Computer Synthesis
Computer Synthesis of Jazz Improvisation
Dhroova Aiylam
Massachusetts Academy of Math and Science
Abstract
In computer synthesis of jazz music, randomly generated notes do not reflect the chord
changes upon which they should be based. Furthermore, those systems that do harmonically
verify the quality of the music perform harmonic analysis independently of the chords,
considering only the intervals between successive notes. The purpose of this project is to design
a program that can improvise over and perform harmonic analysis on a jazz melody. Based on
the moving tones in the chord changes for a tune, a melodic line of guide tones was established.
Music was be interpolated through these guide tones with either discrete tones or scales, based
on the available tensions on the chords and the harmonic analysis on the progression. The notes
chosen are known to be consonant with the corresponding chord. It was determined that the
software written was capable of synthesizing music that both sounded good, adhering to the
musical rules by which a solo must abide, and generated music dynamically and in a way which
could not be repeated. The final project not only contributes to general knowledge regarding
computer applications to synthesis of music, but can also be used as a teaching tool of the jazz
style.
Introduction
Randomly generated music does not always sound good. Most controlled generation of
music is somewhat deterministic – it will allow only a certain degree of randomness within its
own set of rules, in a way that seldom reflects the original. The goal of this project is to design a
computer program that can perform harmonic analysis on a jazz melody and improvise
appropriate music over it. The purpose of the project is to explore the applications of computer
algorithms to synthesis of original music based on a set of chord changes.
Although it is one of the most truly American styles of music, jazz is really a reflection of
cultural diversity and individualism of this country. It is made unique by its emphasis on the
solo, in which performers invent and play music in real time. Although the music is rooted in the
chord changes, there is room for incredible creativity on the part of the performer.
Given the nature of the jazz style, applications of computers to synthesis
of jazz music abound. Computer reproduction of sheet music is well-established and fairly easy,
so the jazz style provides a unique challenge to the engineer in its demand of new and innovative
music generated dynamically. There are musical rules which need to be followed, but they are
quite comprehensive. If they are properly followed, the resulting music will not only sound
harmonious, but will also reflect the music upon which it is based. Computer algorithms that
generated music by these rules, then, are very likely to produce melodic music. Furthermore, a
computer can check that generated music abides by these rules much more quickly and reliably
than a human can.
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Computer Synthesis
Literature Review
Music Theory
Even more so that other styles of music, jazz is a very theoretical style of music. To
completely understand a jazz tune, it is necessary to be able to describe it musically and analyze
it harmonically. Only when a soloist has a very deep understanding of the music they play can he
even begin to synthesize their own music.
Music is, at its most basic, an arrangement of sounds in time. Western, tonal music is
based the note, a sound played for a certain duration of time. Notes are differentiated by the pitch
they resonate at. Although they are technically arbitrarily many possible pitches, the human ear
is essentially unable to distinguish between consecutive notes. While most instruments allow for
inflection, sliding between tones and thereby hitting “non-notes” in between, the piano is only
capable of playing discrete notes.
In an octave, there are 12 different musical notes – C, C#/Db, D, D#/Eb, E, F, F#/Gb, G,
G#/Ab, A, A#/Bb, and B. The note C exists in multiple octaves, but its pitch is an integer
multiple of the frequency of each other C below it. The range of an instrument consists of some
number of octaves – in the case of the piano, there are 8.
Music is written on a staff, a set of five lines with four spaces in between. Lines and
spaces on the staff correspond to white keys on the piano. The clef, written on the left at the very
beginning on the piece, assigns an individual value to lines and spaces. The two most commonly
used clefs are the treble (G) and bass (F) clefs. Each fixes its respective note and all the other
note positions are uniquely determined. When there is no more room on the staff, it is extended
with ledger lines.
Music is divided into measures, each of which has a fixed length. Notes in a measure
must be additionally described by their duration. A whole note has the longest duration of all. All
other notes are determined relative to the whole note – the half note has half its length, the
quarter note ¼, and etcetera. Notes of duration less than a quarter note are denoted with flags.
Each flag halves the duration. Placing a dot after a note gives it 1 ½ times its normal value. A
dotted half note, for example, lasts ¾ as long as a whole note. Rests, breaks in the stream of
musical notes, also have time values like notes. Each type of note has a corresponding rest.
Generally, however, rests are not dotted.
Time is additionally described by a time signature and a tempo. The tempo describes how
fast the music is played. This can be either a word (like allegro), or an actual BPM value (200).
Notes in a tune can be individually modified as well. A note can be played legato, meaning
smoothly, or staccato, meaning choppily. A slur line over a series of notes is used to designate
the former; the latter is indicated by a dot beneath the note.
Time signature describes the amount and type of notes in a measure. The upper value of a
time signature gives the number of notes in a measure, and the lower value gives the type. For
example, 4/4 time, by far the most common in jazz and in all music, describes a measure with 4
quarter notes. The question naturally arises – why do 3/4 and 6/8 time exist as two separate
entities? The difference is in meter. (Introduction to Music Theory, retrieved October 20th , 2011)
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Computer Synthesis
Meter can be either simple or compound. In simple meter, a beat can be broken down into
two notes. In compound meter, the beats are divided into three notes. Odd meter is some
combination of the two. Most jazz tunes are in 4/4 or 3/4 time (both simple meter), but some
exceptions stand out. Dave Brubeck’s Unsquare Dance is in 7/8 time – odd meter. So is his Take
Five. Both are jazz standards, but are clear exceptions. (The Real Book, 2004)
Rather than working in terms of notes, most music is conducted in terms of the interval.
That way, the music can be transposed (shifted) up or down to yield the same song, just in a
different key. A half step is the distance from one key on the keyboard to the next adjacent key.
A whole step is the same as two half steps. Nearly all scales, which form the basis of all music,
are composed solely of whole and half steps in different combinations.
As a result of the way the staff is constructed, it is impossible to play anything other than
a white key without adding notation to denote moves by a half step. These are called accidentals.
An accidental can be either a sharp (#) or a flat (b), sharps raising the note by a half step and flats
lowering them by the same amount. This means that a note can usually be written in many ways.
Consider, for example, the note a half step above C. We could write that note as C#, but also as
Db. In fact, since sharps and flats allow multiplicity, we could write it as B double sharp or D#
double flat. Although these distinctions do not make any difference on their own, they depend
on, and are central to, key of the tune.
