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Algorithmic Composition

Andrew Pascoe

December 7, 2009

1 Introduction

Advances in computing technology have enabled composers to use the computer as

a means of generating musical content. Some of this musical content is presented

as original, and some of it is presented as extending particular composers’ styles.

Regardless of how it is presented, algorithmic processes have caused controversy in

traditional music circles. How is algorithmic music authentic? How can algorithmic

music have meaning? Are human composers destined to become obsolete? How do

these techniques relate to the question of man versus machine?

This paper begins with a discussion of the long history regarding the systematiza-

tion of music. These systematic approaches to music theory provide a foundation for

the possibility of computers to produce “good” music. Only some brief examples are

provided. As such, understanding the role of systematization in music is necessary to

have an intelligent dialogue about this one direction music is heading.

From there, the paper covers some recent methods and approaches to producing

algorithmic compositions. In particular, the works of Benjamin Carson, David Cope,

Peter Elsea, and Microsoft’s MySong  application are examined. Each of these attacks

the problem of automatically generating music in different ways.

Last, the paper discusses musical meaning and the philosophical questions at-

tached to this concept. These are broad questions with perhaps no correct answer.

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However, they serve to provide at least some notion of why algorithmic composition

is a controversial subject. The role and intent of the composer form the basis for this

discussion.

2 Historical Systematization of Music

2.1 The Sixteenth Century

Consider the following piece of music:

 

  2 4

  Figure 1: Bad counterpoint.

This fragment is considered to be poor compositional form, even today.[9] The

technical reason is the  hidden octave  on the second beat. While there is no question

that composers in the sixteenth century functioned under at least the intuition of 

such rules, the real formalization of these practices was completed by Johann Fux in

his  Gradus ad Parnassum  in 1725.[15] As Taruskin describes it:

[Musicians] used it to gain facility in “the first principles of harmony and

composition,” which were regarded by teachers as an eternal dogma in

its own right, a bedrock of imperishable lore that “remains unaltered, let

taste change as it will.”

The text itself divides counterpoint into five   species , along with set of rules con-

cerning prohibition against perfect parallels, hidden parallels (as above), consonances,

dissonances, and also general aesthetics such as restrictions on sequential parallel

thirds and sixths, and a tendency away from parallel motion. These were derived

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from studying the works of Palestrina. Modern composition students still receive

instruction in these rules and aesthetics.

Already one can begin to see how a computer can begin to use these notions of good

composition versus bad composition. It is ultimately simply a matter of eliminatingpossibilities and ranking the remaining possibilities in terms of their adherence to the

given aesthetic.

2.2 The Common Practice Period

The common practice period encompasses most styles associated with the term “clas-

sical music:” Baroque, Classical, and Romantic period styles. The theoretical ground-

work for these styles is based not only in the counterpoint and voice-leading consid-

erations of Fux, but also in chord progressions. Kostka and Payne write:[11]

[Students] must learn which chord successions are typical of tonal harmony

and which ones are not. Why is it that some chord successions seem to

“progress,” to move forward toward a goal, while others tend to wander,

to leave our expectations unfulfilled?

They provide the following examples:

 43

  43

 

   

Figure 2: Tonal harmonic progression.

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 43

  43

 

   

 

Figure 3: Random harmonic progression.

The implication is that there exists a set of guidelines for writing good, tonal music.

These guidelines are what is typically referred to as “music theory,” in imprecise,

casual speech. Kostka and Payne summarize some of these guidelines with a diagram

of possible chord progressions, but are quick to point out:

. . . [B]e aware that Bach and Beethoven did   not   make use of diagrams

such as these. They lived and breathed the tonal harmonic style and had

no need for the information the diagrams contain. Instead, the diagrams

represent norms of harmonic practice observed by theorists over the years

in the works of a large number of tonal composers.

That is to say, these rules and guidelines have been imposed  after the fact, much asFux’s Gradus ad Parnassum  did for the sixteenth century style. Once again, this push

toward systematization continues to reduce the art of composition to an algorithmic

framework.

2.3 The Twentieth Century

The twentieth century is unique in at least one respect to previous centuries: In ad-

dition to theorists imposing theoretical structures on previous composers, composers

themselves were creating systems for generating music. This section provides a couple

examples from each camp.

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2.3.1 Charles Seeger

Charles Seeger, in a twist of Fux’s work, devised a systematic approach to composition

he dubbed “dissonant counterpoint.”[14] Nicholls offers the following example:

    

    

 

Figure 4: Dissonant counterpoint.

