at frequencies up to 150 kHz
• Baleen whales vocalize at about 10-30 Hz, at up to 80 decibels!
• Almost all sounds are a mix of a large number of frequencies
• A sound made of a single-frequency wave sounds artificial
• So what is the difference between a musical tone and noise?
• The musical tone has a regular frequency
• The musical tone is composed of waves that fit together easily
• How frequencies fit together in a musical pitch
• Which wave is the loudest? Which has the highest pitch?
• What is the ratio or proportion between the two frequencies?
• Why doesn’t it make two different notes?
• The wave with greatest amplitude will sound like the “real” note
• The shorter wave fits within the longer wave and reinforces it
• See examples at UNSW Physclips: adding harmonics, composite tone
Harmonics: frequencies that naturally combine as a musical pitch
• Discovered by Pythagoras in the 6th century B.C.(?)
• The lowest tone (longest frequency) is called the “fundamental”
• Each harmonic is a multiple of that fundamental’s frequency
First Five Harmonics of the Pitch A0
Pitch name
Frequency
Interval above previous pitch
E3 (two octaves & 5th)
165 Hz
Minor 3rd
C#3 (two octaves & major 3rd) 137.5 Hz
Major 3rd
A2 (two octaves)
110 Hz
Perfect 4th
E1 (octave & 5th)
82.5 Hz
Perfect 5th
A1 (one octave higher)
55 Hz
Octave
A0 (lowest A on grand piano)
27.5 Hz
(Fundamental)
This video shows a real-world demonstration using an oscilloscope
• “Timbre” is the quality of a musical pitch
• What is the difference between a middle “C” played on a piano, or sung
by a woman, or sung by a man?
• Same fundamental pitch, different combination of harmonics
• Why does your own voice sound funny in a recording?
• You are used to hearing your voice through two media:
• Through the surrounding air, into your ears
• Through your own head (conductive hearing)
• A recording device is only recording the sound in the air
• The recording device is limited to the frequencies it can detect
• The playback device is limited to the frequencies it can reproduce
• Example: telephone audio is only 300 Hz to 3.4 kHz (saves bandwidth!)
Combination of two or more different notes at once
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Distance between two notes is the “interval”
Combination of intervals (3 or more notes) is a chord
Which ones sound good? Why?
We tend to prefer the intervals at the beginning of the harmonic series
Simpler ratios; harmonics of each note clash less
The first interval is called the octave (8va)
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Frequency ratio is 2:1 (top note 2x frequency of lower note)
Harmonics of each note are the same—sound like same note
Most universal interval in all music (men, women sing together at 8va)
Scales repeat at the octave (start the series of notes over again)
In letter notation, each note of an octave is same letter (low C, high C)
The next two intervals are the 5th and 4th (2-3, 3-4 in chart)
• After the octave, these are the most universal intervals
• Most scales split the octave with a step at this point (3 in chart)
• 5 steps from bottom to top notes of 5th (2-3 in chart)
• 4 steps from bottom to top notes of 4th (3-4 in chart)
• Many kinds of folk music use the octave, 5th, and 4th as harmony
• 5th is a 3:2 ratio (frequency of top note is 1½x that of lower note)
• 4th is a 4:3 ratio (frequency of top note is 11/3x that of lower note)
Instruments using this combination go back to ancient times!
The drone pipes on bagpipes are tuned to make this combination:
In Indian raga music the tambura plays this combination as
accompaniment to the sitar soloist
The Western tradition of harmony began during the Middle Ages
with the use of these intervals:
The next intervals up the harmonic series are the 3rds
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These come in two sizes: major (4-5 on chart) and minor (5-6 on chart)
Both called 3rds because take up three notes in scale (C-D-E, E-F-G)
The major 3rd has a 5:4 ratio (frequency of top note is 1¼x that of lower)
The minor 3rd has a 6:5 ratio (frequency of top note is 11/5x that of lower)
The major chord
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Major 3rd joined with minor 3rd (4-5-6 in chart)
Why do we like this sound?
It occurs naturally in the harmonic series
The middle note splits the difference in frequencies of the outer two…
Just like the 5th splits the difference in frequencies in an octave
At this point in the harmonic series, cultures took different paths
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Some notes in the harmonic series weren’t used in Western music
Notes marked in blue in the chart are too flat (low) to fit into our scales
The note marked in red is too sharp (high)
Obviously the intervals involving these notes won’t fit either
This is a cultural preference (and matter of conditioning!)
• Music of Middle East, Southeast Asia has used these notes & intervals
• Several different sizes of 3rd and 2nd, not just major and minor
• Most music cultures have preferred a simpler system!