Music is based on scales. The two simplest types of scales are the major scale and the
minor scales. To construct the major scale of some note X, simply start X and play whole, whole,
half, whole, whole, whole, half, where the intervals stack. This means the X major scale is given
by the notes (X, X + 1, X + 2, X + 2.5, X + 3.5, X + 4.5, X + 5.5, X + 6.5) For example, the C
major scale is given by the notes C, D, E, F, G, A, B, (C).
There are several types of minor scales : the natural minor, harmonic minor, and melodic
minor. The natural minor is given by the sequence whole, half, whole, whole, half, whole, whole.
The harmonic minor is given by sharping the 7th scale tone of the natural minor. The melodic
minor is obtained by raising the 6th and 7th scale tones of the natural minor by a half step. Thus:
C natural minor: C, D, Eb, F, G, Ab, Bb, C.
C harmonic minor: C, D, Eb, F, G, A, Bb, C.
C melodic minor: C, D, Eb, F, G, A, B, C
(Miller, 2005).
Scales give rise to the next basic musical construct – the notion of key. The key of a tune
is the scale upon which the notes of the melody are based. For example, a melody based on the
notes C, D, E, F, G, A, B is in the key of C major. A melody based on the notes C, D, Eb, F, G,
Ab, Bb is in the key of C minor. For brevity, the sharps and flats are placed once that the
beginning of the tune, and are implied on all affected notes throughout. This is the key signature.
Because there are no sharps or flats in the key C major, there is no key signature. C minor has 3
flats – E, A, and B. Thus, the three flats are placed on the corresponding lines and spaces at the
very beginning of the tune, and are implied everywhere else unless otherwise stated. There are a
total of 15 major key signatures and 15 minor ones (Humphries, 2007).
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Computer Synthesis
Figure 1. Major Keys. The 15 major keys in music are uniquely determined by their key signature, which can range
from 7 flats to 7 sharps (“Key and Intervals”, n.d.).
Figure 2. Minor keys. The 15 minor keys in music are uniquely determined by their key signature, which can range
from 7 flats to 7 sharps. Each has a relative major, which is the major key of the same signature, and a parallel major,
which is the major key of the same tonic (“Key and Intervals”, n.d.).
Scales are also the root of the most fundamental concept in jazz and in most music : the
chord. A chord is a collection of notes of specific degree in a scale. Playing all these notes at
once is playing the chord. For example, the major chord is built on the root (1st tone), 3rd (tone)
and 5th of the major scale. The C major chord comprises the notes C, E, G. The minor chord is
built on the root, 3rd and 5th of the minor scale. The C minor chord comprises of the notes C, Eb,
G. (Humphries, 2007)
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Computer Synthesis
The major and minor chords are the only two popular three note chords. Most chords,
especially in jazz, are four note chords. The most popular chord four note chords are shown in
Figure 3.
Figure 3. Four note chords. Most jazz chords are four note chords. The basic, major 7 four note chord consists of the
root, third, fifth, and seventh. Accidentals and substitutions on these tones give different four note chords like the
ones above. (“Key and Intervals”, n.d.).
Construction of a Solo and Melodic Rules for Soloing
Harmonic analysis of a tune exists on several levels. From small to large, there is the
melodic movement over an individual chord, the transitions between chords change, net
harmonic movement over a chord progression (ii – V – I, for example), and the moving tones
throughout the tune as a whole. For any melody or solo to “sound good” over a set of chord
changes, they must abide by a number of rules. All the necessary theory is based on the key of
the tune.
Firstly, the solo must mimic general melodic motion, the largest level of harmonic detail.
The chords “pull the ear” in a certain direction, and a solo trying to go in a completely different
direction will clash with the chord progression. Furthermore, there must be some melodic
continuity or unity that ties the whole solo together, lest it be a collection of random licks.
Repeated phrases and patterns achieve this end. However, one must strike a balance between
unity and creativity – the solo cannot be too repetitive. Any music so generated, however, is
grounded in the melodic motion (Personal Communication, November 28th, 2011).
General melodic motion can be described at several levels. The most simple of these is a
bass-line, which can be as simple as just the root of the chord, or more detailed, like walking
bass. The bass-line, when combined with the guide tones, is usually a good skeleton for melodic
movement. Guide tones, which are usually the moving tones, are the 3rd and 7th of each chord.
Chords in jazz are 4-tone chords as opposed to triads, so each chord consists of a root, a third, a
fifth, and a seventh. Depending on the chord, different accidentals are applied. The third and
seventh of a chord solidify its harmonic identity, but with the root the chord is all but spelled out.
The melody is also an adequate indicator of melodic motion. We know the melody
sounds good against the changes by default. Thus, quoting the melody, playing small, perhaps
articulated fragments of the melody in the solo, constitute a good starting point for a solo.
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Computer Synthesis
Furthermore, harmonies on the melody, like some of the alternate instrument parts and alternate
left hand lines, are ready-made to function over the changes. As with the bass-line, one can never
go wrong.
The next largest level of detail is the individual chord progression. Recognizing these is
fairly easy if you look. Some popular jazz progressions are depicted in Figure 4:
Figure 4. Popular chord progressions. Although there are many variations, most if not all make use of the ii-V-(I)
progression (“Popular Chord Changes”, n.d.).
and others. All standard jazz tunes, however, makes use of the ii – V – I progression. Its
importance and frequency in the jazz style cannot be overemphasized. It is important that a
soloist is aware of lines that sound good over common progressions like this one, so that all they
need do is modulate when playing in a different key. It is usually possible to solo over a common
chord progression with just a scale or two because of the close musical relationship the chords
have to one another. Moving tones usually move stepwise within the group of chords, so chord
voicings and moving tones are greatly simplified (Tomassetti, 2003).
Next is the individual chord change. Sometimes a chord change will take place within a
measure, whereas other times it will occur between measures. Through moving tones or
otherwise, it is important to anticipate the chord change, to make it so the ending notes of each
phrase resolve to the next chord. Some variance is permitted in the time here, and the resolution
can take place slightly before or slightly after the change. Generally, chord changes can be
outlined by connecting the appropriate guide tones of the chords and playing the transition with
some melody connecting the start and end tones. What is allowed as part of this transitory
melody depends on the two chords and their interval.
More quickly moving chords are harder to improvise over for a soloist because they
require you hit chord tones and available tensions, so as to outline the harmony, but that
melodically, the chord change is anticipated. Although this is difficult for the performer because
6
Computer Synthesis
of the amount of information he have to process in such a short span of time, it also diminishes
the time he have to think up of a melodically creative idea – in other words, it takes some of the
ingenuity out of the equation, making it much easier for a computer to do. As is the case with
performers, it is difficult for solos over very repetitive chord changes to be innovative every
time. A single chord with little change, however, makes it easy to find scales that work over the
chord.