Here, the focus is on dissonance as opposed to consonance. This example has no

consonances between the two parts. Moreover, the individual lines themselves have

a tendency toward dissonant intervals, e.g. the B to F in the top line is a tritone.

Repetition of pitches is to be avoided unless they are sufficiently far apart. As the

number of voices increased, rhythmic dissonance also becomes a necessity. All in all,

these rules and guidelines codify a means of creating a new type of music.

2.3.2 Arnold Schoenberg

Arnold Schoenberg created a technique that is known as “serial composition,” “twelve-

tone technique,” or “dodecaphony.”[16] This atonal process begins with a tone row of 

all twelve diatonic pitches. The motivation for this practice is to have the pitches not

relate to any particular key, but only to themselves. From here, only certain musical

transformations are allowed: transposition and inversion.   P   is used to denote the

“prime” tone row. Transposition is denoted through the use of subscripts, so, for

example, a transposition of six semitones would be written as P 6

. Inversion is denotedby   I   , and inversions can also be transposed. Thus, an inversion transposed by six

semitones would be written as  I 6. Taruskin gives the following examples using a tone

row from Schoenberg’s  Suite, Op. 25 :

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                 (a)  P 0

                

(b)   I 0

                    (c)  P 6

                         (d)   I 6

Figure 5: Twelve-tone processes.

These processes are extremely mathematical in nature. Besides just being a gen-

eral sense of what is “good” composition versus what is “bad” composition, the rules

laid forth by Schoenberg comment on what is  possible   composition. Moreover, there

is no question that Schoenberg intended this system to function as hard and fast

rules. Taruskin writes, and perhaps provides a snide comment toward algorithms as

a compositional practice:

Indeed, the use of an exhaustive twelve-note series makes the  Grundgestalt 

function, and the organic unity thus guaranteed, virtually automatic. And

that, of course, was the great breakthrough, the “principle capable of 

serving as a rule,” which allowed the composition of large-scale, abstract,

and autonomous atonal music of constant and at-all-time-demonstrable

motivic coherence despite its renunciation of predefined tonal hierarchies,

and despite its frequent “athematicism.” But beware! As soon as any

musical characteristic becomes the automatic result of a method, it stops

being a compositional achievement.

Regardless of Taruskin’s personal opinions, Schoenberg’s serialism does provide

a rigorous framework that a computer can be easily made to emulate. Whether a

computer can make a “compositional achievement” is a question saved for a later

section of this paper.

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2.3.3 Leonard Bernstein

Leonard Bernstein began to pose new theoretical question related to the structure

of music, and in that sense his theory imposes interpretations on compositions from

the past.[2] His theory has its roots in the linguistics of Noam Chomsky. The Chom-

skian framework of “transformational linguistics” is applied to music. Essentially,

Bernstein equates melody with basic musical meaning, chords as adjectival modifiers,

rhythm as verbs, and mode as negation. He continues this reasoning and explores

the syntactic structures of music by suggesting an underlying “deep structure” to

musical content that goes through a sort of transformational grammar through not

only these modifiers, but also grammatical aspects of deletion and combination. He

freely admits that his ideas are not fully formed, but here are some basic examples

with potential linguistic equivalents:

(a) Jack loves Jill.

 (b) Jack doesn’t love Jill.

    (c) Does Jack love Jill?

 (d) Doesn’t Jack love Jill?

Figure 6: Transformational musical grammar.

This notion is very different from the forms of music theory we have thus far

considered. It does not comment on notes or chords in particular, but rather focuses

on the construction in form of a piece of music. Bernstein likens this to elevating

prose into poetry.

Bernstein’s analysis lends a different type of insight into the process of composi-

tion. This potentially affords computers the opportunity to replicate human creativity

on a separate level. By using musical fragments and applying transformational gram-

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mars to them, new creative structures may emerge. This question is related to natural

language processing.

2.3.4 David Lewin

David Lewin made advances in music theory with his work in generalized musical

intervals and transformations.[12] In many ways it is an extension of Schoenberg’s

atonal practice, but through this extension finds relevance to tonal composers, such

as Chopin. Lewin’s theorization of music relies heavily on the mathematical field of 

abstract algebra. Indeed, Lewin’s book reads more like a math text than a treatise on

music, containing theorems, corollaries, and proofs. In the foreword, Edward Gollin

sums it up succinctly:

The work, a methodical examination of the concept of a musical interval,

explores how the familiar notion of interval as “a distance extended be-

tween pitches in a Cartesian space” is merely one specific case of a more

general idea, one that can embrace different kinds of musical objects (du-

rations, meters, Klangs , timbres, and so on), different (i.e. non-Euclidean)

geometries, and different orientational perspectives (interval as action or

gesture rather than as simply measurement of distance between things).

