From: AAAI Technical Report SS-93-01. Compilation copyright © 1993, AAAI (www.aaai.org). All rights reserved.
EXPERIENCE-BASED
MUSIC
COMPOSITION
CARL WESCOTT and ROBERT LEVINSON
Department of Computerand Information Sciences
University of California, Santa Cruz
Santa Cruz CA 95064 USA
1
Overview
2
"If a complex structure is completely
unredundant - if no aspect of its structure can be inferred from any other - then
it is its ownsimplest description. Wecan
exhibit it but we cannot describe it by a
simpler mechanism." - Herbert Simon,
The Architecture of Complexity, p. 478.
Humancreativity produces new forms, or
patterns, from previous experience, in such diverse activities as composingmusic, writing prose,
and playing chess. We believe that humans have
domain-independent pattern-based neurobiological mechanisms that provide the foundations for
creativity, and propose that systems which combine and alter simple patterns to model complex
systems can effectively simulate creative intelligence.
To
study
these
mechanisms and experience-based creativity, Smurph,
System for Musicomposition Using Repeated Pattern Hierarchies, has been developed. Smurph is
intelligent software that learns to composemusic
based on discovery of repeated musical patterns
and its creative combinations and variations of
those patterns. The goal is for Smurphto learn to
compose original works of music entirely from its
experience of ’listening’ to music and its analyses
thereof, with virtually no music-theoretic knowledge or heuristics.
This paper summarizes related research,
describes the design of our experience-based chess
and music programs, expounds on the patterns,
hierarchical structures, and linguistic properties
of music, and concludes by outlining ongoing research.
119
Related
Research
"[Musical fragments] that please me
I retain in memory, and am accustomed,
as I have been told, to humthem to myself. If I continue in this way, it soon
occurs to me how I mayturn this or that
morsel to account, so as to make a good
dish of it, that is to say, agreeably to
the rules of counterpoint, to the peculiarities of the various instruments, etc. All
this fires mysoul, and, provided I amnot
disturbed, mysubject enlarges itself, becomes methodized and defined, and the
whole, though it be long, stands almost
complete and finished in my mind, so
that I can survey it, like a fine picture
or a beautiful statue, at a glance. Nor
do I hear in nay imagination the parts
successively, but I hear them, as it were,
all at once." Wolfgang AmadeusMozart,
in Vernon, Creativity, p. 55.
The original computer music compositions were stochastic music composed using random numbers or processes [Hiller & Isaacson,
1959] [Xenakis, 1971]. Often, these aleatoric devices were interactive compositional tools to assist
the humancomposer, such a.s Koenig’s mentor systems Project One and Project Two [Laske, 1981].
Another approach has been to use formal grammars to model and generate music [Laske, 1973]
[Bernstein, 1976] [Smoliar, 1976] [Winograd, 1968]
[Holtzman, 1981] [Lerdahl & Jackendoff, 1983]
[Roads, 1978].
More sophisticated
music composition
programs have been written that make use of rules
based on the music-theoretic heuristics of traditional counterpoint species [Schottstaedt, 1984]
[Ebcioglu, 1986]. These systems attempt to minimize penalties for broken rules using backtracking to compose an original piece of music or harmonize an existing one phrase-by-phrase.
More
recently, there have been several neural net implementations of compositional algorithms [Todd,
1991] [Mozer, 1991] [Lewis, 1991] [Kohonen, Laine,
Tiits, & Torkkola, 1991] and algorithms to learn
and produce well-formed melodies [Underwood,
1992] [Gilbert, 1993]. Someresearchers are studying the related field of real-time musical accompaniment [Dannenberg, 1984] [Vercoe, 1984] [Baird,
Blevins, &Zahler, 1989].
Our computational music research builds
on the work of David Cope, whose Experiments in
Musical Intelligence (EMI) software has created
pieces in the style of Bach, Mozart, Joplin, Gershwin, and Bartok, amongothers. In many respects,
Cope combines some of the above techniques: EMI
uses an Augmented Transition
Network (ATN)
grammaras well as a rule-base to describe the syntax of music. EMIbuilds a dictionary of signature
phrases by listening to a composer’s works, and
then composesmusic using these stylistic patterns
and its rule-base [Cope, 1991a].
Smurph does not use transformational
grammarsnor musical heuristics. Instead, it utilizes only its probabilistic analyses of input music
to determine the most suitable patterns to follow
its current output. It stores repeated patterns in
a hierarchical database, and combines and alters
them to form new musical phrases.
3
Morph & Smurph
"While Babbage dreamt of creating
a chess or tic-tac-toe automaton, [Lady
Ada Lovelace] suggested that his Engine,
with pitches and harmonies coded into its
spinning cylinders, ’might compose elaborate and scientific pieces of music of any
degree of complexity or extent.’ " - Douglas Hofstadter, Godel, Escher, Bach, p.