Finally, there is the individual chord. These are the building blocks of the progression,
and each is a canvas for improvisation. Each chord offers a collection of tools, all of which work
over the chord. It is up to the soloist to put them together musically. Generally these tools
include : chord scales, a blues scale, modal scales, chord tones, and available tensions (11ths,
13ths, etc.). If the soloist stays works with these tools and does not stray too far from them, the
solo will come out well.
Finally, and perhaps most obviously, the chords themselves are important soloing tools.
They dictate the musical flow of the tune, so even just playing chords directly in solos will never
fail. Alternate approaches involving chords include arpeggios, playing the notes of the chord
separated, resolved dissonance, where a chord is played with one wrong note that resolves to a
chord tone, and simply playing chords with the left hands. There are many different methods for
voice leading, and chords add texture to solos. One can even play shifted chords based on the
scale tones, which is a powerful way of ensuring multiple notes in unison sound good as a group.
This system of playing spaced intervals on the scale in question is effective in generating
melodic volume, especially for rhythm instruments. Since guitars and pianos normally comp
during solos, the sound of the solo is weakened by held notes and rests. The difference lies in the
inability to achieve and sustain tone like a wind instrument can, so guitars and keyboards require
constant motion in the melody. Playing chords or chord variants in the solo can make up for this
lack of volume. One can take, for example, the I, III and VI of a scale and shift them up as a
“chord”. As the notes are drawn from the same chord scale, they sound good.
Algorithmic Synthesis of Music Using Markov Chains
The stochastic approach is one of several major methods by which music is pseudorandomly generated. For example, a number could be chosen which would correspond to interval
size. Intervals would be weighted differently depending on their scale degree with respect to the
previous note.
This is known as first order approximation because note selection is a function of only
the previous note. By increasing the order of the randomness , the solo is made more structured.
The process is inherently stochastic, however ; to prevent repeated sequences, one could add
exception cases.
Alternatively, Markov Chains offer another solution. Then as opposed to working solely
in the realm of intervals, which do not depend on scale position, the program will take into
account the different states in which the program could be (different notes), and change the
probability distribution accordingly. Then, the software would not treat a minor 3rd on the
supertonic the same way it would a minor 3rd on the submediant. The Markov Chain is rigid, but
7
Computer Synthesis
still stochastic. It can also be easily nested and parallelized, so that the notes and their
organization in time, two completely different but related things, could be randomized in parallel
(Franz, 1998).
There is always the question of total randomness in generation of lines. The programmer
must place some sorts of limits on the musical range of a phrase, lest it jump around the
keyboard too much. One can approach the task by simply mapping guide tones and resolutions,
and focusing only on the connection between two consecutive guide tones. Naturally, any string
of connecting tones can be decomposed into a number of ascending and descending lines (Franz,
1998).
Rest D1
Ab1 A1
B1
Db2 D2
Rest 0.52 0
0
0
0.1
D1
0
0
0
0
0
B1
0
E2
F2
Gb2 G2
Ab2 A2
0.01 0.02 0.01 0
0
Bb2 B2
C3
Db3 D3
Eb3 E3
Total
0.08 0
0
0.07 0
0.03 0.02 0.05 0.03 0.03 0.01
87
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0.07 0.07 0.14 0
0.07 0.64 0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0.5
0
0
0.5
0
0
0
0
0
0
0
0
0
0
2
D2
0.04 0
0
0
0.2
0
0
0
0
0.36 0
0
0.36 0
0.04 0
0
0
0
0
25
E2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
F2
0.5
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0
0
0
0
0
0
2
Gb2 0.1
0
0
0
0.02 0
0.34 0
0
0
0
0
0.46 0.05 0
0
0.02 0
0
0
41
G2
0
0
0
0
0
0
0
0
0.33 0.33 0
0
0.33 0
0
0
0
0
0
0
3
A2
0.26 0
0
0
0
0
0
0
0.03 0.45 0.03 0.16 0
0
0
0.03 0.03 0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
B2
0.05 0
0
0
0
0
0
0
0
0
0
0
0.9
0
0
0
0
0
0
0.05
20
C3
0
0
0
0
Db2 0
Bb2 1
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0
0
0
0.5
4
Db3 0.13 0
0
0
0
0
0.03 0
0
0
0
0
0.13 0.03 0.17 0
0
0.33 0
0.17
30
D3
0
0
0
0
0
0
0
0
0
0
0
0
0.09 0
0.91 0
0
0
0
0
11
E3
0.9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.1
0
0
10
F3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
Figure 5. First order Markov Matrix. This is an example stochastic matrix, which gives the probability of any given
state following the current state. (“Markov Chains as Tools”, n.d.).
8
Computer Synthesis
Rest
Rest
Rest
Rest
Rest
Rest
B1
B1
B1
Db2
D2
D2
D2
D2
E2
F2
Gb2
Gb2
Gb2
Gb2
Gb2
G2
G2
A2
A2
A2
A2
A2
Bb2
B2
B2
B2
C3
C3
Db3
Db3
Db3
Db3
Db3
Db3
Db3
D3
E3
E3
F3
Rest
B1
Db2
D2
E2
B2
D1
Db2
D2
D2
Rest
B1
Gb2
B2
Rest
G2
Rest
B1
D2
A2
Bb2
Gb2
A2
Rest
F2
Gb2
G2
Db3
Rest
Rest
A2
E3
A2
E3
Rest
D2
A2
Bb2
B2
D3
E3
B2
Rest
D3
Rest
Rest
0.61
0
0
0.5
1
0.33
0
0
0
0
1
0
0
0
0.5
0
1
0
0
0.33
1
1
0
0.63
1
0
0
0
0
0
0
1
0
1
0.5
0
0
1
0
0
0.8
0
0.33
0
1
D1
0
0.11
0
0
0
0
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0
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0
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0
0
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0
0
0
0
0
0.33
0
0
0
0
0
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0
0
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0
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0
0
0
0
0
0
0.67
0
0
0
0
0
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0
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0
0
0
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0
0
0
0
0
B1
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0.42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Db2
0
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0
0
0
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0.78
1
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1
0
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0
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0.4
0
0
0
0
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0
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0
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0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
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0
0.5
0
0
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0
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0.16
0
0
0.5
0
0
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1
0.11
0
0
0
0
0
0
0
0
0
0.58
0.67
0
0
0
0.25
0
0
0
0
0
0
0
0
0
0
0
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0.67
0
0
0
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0.5
0
0
0
0
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Ab2
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0
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0.06
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0.67
1
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0.89
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0.89
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0.6
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0.67
1
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0
B2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
1
0
0
0
1
0
0
0
0
0
C3
0.06
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Db3
0.03
0
0
0
0
0
0
0
0
0
0
0
0.11
0
0.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0.33
0
0
0
0
0
0
0
0.33
0
0
0
0
0
0.11
0
0
D3
0.03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.2
0
0.22
0
0
Eb3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.33
0
0
E3
0.03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Total
31
9
1
2
1
3
1
1
9
1
1
3
9
1
2
1
4
1
12
9
2
1
1
8
1
10
1
1
3
1
5
1
2
2
4
1
3
1
5
10
5
10
9
1
2
Figure 6. Second Order Markov Matrix. The following is the stochastic matrix of a Markov Chain that generates notes
based upon two-note series. (“Markov Chains as Tools”, n.d.).