By far the most mathematical example covered in this paper, Lewin’s work finds

a fit in the world of computation. Not just composition, but   sound itself   can be

analyzed rigorously within Lewin’s framework. This opens the door for computers

to not only compose well, but to also construct interesting collections of frequencies

that evolve over time for synthetic instrument creation—aspects of music that are

hardly intuitive for traditional composition practitioners. Thus, the computer can

more easily express musical ideas than a human can.

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3 Recent Methods

This section of the paper now looks at approaches to algorithmic composition from a

few perspectives, namely Benjamin Carson, David Cope, Peter Elsea, and Microsoft’s

MySong  application.

3.1 Peter Elsea

Peter Elsea has explored algorithmic composition through the use of fuzzy logic

systems.[8, 7] Pitch classes are represented as sets that denote membership in a par-

ticular chord or scale. For example:

       (1 0 1 0 1 1 0 1 0 1 0 1)

Figure 7: Fuzzy logic set of notes.

This example in the major scale does not contain any real fuzzy logic (though the

set still can function as a fuzzy logic set). The example of the minor scale, in which

the seventh can be raised, provides a fuzzier set:

            (1 0 1 1 0 1 0 1 1 0 0.7 0.6)

Figure 8: Fuzzier logic set of notes.

Note that these are not probabilities, but merely demonstrate a preference for the

flatted seventh over the naturalized one.

This fuzzy logic system affords a host of mathematical operations that can be per-

formed. Transposition is accomplished by circularly rotating the set. Multiplication

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between sets is available. Set unions and intersections are accomplished by taking the

maximum and minimum, respectively, of two numbers with the same index. These

operations allow for simple processing in tonal harmony applications.

Elsea’s software functions by reading in a MIDI note and outputting a harmoniza-tion for that note. The basic set of rules are, with regards to chord inversions:

If root position keeps common tones, then root position.

If first inversion keeps common tones, then first inversion.

If second inversion keeps common tones, then second inversion.

If last position was root, then first inversion or second inversion.

If there have been too many firsts in a row, then root or second.

If there have been too many seconds in a row, then root or first.

If last position was not root, then root.

The first three rules ensure that the harmonization does not fly around too wildly.

The next three rules ensure that the harmonization is not too static. Of particular

note for these rules is the use of the fuzzy concept of “too many.” Thus, programmed

into Elsea’s code is a sense of what “too many” actually means. The last rule has a

relatively low weight of being implemented so that it does not interfere with the main

rules too much.

The question, once we move beyond simple inversions, is how to harmonize melodic

notes given their context not only in the key, but also in the context of the preceding

chord. Elsea constructs three candidate chords by using these aforementioned fuzzy

logic sets: one with the note as the root, one with the note as the third, and one

with the note as the fifth in the chord. Then, the actual roots of these chords are

compared with more fuzzy logic sets that are based on the tonal harmony (the dia-

grams) provided by Kostka and Payne. The best candidate, based merely on taking

the maximum of the resultant computations, is then constructed and played. So for

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example, in the key of C, if the user plays a G, there are three basic triadic chords in

the key of C that harmonize G, not including their inversions:

 V  

I     iiiFigure 9: Triadic chords in C that harmonize G.

Which chord to choose is, once again, dependent on the context. If the preceding

chord is a root position I chord, then the following is a possibility:

I(6)

I

Figure 10: One possible progression.

But if the preceding chord is a ii chord, the next two examples show a “good”

progression and a “bad” progression:

 V(6,4)

ii

(a) Good progression.

iii

ii

(b) Bad progression.

Figure 11: Progressions of varying favoritism.

In short, Elsea takes a mathematical approach to the tonal theory of the common

practice period, and thus the computer is able to make informed, real-time compo-

sitional decisions based on melodic user input. This would not have been possible

without a systematization of the music of the period in the first place.

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3.2 Benjamin Carson

Benjamin Carson, in his compositional practice, takes an algorithmic approach to

rhythm.[4] The software he has developed in collaboration with a software engineer

focuses on syncopation over an underlying music pulse, as opposed to the practice of 

new complexity featuring such methods as nested tuplets. The software is designed

to give the user a fine-tuned control of multiple aspects of the composition process.