Last two intervals we need are the seconds (two adjacent notes)
• Western music uses sizes most common in upper end of the harmonic series
• Major 2nd (8-9 on chart)
• Commonly called a “whole step”
• Interval 9-10 is almost a major 2nd but is a little flat
• Minor 2nd (15-16, 16-17, 17-18, 18-19)
• Commonly called a “half step”
• Intervals on high end of the series are actually successively smaller, but
the differences are within the threshold of our ability to detect
What is a scale?
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“Scale” is from the Italian “scala,” and means “ladder”
A way of climbing up and down in pitch during a melody
The “rungs” of the ladder are the individual notes
Can be fixed in many different positions!
• Modern Western music uses major and minor
• Karnatic (South Indian) music has 72 different melas (scales)
• In many musical cultures, certain scales are associated with certain moods
• Common ground across cultures
• Every theory of scales uses divisions of the octave (Impossible to avoid!)
• Every(?) theory of scales splits the octave at the 5th
• Almost every scale is either 5 or 7 different notes
• The Pentatonic (5-note) Scale
• Found in folk music and children’s songs around the world
• Also fundamental to blues, jazz, rock, pop music
• Major Pentatonic
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Made of only 2 different intervals: major 2nd, minor 3rd
Called “major” because of emphasis on major 3rd (DO-re-MI)
Black keys on piano are arranged (by coincidence) in major pentatonic
Common arrangement is: maj. 2nd, maj. 2nd, min. 3rd, maj. 2nd, min. 3rd
Many (Most?) children’s songs use pentatonic scales.
Note that the child is most in tune on the octave & 5th
(bottom, middle, and top notes of the tune).
These men are celebrating their safe return from
fighting the 2009 La Brea forest fire in California.
The Irish hymn “Rop Tú mo Baile”
(“Be Thou my Vision”) is mostly pentatonic.
The same intervals can be ordered: maj. 2nd, min. 3rd, maj. 2nd, maj. 2nd, min. 3rd
“Arirang” is a famous folk song in Korea
• Arranges intervals: min. 3rd, maj. 2nd, maj. 2nd, min. 3rd, maj. 2nd
• Called “minor” because of emphasis on min. 3rd (LA-DO)
One of the earliest forms of the blues scale probably came from
adding minor 2nds to the minor pentatonic.
Big Mama Thornton, “Hound Dog”
(the original version)
• Some minor pentatonic scales use minor 3rds, major 2nds, and minor 2nds
• Particularly common to folk music of Southeast Asia
• A common arrangement is: maj. 2nd, min. 2nd, min. 3rd, min. 2, min. 3rd
One form of the Japanese hirajoshi scale
This tune is “Sakura” or “Cherry blossom.”
The cherry tree is a national symbol of Japan.
• European music based on
7-note combinations of
major, minor 2nds
• From ancient Greece through
the Western Renaissance,
there were several different
7-note scales or “modes”
• In the modern period, most
Western music uses just 2:
major and minor
• Some folk and popular music
still uses the older modes
Maj. Maj.Min.
Maj. 2nd 2nd 2nd
Min.
Maj.
Maj.
nd 2nd 2nd
2
nd
2
C major scale
Min. Maj. Maj.
Min.Maj.Maj. 2nd 2nd 2nd
Maj. nd nd 2nd
2 2
2nd
C minor scale
One of the other modes that turns
up often is called “Dorian”
• Like minor, except minor 2nd moved
from 5th-6th notes to 6th-7th notes
• Common in folk music, rock, jazz
Appalachian hymn “Wondrous love”
Phrygian mode was common in the
Renaissance, and was revived in
modern jazz
• Sounds neither major nor minor
(but leans toward minor)
• Unusual for having a minor 2nd above
the key-note
Psalm tune by Thomas Tallis, 1567
• Scales of the classical music of Middle East, India & Pakistan
are based on smaller intervals than used in Western scales
• Theoretically divides the octave into quarter-steps, not half-steps
• In addition to min. 2nd (half-step) and maj. 2nd (whole-step) …
• ¼-step
• ¾-step
• 1¼-step
• These intervals are also in the harmonic series, just not used in West
• Concept of “scale” is more complicated
• Still 7-note scales, but many different forms (not just major & minor)
• Scale includes not just series of notes, but mood, style, melody ideas
Arabic maqām (Turkish makam)
• Made by stacking two tetrachords
(four-note groups)
• Lowest, highest notes are octave, really
just 7 different notes
• Upper tetrachord usually starts a
perfect 5th above octave
Many maqām, but some little used
• Best-known in the West is the “Hijaz”
• Lower tetrachord is the “Hijaz” tuning
The “Bayati” maqām
• Like a Western minor scale except…
• Uses two ¾-steps at the bottom
instead of whole-step, half-step
• That is, the second note from lowest
sounds ¼-step flat to Westerners
• If this is not learned from childhood,
difficult to hear, much less to sing!