Random Music and Binary Trees
Another approach is given by binary trees. The approach involves stringing out triads
in a linear representation and then piecing together the tones differently. The first note so
generated is the root of the tree. The subsequent notes are compared, and smaller sub-trees are
established again and again until the binary tree is complete. The advantage is that it is a good
way of combining strings of known notes with controlled variability. A sizeable disadvantage is
its inability to deal with repeated notes effectively. These can by synthetically introduced,
however (Chen, 1992).
9
Computer Synthesis
One way to construct and ascending/descending line is randomly, that is by choosing a
note lower than the higher note, then choosing another note lower than that, and so on until the
lower note is reached. However, this does not adequately consider the melodic quality of these
notes. For running eighth note lines, however, this is often sufficient; connecting tones are not
always heard distinctly (Chen, 1992).
The Markov chain approach works here as well. Because a note can never be taken to a
note higher than itself, the stochastic matrix is triangular. This reduces total multiplications from
n3 to n2.
Dynamical systems provide yet another approach. When one wishes to “ornament” a note
(articulate it), one can use a discrete dynamical system with complex eigenvalues (norm < 1) as a
way to ensure that the note of choice is the one that is landed on at the end of the phrase, but that
there is controlled variance in between.
Dynamical Systems
A dynamical system is a system whose state vector can be modeled by matrix
multiplication. It the state vector is of dimension n, the transform matrix is n x n. The first
coordinate of the matrix entry will give the current state, and the second will give the state under
transformation. The value of the entry is the probability that this change happens (Bretscher,
2008).
The underlying mathematics of a Markov Chain is recursion. When expanded, the
equation
gives a recursion of n linear functions in terms of themselves, which can clearly be computed.
Diagonalizing is a means to solve this in closed form for t, provided the eigenvalues can
be obtained. If the matrix can be diagonalized, the number of computations goes from n3 to n, as
only entries along the diagonal have to be multiplied.
Dynamical systems can be both discrete and continuous. Discrete dynamical systems
satisfy the matrix equation above, and they only exist in stages. Alternatively, the rate of change
of the state vector can be given by the matrix product, in which case the system becomes
discrete. For a discrete model, it is enough to consider the discrete system, as long as points are
chosen properly (Bretscher, 2008).
JFugue and the MusicString
After downloading the jfugue.jar library simply create a project and import to start
playing music. Soundbanks are available for download from the Sun website (Koelle, 2008).
10
Computer Synthesis
The MusicString is the input form with which the player object works. This makes it very
easy to embed JFugue into Java code, because the MusicString is a string and can therefore be
worked with in non-musical Java code.
Player player = new Player();
player.play("C");
player.play("C7h");
player.play("C5maj7w");
player.play("G5h+B5h+C6q_D6q");
player.play("G5q G5q F5q E5q D5h");
player.play("T[Allegro] V0 I0 G6q A5q V1 A5q G6q");
player.play("V0 Cmajw V1 I[Flute] G4q E4q C4q E4q");
Figure 7. Basic player elements in JFugue. It is very easy to specify almost completely the sequence of notes with all
vital musical information in but a single line of code. (“Complete Guide to JFugue”, n.d.).
JFugue is also set up to handle algorithmic music very well. As opposed to using a name,
one can specify a note by its MIDI value, which eliminates time spent trying to convert between
the two with a lookup table. Algorithmic work can be done by the program, which will pass only
a final string to main() to play (Koelle, 2008).
Notes and Chords in JFugue
Octave
0
1
2
3
4
5
6
7
8
9
10
C
0
12
24
36
48
60
72
84
96
108
120
C#/Db
1
13
25
37
49
61
73
85
97
109
121
D
2
14
26
38
50
62
74
86
98
110
122
D#/Eb
3
15
27
39
51
63
75
87
99
111
123
E
4
16
28
40
52
64
76
88
100
112
124
F
5
F#/Gb
6
17 18
29 30
41 42
53 54
65 66
77 78
89 90
101 102
113 114
125 126
G
7
19
31
43
55
67
79
91
103
115
127
G#/Ab
8
20
32
44
56
68
80
92
104
116
A
9
21
33
45
57
69
81
93
105
117
A#/Bb
10
22
34
46
58
70
82
94
106
118
B
11
23
35
47
59
70
83
95
107
119
Figure 8. MIDI value table for notes. Algorithmic music generation is much easier when conversions between notes
and MIDI values can be skipped, which JFugue allows for. (“Complete Guide to JFugue”, n.d.).
11
Computer Synthesis
JFugue Name
Maj
Min
Aug
Dim
dom7
maj7
min7
sus4
sus2
maj6
min6
dom9
maj9
min9
dim7
add9
min11
dom11
dom13
min13
maj13
dom7<5
dom7>5
maj7<5
maj7>5
minmaj7
dom7<5<9
dom7<5>9
dom7>5<9
dom7>5>9
Intervals (0 = root)
0, 4, 7
0, 3, 7
0, 4, 8
0, 3, 6
0, 4, 7, 10
0, 4, 7, 11
0, 3, 7, 10
0, 5, 7
0, 2, 7
0, 4, 7, 9
0, 3, 7, 9
0, 4, 7, 10, 14
0, 4, 7, 11, 14
0, 3, 7, 10, 14
0, 3, 6, 9
0, 4, 7, 14
0, 7, 10, 14, 15, 17
0, 7, 10, 14, 17
0, 7, 10, 14, 16, 21
0, 7, 10, 14, 15, 21
0, 7, 11, 14, 16, 21
0, 4, 6, 10
0, 4, 8, 10
0, 4, 6, 11
0, 4, 8, 11
0, 3, 7, 11
0, 4, 6, 10, 13
0, 4, 6, 10, 15
0, 4, 8, 10, 13
0, 4, 8, 10, 15
Figure 9. Chord symbols in JFugue. In order to generate left hand voicings, it is necessary to have the full chords at
easy access. JFugue comes with this functionality. (“Complete Guide to JFugue”, n.d.).