Fundamentally, the software develops an aesthetic based on the complexity of 

durations of musical events. For example, a series of musical events may have metric

times of    416

,   716

, and   1316

. These durations are randomly generated, and depend upon

the composers’ input as to how complex he wishes a certain series of rhythmic events

to be.

Beyond this, the software allows a composer to view his work from a variety of dif-

ferent dimensions. Rhythmic complexity can be tied to pitch classes or dynamics, for

example. Thus, even though the underlying algorithmic production of these durations

is inherently random, the composer is free to choose some sort of logical framework for

how rhythmic complexity interacts with the rest of the composition’s aspects. This

affords a unique mix of both the computer’s input and the compositional goals and

ideas of the composer.

These syncopated rhythmic grammars can be variably juxtaposed to the underly-

ing ordered pulse of the music. This can be accomplished by shifting the syncopation

over the underlying pulse, or by spreading out the underlying pulse in clock time.

These processes generate psychological musical effects for the listener. Once again, it

is at the composer’s whim when to produce such rhythmic effects as part of the cre-

ative process. In particular, Carson describes this feature of his software as a means of 

maintaining interesting rhythmic flows that do not grow stale, but still maintain some

sort of logical structure. The goal is not to be completely random, but instead to have

a certain level of ordered randomness. Thus, the piece has a concrete development

over its course without devolving into either banal repetition or pure chaos.

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Carson also makes a distinction between metric time and clock time. That is, a

32nd note does not lose its “32nd-ness” under tempo changes. Its musical function

does not change despite its variation in actual clock time. To this extent, Carson also

experiments with an algorithmic approach to changes in tempi.Carson’s software is in at least part a practice in “compositional economy.” By

automating certain musical processes, he finds himself free to focus on other aspects

of his composition he finds either more interesting or more important. However, the

software allows for a large range of input by the composer, allowing him to express

his “musical impulses” without necessarily having the computer completely control

the output. Carson’s idea of musical impulses will be covered in the next section of 

this paper.

3.3 David Cope

David Cope has long been involved in the field of algorithmic composition, and much

of his focus has been on making computer models of musical creativity.[6] His pro-

gram, Experiments in Musical Intelligence (EMI), employs a variety of techniques to

accomplish not only algorithmic composition in the styles of particular composers,

but also to produce new, “creative” output.

Cope’s approach is fundamentally database driven. He compiles musical sources

from a particular composer (or particular composers), all of which go through a series

of analyses. From here, the program sets to work using models of recombinance,

allusion, learning, form and structure, and influence. This paper presents a summary

of this ideas and their function.

3.3.1 Recombinance

Recombinance is essentially taking musical material from the database and replacing

sections of it with other material acquired from the database. Cope’s book provides

a simple example of this process:

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  43 

8

 43 

 43 

 43

 

(a) Original Bach.

 43 

   43

   43

8

   43

 

(b) EMI output.

Figure 12: Recombinance in action.

The EMI output replicates the original Bach Chorale no. 188 on the first beat,

but diverges from there, instead replacing it with a fragment from Bach’s Chorale

no. 157. EMI accomplishes this by forming examining the database and searching for

alternative candidates following from the given first beat. This process is continued

throughout the algorithmically generated composition.

However, this process will ultimately result in free-flowing melodies without any

sense of direction. Cope writes:

In order to provide some sense of this logic and larger structure, and again

wanting to avoid coding my own knowledge of musical form as rules, I

rewrote the program to inherit more of the structural aspects of the music

in its database. This inheritance involved extending the analysis process

so that the program could store other information about the music being

analyzed in each grouping along with destination notes. For example, I

had the program analyze the original music’s distance to cadence, position

of groupings in relation to meter, and other context-sensitive features.

The program is also sensitive to “compositional signatures,” which are larger frag-

ments of music that give a particular composer a sense of musical identity. Thus, there

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is an aspect of the program that resists the complete fragmentation of raw recombi-

nance. Due to similar concerns of over-fragmentation, EMI also tries to maintain a

cohesion in musical texture by comparing density of notes and rhythmic characteris-

tics between groupings, and searching the database for passages of similar quality intexture.

3.3.2 Allusion

Allusion refers to the practice of composers to borrow material from other composers.

Cope breaks down allusion into five categories: quotations, paraphrases, likenesses,

frameworks, and commonalities. He freely admits that the boundaries between these

categories are not necessarily clear.