¾
step
¾
step
Maj.
2nd
Maj.
2nd
Min.
2nd
Maj.
2nd
Maj.
2nd
South Indian Karnatic tradition (other is Hindustani)
• Octave divided into 22 shruti (smallest perceptible difference in pitch?)
• Scale (mela) made of combining two tetrachords (as in Middle East)
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“SA” and “PA” stay the same (octave and 5th!)
“MA” has a low position and a high position
“RI,” “GA,” “DA,” and “NI” each have a low, middle, and high position
Unlike Western music, a “RI sharp” is not the same as a “GA flat”
Mela or thaat (Hindustani) is the
foundation for a raga
• Raga is not only scale, but melodic
ideas, style, mood, rhythmic patterns
• Each raga is associated with a time
of day, sometimes also with a season
• Considered inappropriate (even
unlucky!) to play a raga at the
wrong time
• Improvisation is essential to raga, will
never be played same way twice
Tansen, the great 16th-century musician,
was said to have made it rain by
playing a raga for monsoon season!
Raag Khamaj
• Built on one of the scales common to
the ancient Hindustani thaat and
more modern Karnatic melas
• To be played in the mid-evening
• Scale equivalent to:
• Major scale when ascending,
but…
• 7th note flatted when descending
Performance by Ravi Shankar (sitar)
and his daughter Anoushka Shankar
(sitar); player of tabla unidentified
This flat-7 scale is called “Mixolydian”
in Western music.
This chart shows all 72 Karnatic melas (all possible combinations of note positions)
From the simplest drone harmony to the most complex jazz chords,
from the pentatonic scale to the 72 Karnatic melas, everything
comes back to the harmonic series. As different as our music is, it
all has elements in common.
THE END
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Sound waves and music. The Physics Classroom. http://www.physicsclassroom.com/class/sound/
Music acoustics. University of New South Wales. http://www.phys.unsw.edu.au/jw/basics.html
“Hearing range.” Wikipedia. http://en.wikipedia.org/wiki/Hearing_range
Physics of music notes: Frequencies for equal-tempered scale. http://www.phy.mtu.edu/~suits/notefreqs.html
“What is the frequency response of the NAPSTN?” Hubtechinsider.
http://hubtechinsider.wordpress.com/2009/06/03/what-is-the-frequency-response-of-the-north-americanpublic-switched-telephone-network/
Courtney, David. “Rag Khammaj (Khamaj).” Indian Classical Music.
http://chandrakantha.com/raga_raag/khammaj/khammaaj.html
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http://commons.wikimedia.org/wiki/File:Ripple_effect_on_water.jpg
http://commons.wikimedia.org/w/index.php?title=File:CPT-sound-physical-manifestation.svg&page=1
http://commons.wikimedia.org/wiki/File:Wave_frequency.gif
http://commons.wikimedia.org/wiki/File:Modulation_d%27amplitude_figure_2.2.1.3.png
http://commons.wikimedia.org/wiki/File:Amfm3-en-de.gif
http://images.tutorvista.com/content/waves/noise-music.gif
http://commons.wikimedia.org/wiki/File:Aulos_player_MAR_Palermo_NI22711.jpg
http://en.wikipedia.org/wiki/File:C_major_pentatonic_scale.PNG
http://upload.wikimedia.org/wikipedia/commons/0/08/Green_harp_flag_of_Ireland.svg
http://commons.wikimedia.org/wiki/File:C_major_scale.PNG
http://commons.wikimedia.org/wiki/File:C_minor_pentatonic_scale.png
http://commons.wikimedia.org/wiki/File:Aeolian_mode_C.png
http://commons.wikimedia.org/wiki/File:Dorian_mode_C.png
http://upload.wikimedia.org/wikipedia/commons/c/ca/Hijaz_scale.png
http://en.wikipedia.org/wiki/File:Bayati.png
http://commons.wikimedia.org/wiki/File:Akbar_and_Tansen_visit_Haridas.jpg
http://commons.wikimedia.org/wiki/File:Melakarta.katapayadi.sankhya.72.png
“Rop Tú mo Baile” sung by Gareth Hughes. http://en.wikipedia.org/wiki/File:Rop_tu_mo_baile.ogg