Engineering Proposal
Even controlled “random” music generation over jazz chord changes does not always
adequately analyze the tune harmonically before synthesizing music, and often any analysis
is independent of the chords themselves, so the music does not outline the harmonies.
The engineering goal is to write code that can take as input the chord changes for a tune,
analyze it harmonically, and synthesize music that reflects that analysis.
Based on the moving tones in the chord changes for a tune, a melodic line of guide tones
will be established. Music will be interpolated through these guide tones with either discrete
tones or scales. The tones will be based on the available tensions on a chord while the scales
will be chosen based on the harmonic analysis. The scales will be chosen from a set of scales
unique to each chord, which are known to sound good over that specific chord. (Insert results
here, along with summary of outcome).
12
Computer Synthesis
The following are the design criteria and secondary goals:
1.
2.
3.
4.
The generated music sounds good over the chord changes
The generated music outlines the harmony
The user interface is manageable
Generated music is new and varied each time
The device will be tested by comparing the generated music against the set of musical
rules that dictate improvisation. Having verified that the results sound good, they will be
further checked to make sure there is not too much musical repetition
Methodology
The Java programming language and JFugue libraries (open source) were used as a way
for the computer to produce controlled sound. Java code was written to internally generate a
sequence of notes that was then be passed to the player to play.
First, the basic musical elements were constructed internally to the code. These included
chords, notes and scales, each of which the program used to process and create music
dynamically. The program took as input the chord changes for the tune, in the form of the
JFugue musicstring. Once the computer had obtained, as input, the changes and the key, it began
harmonic analysis on the tune.
This involved breaking all chords down into their scale degrees and identify moving
tones. Moving tones were obtained by comparing consecutive chord forms, whereas scale
degrees were obtained from the key of the tune. Moving tones were used to decide how to voice
chords with the left hand in addition to the primary purpose of outlining the harmony. The code
took into account the chord, the tones to be connected, scales that work over the chord, and the
key of the tune in synthesizing a line over a measure.
Using the analysis, a set of guide tones were established, which outlined the general
melodic motion of the tune. Then, lines were interpolated through the guide tones, which serve
as but a melodic skeleton for the program. Music was interpolated in four different ways – tone
based, harmonic based, chord based, scale based.
Tone based interpolation is two-fold. In one method, two notes are connected using notes
from a fixed set. This is similar to the scale based method, but it includes chord tensions. Every
valid note between the two was strung out, and notes were dropped randomly. In another
method, the space between consecutive guide tones is small enough that there need not be any
significant melodic motion. Here, notes are weighted by how musically relevant they are to the
chord; as a consequence, most of the notes that are generated are either chord tones or available
tensions on the chord. The number of notes was chosen to fit the time signature, and each line
was appended to the final musicstring after completion.
Additionally, chord based interpolation was used to give a fuller sound to the solo. Chord
based interpolation is simply a variant on tone based interpolation where instead of notes, triads
13
Computer Synthesis
built on the chord scale were selected. The process for root selection was identical to the tone
based system. All root notes are chosen from the chord’s guide tones.
In scale based interpolation, guide tones will be connected using scales known to sound
good over the chord. Since the guide tones are specific notes of the chord, they are contained in
the chord scale and in other functional scales. The scale will then be split into its constituent
tones, rearranged, and pieced back together semi-randomly to generate the phrase.
Harmonic interpolation is a method in which every note between the two guide tones is
played in the phrase. It is normally reserved for intervals that are small, so this was reflected in
the code. Based on the size of the gap between two notes, different methods are used to
interpolate harmonically.
Finally, the program will be given a specific function for articulation. This will take
spaces reserved for held notes, rests, or articulation and replace them with small, articulated
phrases. These will be hard-coded, since they are unlikely to occur synthetically. The final
product, the musicstring, was played by the player after computation was finished. Tests were
conducted to measure the frequencies of specific phrases to ensure no phrase occurred
disproportionately frequently.
The only materials used in the construction of the device were the Java programming
language and JFugue libraries.
Results
Design Criteria and Secondary Goals
1.
2.
3.
4.
The generated music sounds good over the chord changes
The generated music outlines the harmony
The user interface is manageable
Generated music is new and varied each time
The device was tested by comparing the generated music against the set of musical rules
that dictate improvisation. Having verified that the results sound good, they were further
checked to make sure there is not too much musical repetition.
Prototype Designs and Diagrams
An initial prototype of this device focused on the ability to play processed music as
opposed to focusing on improvisation. The prototype voiced chords in the left hand in one of
several different ways, based on user input. Being a prototype, however, input was in the
musicstring format, internal to the program. The prototype not only give an idea of the
plausibility of the project, but it demonstrated the ability to take chords, process them, and
generate varied sequences of tones.
14
Computer Synthesis
Criteria
1. Generated music sounds
good*
2. Generated music is new
each time
3. Generated music reflects the
chord changes of the original
music
4. Harmonic analysis is
displayed and explained
5. Chords or a bass-line are
added to the LH
6. Easy to implement
7.
User
manageable






interface
is
Design
A
Design
B
Design
C
Design
D
Design
E
Design
F
8/10
8/10
8/10
8/10
9/10
9/10
5/10
5/10
9/10
9/10
10/10
10/10
7/10
7/10
9/10
9/10
9/10
9/10
7/10
5/10
9/10
8/10
10/10
9/10
6/10
6/10
9/10
9/10
10/10
10/10
5/10
8/10
2/10
5/10
2/10
4/10
10/10
6/10
10/10
6/10
10/10
6/10
Design A: The music is based only on the chord and chord scale.
Design B: The music is based only on the chord and chord scale. User interface is not
graphical.
Design C: Using binary trees and Markov chains for quasi-stochastic tone generation.
Design D: Using binary trees and Markov chains for quasi-stochastic tone generation.
User interface is not graphical.