Quotations are as one would expect: direct pitch and rhythm copying. Para-

phrases use similar intervallic structures to the source material and can also incor-

porate rhythmic differences. Likenesses are similar to paraphrases, but allow more

freedom in the differences, as well as changes in harmonic content. Frameworks take

source material and insert notes between the pitches and rhythms of the source mate-

rial. Such processes can be illuminated through textural reductions. Commonalities

are simplistic musical materials, not unlike Bernstein’s concept of “deep structures.”

Cope developed a secondary program called Sorcerer that can sniff out these allu-

sions. A user provides Sorcerer with a database of musical material and a work that

potentially contains allusions that are in the database. The program compares not

only pitches but intervals between pitches, allowing for variation in these parameters,

and also allows for a certain number of notes to fall within the source material (the

framework idea). Users can specify how sensitive they wish Sorcerer to perform, pick-

ing out only quotations, or running the whole gamut up to commonalities. Bounds

on the length of patterns must also be set by the user.

EMI, because of its construction in accessing databases, is naturally inclined to at

least include some elements of allusion. Cope tells a story about how he recognized

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in one of EMI’s pieces an allusion to Vivaldi, despite the database being entirely

comprised of works by Bach. Bach himself transcribed a series of Vivaldi pieces. Did

EMI reveal a hidden allusion in Bach to the music of which he himself had intimate

knowledge?

3.3.3 Learning

Cope describes another program he worked on called Gradus (named after Fux’s

Gradus ad Parnassum ) which attempts to learn the rules of first species counterpoint.

Other programs in the past have codified solutions to this problem, but they do not

learn in particular.

A melodic line is given to these programs (called a  cantus firmus ). The goal is to

write suitable counterpoint against this line. Previous programs begin with the first

note and proceed to the next. As any student of counterpoint can attest to, this naı̈ve

approach can quickly run into serious problems. Some beginning solutions resolve in

dead ends where there are no possible notes to write that will conform to the rules.

Therefore, such a program needs to backtrack to the last good note and attempt to

replace it with another possible solution, and then continue on from there, potentially

running into the same problem all over again.

Cope’s program stores its mistakes and avoids replicating them again in the future.

So the program starts by having to backtrack, but the more the program “practices,”

the less it must backtrack to find a solution to the given cantus firmus. While Cope’s

example has limited application to sixteenth century first species counterpoint, the

underlying philosophy has large implications for algorithmic composition as a whole.

The ability of programs to learn what to avoid can not only increase efficiency, but

also produce higher quality work.

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3.3.4 Form and Structure

Cope considers structure in the form of SPEAC analysis: statement, preparation,

extension, antecedent, and consequent. These all refer to relatively brief musical

gestures that find their characteristics in the amount of tension they provide to the

listener’s ear. The interactions between these different aspects of music create logical

surface structures. Alas, Cope’s book does not go into detail about how such an

analysis is implemented in his programs. He writes, “I simply ask readers to imagine

the possibilities, and to investigate the realities on their own.”

As for form, SPEAC analysis is applicable. Cope outlines another program called

Alice that analyzes a database searching for broad compositional forms. It begins

by attempting to identify themes. If this attempt is unsuccessful, it analyzes texture

changes to deduce the form. Failing that, it relies on simple cadences. If that process

also fails, Cope says Alice “takes its best guess.” From what little details Cope gives

in his book, it appears Alice searches for “expectation, fulfillment, and deception of 

themes or progressions,” and tries to replicate these structures in its database.

3.3.5 Influence

Influence is separate from relying on a database or merely composing in another’s

style. Instead, influence is about creating a new style that has its roots in a previous

style. Cope gives three examples of his experiments with EMI and musical influence.

The first example is a feedback loop. EMI begins with a database of a particular

composer’s work. As has already been described, it produces compositions based

on this database. Once a composition is completed, it is inserted back into the

database. By repeating this process thousands of times, Cope found that the output

showed obvious “influence” from the original source material, but the overall style

was exceptionally different.

The second example uses multiple EMI programs all using databases from different

composers. Here, the instances of EMI communicate with one another about their

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compositions. Cope programmed in a metric for what a “good” composition is: the

kinetic energy of the music. Each program has a slightly different metric, and hands

over to the other programs music it evaluates as aesthetically acceptable. In this way,

the programs are attempting to influence each other, resulting in compositions thatdemonstrate disparate sources. The author finds a similarity between this idea and

Bohm Dialogues.

Last, Cope describes influence as a form of exploration. He created a web-crawling

application called Serendipity that would download MIDI files (and text files) that

would be added to databases. At first, this process resulted in a mish-mash of styles

in one composition that was not aesthetically pleasing. So Cope produced filters

that would determine if a given MIDI file was good enough, or even appropriate,

for inclusion in EMI’s database. This resulted in much more cohesive and enjoyable

compositions.

3.4 MySong

MySong   is a consumer application that has been produced by a Microsoft research

team.[13] While its application is not as serious as what has been previously exam-

ined, the author felt its inclusion to be beneficial as an example of giving a “taste

of composition” to musically untrained individuals. That is to say, algorithmic com-

position is becoming a tool for users to create their own content. It also functions

differently than other work presented in this paper.

However, there are some similarities to the other work. Like Elsea’s work,  MySong 

attempts to harmonize melodic input by users, and like Cope’s work, it does so

by using a database of music. The distinctions lie in the implementation of these

practices.

To begin with, users specify a tempo and are provided with a metronome track

that delimits bar lines, or measure boundaries, in their melodic input. Users then sing

a melodic line into a microphone. The software then uses a pitch detection algorithm,

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and takes all of the notes in a particular measure and compiles them into a set. Here

is an illustration:

    (a) Sung line.     (b) Pitch classes.Figure 13: Pitch sets derived from melodic lines.

The database MySong  employs is a collection of about three hundred lead sheets.

Lead sheets contain melodic content along with chord progressions. These lead sheets

come from a variety of popular music genres, including pop, rock, and country. As

such, these styles of music usually find changes in harmony at the bar line. Here is

an example of what a lead sheet looks like:

G

  C

  F

Figure 14: Simple lead sheet example.

The method for algorithmic composition is based in Hidden Markov Models (HMM).

Essentially, a Markov model represents a stochastic process through transition prob-

abilities. Based on an analysis of the database, we might conclude that a C major

chord will move to a G major chord 30% of the time, and move to an F major chord

20% of the time. What makes the Markov model hidden in this application is that

the chord progression is unknown—all that is available are the pitch classes derived

from the user input. Thus, there is another level of analysis involving the probability

of a chord for the measure given the pitch class.

The way to find the optimal solution given a set of observances in an HMM is to

use the Viterbi algorithm. A mathematical discussion of the Viterbi algorithm and

why it works is beyond the scope of this paper, but it is important to know that there

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is an input parameter  k  to which the users of  MySong  are given access.

This   k  is exhibited in  MySong  as the “Jazz Factor.” If   k  = 0, then the program

effectively ignores changes in the melodic line altogether and produces the most typical

chord progression deriving from the first measure. If  k = 1, then the program ignoresstandard chord progressions and the harmonization for each measure is determined

solely by the pitch class for that measure. That is, when the Jazz Factor is increased,

the program is more likely to make bold harmonic choices. If  k  = 0.5, then for each

measure the program equally accounts for the user’s input and the chords in the

preceding and succeeding bars.

The other main user control in   MySong   is the “Happiness Factor,” which also

ranges from 0 to 1. Chord progressions for major and minor modes differ, and the

application accounts for this. When   h   = 0, the chord progression is guaranteed to

be in the minor mode, and when  h = 1, the chord progression is guaranteed to be in

the major mode. As can probably be deduced, when  h = 0.5, the program will freely

choose the best chord based on the Viterbi algorithm and the value of  k, whether or

not it is a major or minor chord.

Once the Viterbi algorithm is complete, users are then free to tweak their chord

progressions if they so choose. From there, the user can select a particular style of 

accompaniment that adds instrumentation and rhythm to the final chord progression,

and output their song to a sound file. Morris did not elaborate on how this stylization

is accomplished.

MySong   is one foray into the public sphere for algorithmic composition. Morris

notes that given the input of a melody from a famous pop song, the program will at

least sometimes produce the same chord progression in the studio version of the song.

He also touts the ability of   MySong   to produce interesting variations on common

songs by tweaking the Jazz and Happiness Factor controls.

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4 Musical Meaning

Let us consider the following musical fragments:

  42      ff        Figure 15: Opening theme from Beethoven’s Symphony no. 5.

               

  42               p       

               

Figure 16: Subject from Shostakovich’s Fugue no. 5, Op. 87.