Design E: Using binary trees, Markov chains, and dynamical systems for controlled tone
generation.
Design F: Using binary trees, Markov chains, and dynamical systems for controlled tone
generation. User interface is not graphical.
* The notes are generated by algorithms that are based upon musical criterion for a melodic solo.
15
Computer Synthesis
Data and Graphs
T120 C4w+B4w+[43]i [45]i [47]i [48]i C4w+B4w+[55]i [52]i [53]i [54]i
C4w+Bb4w+[50]i
[49]i
[48]i
[51]i
F4w+A4w+[51]i
[48]i
[49]i
[50]i
Bb3w+A4w+[55]i
[53]i
[58]i
[58]i
Bb3w+A4w+[53]i
[51]i
[53]i
[55]i
Bb3w+Ab4w+[40]i [39]i [38]i [41]i Eb4w+G4w+[41]q [42]i [43]i Ab4w+C5w+[41]i
[39]i [37]i [36]i Ab4w+C5w+[36]i [33]i [34]i [35]i D4w+C5w+[48]i [50]i [52]i
[50]i G4w+B4w+[45]i [43]i [41]i [40]i C4w+B4w+[39]q. [38]i A4w+C5w+[38]i
[41]i [41]i [41]i D4w+C5w+[43]i [45]i [43]i [41]i G4w+B4w+[43]i [45]i [47]i
[45]i C4w+B4w+[47]i [48]i [48]i [48]i C4w+B4w+[47]i [48]i [47]i [45]i
C4w+Bb4w+[38]i
[43]i
[45]i
[46]i
F4w+A4w+[49]i
[48]i
[47]i
[46]i
Bb3w+A4w+[43]i
[41]i
[39]i
[38]i
Bb3w+A4w+[38]i
[39]i
[38]i
[36]i
Bb3w+Ab4w+[48]i
[46]i
[48]i
[48]i
Eb4w+G4w+[43]i
[44]i
[44]i
[44]i
Ab4w+C5w+[43]q [44]i [45]i Ab4w+C5w+[46]i [51]i [49]i [48]i D4w+C5w+[51]q.
[50]i G4w+B4w+[50]i [52]i [52]i [53]i C4w+B4w+[52]i [50]i [48]i [47]i
C4w+B4w+[47]i [47]i [50]i [47]i C4w+B4w+[47]i [48]i [50]i [50]i C4w+B4w+[39]i
[38]i [37]i [40]i D4w+C5w+[40]q [41]i [42]i D4w+C5w+[43]i [45]i [43]i [45]i
G4w+B4w+[45]i [41]i [40]i [38]i G4w+B4w+[38]i [40]i [41]i [43]i C4w+B4w+[47]h
C4w+B4w+[47]i
[45]i
[47]i
[48]i
A4w+Db5w+[49]i
[50]i
[52]i
[53]i
A4w+Db5w+[55]i
[55]i
[55]i
[55]i
D4w+C5w+[56]i
[55]i
[54]i
[53]i
D4w+C5w+[46]i [45]i [44]i [47]i G4w+B4w+[47]i [52]i [50]i [48]i G4w+B4w+[41]i
[40]i [38]i [36]i D4w+C5w+[36]i [33]i [34]i [35]i D4w+C5w+[38]i [38]i [43]i
[43]i G4w+B4w+[38]i [41]i [43]i [38]i G4w+B4w+[43]i [38]i [40]i [41]i
C4w+B4w+[47]i
[48]i
[50]i
[52]i
C4w+B4w+[55]i
[52]i
[53]i
[54]i
C4w+Bb4w+[55]i
[57]i
[57]i
[58]i
F4w+A4w+[53]i
[50]i
[48]i
[46]i
Bb3w+A4w+[45]i
[46]i
[46]i
[46]i
Bb3w+A4w+[41]i
[36]i
[38]i
[39]i
Bb3w+Ab4w+[46]i
[44]i
[43]i
[41]i
Eb4w+G4w+[37]i
[37]i
[37]i
[41]i
Ab4w+C5w+[36]i
[37]i
[37]i
[37]i
Ab4w+C5w+[43]i
[44]i
[43]i
[41]i
D4w+C5w+[42]q. [41]i G4w+B4w+[40]i [41]i [36]i [41]i C4w+B4w+[36]i [33]i
[34]i [35]i C4w+B4w+[36]i [33]i [34]i [35]i C4w+B4w+[42]i [41]i [40]i [43]i
C4w+B4w+[43]i [38]i [40]i [41]i
Figure 10.The musicstring output for trial 1 of the software on the same set of chord changes, to Afternoon in Paris.
16
Computer Synthesis
C4w+B4w+[43]i
[43]i
[47]i
[45]i
C4w+B4w+[47]i
[50]i
[49]i
[48]i
C4w+Bb4w+[39]i
[36]i
[37]i
[38]i
F4w+A4w+[45]i
[51]i
[48]i
[51]i
Bb3w+A4w+[45]h Bb3w+A4w+[46]i [49]i [48]i [47]i Bb3w+Ab4w+[36]i [41]i [37]i
[41]i Eb4w+G4w+[41]i [46]i [44]i [46]i Ab4w+C5w+[48]i [45]i [46]i [47]i
Ab4w+C5w+[56]i [53]i [54]i [55]i D4w+C5w+[40]h G4w+B4w+[41]i [43]i [41]i
[41]i C4w+B4w+[43]i [44]i [45]i [46]i A4w+C5w+[47]i [44]i [45]i [46]i
D4w+C5w+[57]i [62]i [60]i [59]i G4w+B4w+[57]i [60]i [59]i [58]i C4w+B4w+[50]i
[48]i [45]i [43]i C4w+B4w+[43]i [40]i [41]i [42]i C4w+Bb4w+[43]i [43]i [46]i
[43]i F4w+A4w+[46]i [50]i [48]i [53]i Bb3w+A4w+[53]i [50]i [51]i [52]i
Bb3w+A4w+[58]i
[60]i
[62]i
[60]i
Bb3w+Ab4w+[41]i
[39]i
[41]i
[43]i
Eb4w+G4w+[35]i
[34]i
[33]i
[36]i
Ab4w+C5w+[36]i
[36]i
[39]i
[43]i
Ab4w+C5w+[43]i
[37]i
[39]i
[41]i
D4w+C5w+[48]i
[48]i
[48]i
[50]i
G4w+B4w+[43]i [47]i [45]i [47]i C4w+B4w+[40]i [41]i [45]i [47]i C4w+B4w+[39]i
[38]i [37]i [40]i C4w+B4w+[40]i [40]i [43]i [40]i C4w+B4w+[43]i [45]i [48]i
[50]i D4w+C5w+[53]i [55]i [55]i [55]i D4w+C5w+[57]i [55]i [57]i [57]i
G4w+B4w+[55]i [55]i [59]i [55]i G4w+B4w+[59]i [56]i [57]i [58]i C4w+B4w+[55]i
[53]i [52]i [48]i C4w+B4w+[45]i [43]i [40]i [37]i A4w+Db5w+[37]i [38]i [40]i
[40]i A4w+Db5w+[40]i [37]i [38]i [39]i D4w+C5w+[50]q. [51]i D4w+C5w+[51]q.