    

    43        

 Figure 17: Opening output of EMI of a Bach-style lute suite.[6]

What, if anything, do these bits of music mean? Taking a cue from  MySong ’s

use of a Happiness Factor, should we conclude that Beethoven was having a bad day,

and Shostakovich happened to be feeling jubilant when they wrote their respective

pieces? One of the author’s past professors suggested that such interpretations were

dangerous, but Aldwell and Schachter suggest that our connotations of the major

mode being “happy” and the minor mode being “sad” should not be dismissed too

carelessly.[1] Of course, this begs the question, “What was EMI feeling?”

Hofstadter finds these questions, given the quality of EMI’s output, disturbing.[10]

He writes:

. . . I was going to grapple with this strange program that was threatening

to upset the apple cart that held many of my oldest and most deeply

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cherished beliefs about the sacredness of music, about music being the

ultimate inner sanctum of the human spirit, the last thing that would

tumble in AI’s headlong rush towards thought, insight, and creativity.

Having a personal affinity for Chopin and being surprised at how well EMI emu-

lated Chopin, Hofstadter boils his worries down to three possible outcomes, each of 

which he finds unsatisfactory as a lover of music and as a human being:

(1) Chopin (for example) is a lot shallower than I had ever thought.

(2) Music is a lot shallower than I had ever thought.

(3) The human soul/mind is a lot shallower than I had ever thought.

These concerns are strange since Hofstadter claims he has long been convinced

that humans are effectively machines anyway. He claims his surprise lies in the fact

that the machines producing EMI’s output are many orders of magnitude simpler than

human biological construction. Regardless, the author is not particularly surprised

by such developments in the production of machine music—the long historical trend

of the systematization of music lends itself to mechanical replication.

But Hofstadter is not alone. Cope has found resistance in music circles to havingEMI’s output performed by trained human musicians, saying responses were mostly

negative.[5] Why do people have such revulsion to the idea that a computer can

compose well? Do people read that much meaning into music?

Bernstein rejects the notion of any sort of extra meaning in music.[3, 2] For him,

the meaning of music is contained entirely within the notes themselves. He declares

that music does not have the same function as language, and any meaning it has is

ineffable. Hofstadter’s claim that music functions as “direct soul-to-soul messages”

does not find a place in Bernstein’s philosophy of music. As Bernstein says:

. . . [L]anguage has a communicative function and an aesthetic function.

Music has an aesthetic function only. For that reason, musical surface

structure is not equitable with linguistic surface structure.

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Cope also rejects Hofstadter’s objections.[6] He writes:

Interestingly, one of my favorite analogies is that mathematics is to physics

as music is to language. The first instances—mathematics and music—

are abstract, while the second instances—physics and language—relate

more to the real world. Mathematics and music also deal in proportions,

while physics and language attempt to develop meaning. . . Though sim-

plistic, this analogy nonetheless serves to emphasize music’s reliance on

relationships rather than on meaning and representations of meaning.

Carson, too, suggests that music has no inherent meaning beyond its notes, and

says he agrees with Bernstein.[4] He states that music is nothing more than a surface

structure, and it has no need for semiotics. Beyond this, Carson is glad that the study

of algorithmic composition is finally bringing these issues to light, that the concept

of “depth” in music is completely misguided, in that it necessarily implies a mystical

and mysterious element to the composition process that is just simply not present.

Carson claims that the use of algorithmic processes for compositional practices

does indeed distance the composer from his work. He also states that the highestlevel of intimacy a composer can have with his composition is when the composer

specifies each element in the work himself. However, this is not necessarily beneficial.

For one, as already mentioned previously in this paper, is the issue of economy.

Carson says that with modern technology, a composer would have to be “crazy” not

to automate parts of a composition that have a fundamental structure that could be

mechanically composed. This enables the composer to focus on other aspects of the

work. Second, a là John Cage, removing the ego of the composer grants opportunities

for musical exploration to which the composer’s mind may never have led him.

In response to a follow-up question relating to economy, that perhaps the most

economical action to take is to simply rely on algorithmic composition for all parts

of the process, Carson says that he sees no real issue in this. Composition, he states,

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is the act of recording “musical impulses.” These musical impulses function not only

consciously, but subconsciously. Using an algorithm, or even developing an algorithm,

inherently incorporates musical impulses.

Will human composers become obsolete? Carson does not think so. Humans havea natural tendency and demand to relate to other humans, and thus have a desire

to experience compositions produced by human composers. However, as stated, even

an algorithm expresses some element of a composer’s will and aesthetic. Carson even

extends the musical impulse to a user merely “pushing play” on some automatic

composition device.

He also does not take a post-modern stance of all music being equal. In response

to Hofstadter, Chopin is still great whether or not his style is replicable by machines.

Yes, music is a shallow surface structure, but Chopin’s greatness can be attributed

to his ability to produce surface structures of enormous musical complexity. Car-

son concludes that Chopin himself is essentially an algorithm of both conscious and

subconscious processes—but he is a very good algorithm.

The shallowness of music, according to Carson, is not a fundamental problem.

Music still has value. People associate with music because it relates to them on a

multitude of levels, including cultural and emotional levels. Audiences may incorpo-

rate meaning into their musical experiences, and there is nothing inherently wrong

with this. However, there is a benefit in increasing musical understanding by dis-

pelling these myths about composition as some sort of divine, mystical, or spiritual

process. Knowledge of actual compositional processes should aid audiences in their

appreciation of music as an art form.

The question about what EMI was “feeling” when it output the music above is

perhaps a misguided question. The real question could easily be, “What were David

Cope’s musical impulses when he wrote EMI, compiled a database of Bach lute suites,

and pressed the ‘generate’ button?”

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5 Conclusion

Algorithmic composition is still a relatively nascent field given the long course of 

music history. Its full potential is yet to be explored, and it has yet to completely

break into the public consciousness. Hofstadter asks:[10]

Where will we have gotten in twenty years of hard work? In fifty? What

will be the state of the art in 2084? Who, if anyone, will be able to tell

“the right stuff” from rubbish? Who will know, who will care, who will

loudly protest that the last (though tiniest) circle at the center of the

style-target has still not been reached (and may never be reached)? What

will such nitpicky details matter, when new Bach and Chopin masterpieces

applauded by all come gushing out of silicon circuity at a rate faster than

H2O pours over the edge of Niagara? Will that wondrous new golden age

of music not be “truly a thing of beauty?”

And he concludes:

. . . [T]he day when music is finally and irrevocably reduced to syntacticpattern and pattern alone will be, to my old-fashioned way of looking at

things, a very dark day indeed.

The author shares a curiosity in Hofstadter’s questions, but applies a separate

moral judgment on the future of music. Sharing in Carson’s idea of “musical impulse,”[4]

the future looks bright for composers to continue to develop systems, as theoreticians

and composers alike have done throughout history, that will explore new avenues of musical expression and insight. Algorithmic processes do not detract from our hu-

manity in the slightest. When all is said and done, an algorithm is still a creation

founded in the human mind, and creations are inherently imbued with the wills of 

their creators.

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References

[1] Edward Aldwell and Carl Schachter.   Harmony and Voice Leading . Schirmer,

New York, New York, third edition, 2002.

[2] Leonard Bernstein.   The Unanswered Question . Harvard University Press, Cam-

bridge, Massachusetts, 1999.

[3] Leonard Bernstein.   The Joy of Music . Amadeus Press, LLC, Pompton Plains,

New Jersey, 2004.

[4] Benjamin Carson. Personal Interview, December 4, 2009.

[5] Jacqui Cheng.   Virtual composer makes beautiful music—and stirs 

controversy .   http://arstechnica.com/science/news/2009/09/

virtual-composer-makes-beautiful-musicand-stirs-controversy.ars,

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[6] David Cope. Computer Models of Musical Creativity . The MIT Press, Cambridge,

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[7] Peter Elsea.   Fuzzy Logic and Musical Decisions , 1995.   ftp://arts.ucsc.edu/

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[10] Douglas Hofstadter.   Sounds Like Bach .   http://www.unc.edu/~ mumukshu/

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[12] David Lewin.   Generalized Musical Intervals and Transformations . Oxford Uni-

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[13] Daniel Morris.   MySong: Automatic Accompaniment for Vocal 

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 mysong-automatic-accompaniment-for-vocal-melodies, Accessed Decem-

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[14] David Nicholls.  American Experimental Music: 1890-1940 . The Press Syndicate

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[15] Richard Taruskin.  The Oxford History of Western Music , volume I,  The Earliest 

Notations to the Sixteenth Century . Oxford University Press, Inc., 198 Madison

Avenue, New York, New York, 2005.

[16] Richard Taruskin.  The Oxford History of Western Music , volume IV,  The Early Twentieth Century . Oxford University Press, Inc., 198 Madison Avenue, New

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