[50]i G4w+B4w+[43]i [41]i [40]i [38]i G4w+B4w+[38]i [41]i [43]i [47]i
D4w+C5w+[47]i [45]i [41]i [40]i D4w+C5w+[40]i [43]i [45]i [47]i G4w+B4w+[45]i
[47]i [48]i [50]i G4w+B4w+[45]i [43]i [41]i [43]i C4w+B4w+[52]i [47]i [48]i
[50]i C4w+B4w+[52]i [50]i [52]i [53]i C4w+Bb4w+[42]i [41]i [40]i [39]i
F4w+A4w+[39]i
[39]i
[41]i
[39]i
Bb3w+A4w+[41]i
[44]i
[43]i
[42]i
Bb3w+A4w+[41]i
[44]i
[43]i
[42]i
Bb3w+Ab4w+[55]i
[53]i
[51]i
[49]i
Eb4w+G4w+[44]i
[46]i
[46]i
[49]i
Ab4w+C5w+[44]i
[39]i
[41]i
[43]i
Ab4w+C5w+[44]i
[46]i
[48]i
[46]i
D4w+C5w+[40]i
[37]i
[38]i
[39]i
G4w+B4w+[48]i [50]i [52]i [50]i C4w+B4w+[43]i [43]i [48]i [48]i C4w+B4w+[43]i
[40]i [41]i [42]i C4w+B4w+[48]i [47]i [45]i [47]i C4w+B4w+[48]i [45]i [46]i
[47]i
Figure 11.The musicstring output for trial 2 of the software on the same set of chord changes, to Afternoon in Paris.
17
Computer Synthesis
T120 C4w+B4w+[50]i [50]i [50]i [52]i C4w+B4w+[50]i [48]i [47]i [48]i
C4w+Bb4w+[45]i
[43]i
[41]i
[39]i
F4w+A4w+[39]i
[39]i
[41]i
[41]i
Bb3w+A4w+[46]i
[43]i
[44]i
[45]i
Bb3w+A4w+[58]i
[63]i
[62]i
[60]i
Bb3w+Ab4w+[48]i
[47]i
[46]i
[49]i
Eb4w+G4w+[49]i
[44]i
[48]i
[49]i
Ab4w+C5w+[35]i
[34]i
[33]i
[36]i
Ab4w+C5w+[36]i
[39]i
[38]i
[37]i
D4w+C5w+[41]i [36]i [38]i [40]i G4w+B4w+[41]i [43]i [45]i [47]i C4w+B4w+[44]i
[43]i [42]i [45]i A4w+C5w+[45]i [47]i [48]i [47]i D4w+C5w+[45]i [47]i [45]i
[50]i G4w+B4w+[50]i [47]i [48]i [49]i C4w+B4w+[50]i [52]i [52]i [55]i
C4w+B4w+[55]i
[57]i
[55]i
[53]i
C4w+Bb4w+[42]i
[41]i
[40]i
[43]i
F4w+A4w+[43]i
[46]i
[48]i
[50]i
Bb3w+A4w+[53]i
[55]i
[55]i
[57]i
Bb3w+A4w+[57]i
[60]i
[59]i
[58]i
Bb3w+Ab4w+[39]i
[41]i
[44]i
[44]i
Eb4w+G4w+[37]i
[36]i
[37]i
[37]i
Ab4w+C5w+[36]i
[37]i
[37]i
[37]i
Ab4w+C5w+[43]i
[48]i
[46]i
[44]i
D4w+C5w+[46]i
[45]i
[44]i
[47]i
G4w+B4w+[47]i [47]i [47]i [47]i C4w+B4w+[43]i [40]i [41]i [42]i C4w+B4w+[52]i
[49]i [50]i [51]i C4w+B4w+[39]i [38]i [37]i [40]i C4w+B4w+[40]i [37]i [38]i
[39]i D4w+C5w+[50]q [51]i [52]i D4w+C5w+[53]i [59]i [57]i [55]i G4w+B4w+[52]h
G4w+B4w+[39]i [38]i [37]i [40]i C4w+B4w+[40]i [38]i [36]i [40]i C4w+B4w+[36]i
[36]i [40]i [38]i A4w+Db5w+[40]i [43]i [45]i [46]i A4w+Db5w+[51]i [50]i [49]i
[48]i D4w+C5w+[47]i [43]i [48]i [48]i D4w+C5w+[41]i [38]i [39]i [40]i
G4w+B4w+[40]i [40]i [38]i [41]i G4w+B4w+[38]i [40]i [40]i [45]i D4w+C5w+[45]i
[47]i [52]i [53]i D4w+C5w+[57]i [57]i [57]i [57]i G4w+B4w+[57]i [57]i [59]i
[59]i G4w+B4w+[57]i [60]i [59]i [58]i C4w+B4w+[48]i [45]i [46]i [47]i
C4w+B4w+[55]i [53]i [52]i [53]i C4w+Bb4w+[45]q [44]i [43]i F4w+A4w+[43]i
[45]i [46]i [48]i Bb3w+A4w+[50]i [47]i [48]i [49]i Bb3w+A4w+[57]i [58]i [57]i
[55]i Bb3w+Ab4w+[51]i [48]i [53]i [53]i Eb4w+G4w+[48]i [48]i [48]i [51]i
Ab4w+C5w+[51]i
[46]i
[48]i
[49]i
Ab4w+C5w+[51]i
[54]i
[53]i
[52]i
D4w+C5w+[45]i [42]i [43]i [44]i G4w+B4w+[50]i [50]i [50]i [50]i C4w+B4w+[42]i
[41]i [40]i [43]i C4w+B4w+[43]i [50]i [47]i [45]i C4w+B4w+[49]q. [48]i
C4w+B4w+[48]i [53]i [52]i [50]i
Figure 12.The musicstring output for trial 3 of the software on the same set of chord changes, to Afternoon in Paris.
Table 1. In 100 trials of the software on a single set of chord changes, following table depicts those musical phrases that appear
at least 5 times, along with the number of such phrases and the percentage of phrases they account for.
Number
of 8
Appearances
Percentage of 0.44%
all phrases
Number
of 2
such phrases
18
7
6
5
0.97%
1.6%
3.2%
5
10
23
Computer Synthesis
Data Analysis and Discussion
The data show that any particular phrase has a very low probability of being repeated as
is in a single improvisation – no phrase accounts for more than 0.1% of all phrases and no phrase
appears more than 8 times in any of the 100 trial runs (each with 36 phrases). In fact, the
frequencies were low enough that the expected number of times one would have to run the
program to get it to produce the same phrase is more than 20. Thus the program abides by the
fourth element of the design criteria: the generated music is new and varied each time
Conclusions
Given the immense amount of variety possible in a piece of music, it is no surprise that it
is quite easy to generate, even algorithmically, music that is quite irreplicable. Music that is
generated algorithmically, however, is guaranteed to abide by the rules upon which it is based.
The program did both of these – the music was new and varied and abided by the set of musical
rules which guaranteed its consonance. Guide notes were chosen from chord tones, so as to
outline melodic motion and match the chord progression in tonality. Each method for
interpolation between the guide notes was used consistently in improvising the final musicstring.
Limitations and Assumptions
Because of the incredible variety of tunes within the jazz style, several assumptions were
made in the development of the program for the sake of simplicity. It is designed to improvise
over swing tunes, where time is divided into even 8ths. Additionally, all time signatures are
assumed to be 4/4. These assumptions eliminate the need to consider different rhythms and time
subdivisions for different tunes. However, 4/4 swing is by far the most popular jazz time feel, so
the assumption is minimally restrictive.
The program is also incapable of combining different methods of improvisation within a
phrase, like a performer might. Because there is no reliable way to “blend” two phrases, the
program instead chooses a single improvisation method for each pair of guide tones. Although
this may seem like a very limiting assumption, it is not so, due to the multiple different methods
the program is capable of executing and the fact that there are 2 guide tones per measure.
The most significant assumption made is that all of the standard musical rules are enough
to guarantee a good quality solo. While they must be followed to ensure the solo is good, they
may be necessary but not quite sufficient. While one can guarantee that the solo is not dissonant,
it cannot be melodically creative enough to compare to a real soloist.
In terms of execution, the biggest limitation is the absence of a GUI. Input is currently
read from text files that correspond to the changes of the tune, which have to be transcribed
manually. A graphical UI would make the process of user input easier for the user.
19
Computer Synthesis
Applications and Future Experiments
The purpose of the project is to explore the applications of computer algorithms to
synthesis of original music based on a set of chord changes. Although it is not immediately
applicable to a problem, the results of the project, whether affirmative or negative, could help
contribute to general knowledge in the field of computer music generation. A functional project
could also (after further refinement) serve as an introductory teaching tool of the jazz style.
Although they were not implemented in this project, more advanced Markov Chain
methods could be used for a different method of improvisation. Dynamical systems, while not
implemented, could also be used. Both provide a better method of improvising over chords
which are held for several measures, because they create more continuous melodic motion. The
methods used in this project are better suited to chords that move quickly.
Future research could also include development of methods for computer music
transcription, which would make a solo even more authentic. If it were possible to transcribe
recorded solos with accuracy, it would add great variety to computer generated solos. Further, it
might be possible to analyze musical styles based on transcribed music. Computer generated
music would be given a whole new dimension if music could be synthesized in the style of a
particular musician. Alternative algorithms and styles of music could also be experimented with.
Since the program can only be measured against the standards by which it abides (by
construction), sources of error are more subjective than they are quantifiable. They can still,
however, be measured. The two major potential sources of error are repetition and musical
dissonance. The first can be measured by running the program over a single tune a large number
of times, and counting individual phrases to monitor their frequency. The second, however, is
more difficult. Passing dissonance and even sustained dissonance are frequent in many jazz
tunes, so discrediting dissonance of any sort would be a mistake. Again, although perhaps with
less success, relative frequency of dissonance can be measured.
Literature Cited
Bretscher, O. (2008). Linear Algebra (3rd Edition).
Chen, D. (1992). Computer Improvisation of Jazz Solos. Retrieved October 3, 2011, from
https://ritdml.rit.edu/bitstream/handle/1850/11088/DChenThesis07-131992.pdf?sequence=1
Franz, D. (1998). Markov Chains as tools for Jazz Improvisation. Retrieved October 31, 2011,
from http://scholar.lib.vt.edu/theses/available/etd-61098-131249/unrestricted/dmfetd.pdf
Gannon, P. (1999). Automatic Improvisation System and Method (Patent). Retrieved
September30,2011http://www.google.com/patents?id=YgUZAAAAEBAJ&printsec=
abstract&source=gbs_overview_r&cad=0#v=onepage&q&f=false
Humphries, C. (2007). Piano Workbook. Jawbone Press.
20
Computer Synthesis
Hal Leonard Corporation (2004) The Real Book (6th ed.). Hal Leonard Corporation.
Introduction to Jazz (n.d.) Retrieved October 15, 2011 from http://jazz.about.com/
Introduction to Music Theory (n.d.) Retrieved October 18, 2011 from
http://www.8notes.com/theory/
Keys and Intervals (n.d.) Retrieved October 28, from http://library.thinkquest.org/15413/
theory/intervals.html
Koelle, D. (2008). The Complete Guide to JFugue: Programming Music in Java. Retrieved from
http://www.jfugue.org
Miller, M. (2005) The Complete Idiot’s Guide to Music Theory (2nd ed.) Penguin Group.
Popular Chord Changes (n.d.) Retrieved October 14, 2011 from http://www.guitar-chordtheory.com/images/chordprog2.jpg
Tomassetti, B. (2003). Beginning Blues Improvisation Pedagogy for the Non-Jazz Specialist
Music Educator [electronic version]. Music Educators Journal, 89 (3), 17-21.
van der Linden, P. (1999). Just Java 2 (4th ed.). Sun Microsystems Press
Acknowledgements
The author wishes to thank Mr. James Barys for advising the project and helping guide it
to completion. Additionally, he would like to thank Dr. Judith Sumner for reading and helping to
edit the project paper and Mr. Richard Odgren for teaching him the fundamentals of jazz theory.
21