25.
Morph, an experience-based,
adaptive,
pattern-oriented program that learns to play chess
by watching or playing games, has already been
built [Levinson, 1991]. Morph was developed
based on our APS (Adaptive-Predictive
Search)
paradigm for machine learning. Starting with little a priori knowledge, Morphstores the patterns
that it finds on the chess board in a hierarchical
database, along with its estimated weight for each
120
pattern ranging from 0 to 1, with 0 indicating a
sure loss and 1 indicating a win. Unlike most intelligent chess programs, Morph does not search
the tree of possible movesfor future consequences
of its actions. Instead, Morphevaluates the patterns that it finds in its possible legal movesand
chooses the movewith the best possible combination of patterns. After the game is over, Morph
adds and deletes patterns and adjusts its patternweights using temporal difference learning [Sutton, 1988] and the simple feedback of whether it
won, drew, or lost the game.
To study the application of similar principles to another domain besides chess, music composition was chosen, since:
¯ Music has relatively simple, discrete patterns
that can be sequentially analyzed and unambiguously represented.
* Due to the hierarchical structure of music,
each note can be interpreted on manydifferent levels, as part of a bar, motive, phrase,
section, or theme.
¯ Music composition, like winning chess, is often cited as an exampleof intelligent and creative behavior.
¯ There are digitally stored musical databases
that can easily be accessed on-line.
¯ Psychological aspects of human music composition have been widely studied and published.
Like Morph, Smurph stores musical patterns that it recognizes in a hierarchical database
using a more-general-than operator.
Rather
than storing weights with these patterns, though,
Smurph keeps track of the probabilities
of occurrence of these patterns, modeling music as
the result of a multiple-order Markovinformation
source. Thus, when composing, Smurph combines
these smaller patterns to produce music that has
some of the style or signatures of the input music
pieces that it has listened to.
Smurph’s patterns currently use only the
melodyof a musical piece, but Smurphwill eventually analyze all the voices in the input data stream.
The input music is all transposed to the key of C,
and rhythms are represented only in a temporally
relative manner. Thus, two eighth notes followed
by a quarter note are perceived to be identical to
two quarter notes and a half note, assuming of
course that the pitches mapone-to-one after transposition. Smurph’s database routines are written
in C++ and interface with Macintosh MIDILISP
code to parse and output MIDIevents to and from
the computer.
4
unary operators like Generalize, Invert, and Re?)erse.
5 The Hierarchical
Structure of Music
Patterns
"One of the most interesting aspects
of the world is that it can be considered
to be made up of patterns. A pattern is
essentially an arrangement. It is characterized by the order of the elements of
which it is made, rather than by the intrinsic nature of these elements." - Norbert Wiener, in Gonzalez & Thomason,
Syntactic Pattern Recognition: An Introduction, p. 1.
The easiest way to form complex patterns
from simple ones is to group the smaller patterns
together. Experimental evidence shows that the
Gestalt principles of temporal proximity and similarity are important determinants of grouping in
music. Grouping objects together improves perception and recognition visually as well as aurally:
"Regular, symmetrical, simple shapes will be more
readily perceived, appear more stable, and be better remembered than those which are not. Thus,
for instance, conjunct pitch sequences (the law of
proximity), continuing timbres (the law of similarity), cyclic formal structures (the law of return)all help to facilitate perception, learning, and understanding." [Deutsch, 1982]
Musical groups or phrases can also be
altered by the simple procedures of retrograde,
inversion, and transposition.
"Tonal melodies
are often generated, either consciously or unconsciously, from one or more motives (gestures less
than a phrase long). These typically fall so naturally into the logic of the line as not to be distinguishable. Motives are varied by transposition
(different levels of the scale), by inversion (intervals in the opposite direction), and by extension
or truncation." [Cope, 1991a] Traditional fugues
consist almost entirely of multivoice variations on
their melodic themes. Marvin Minsky believes
that the most significant aspect of these similar phrases, motives, and rhythms is the higher
level differences between otherwise identical objects. [Minsky & Laske, 1992]
Currently Smurph stores only patterns
that actually occur in the music that it listens
to, but mechanisms are being added so that variants can be produced by using binary pattern
transforms such as Most CommonSubpattern, and
121
"As a piece of music unfolds, its
rhythmic structure is perceived not as
a series of discrete independent units
strung together in a mechanical, additive
way like beads, but as an organic process in which smaller rhythmic motives,
while possessing a shape and structure
of their own, also function as integral
parts of a larger rhythmic organization."
- Grosvenor Cooper & Leonard Meyer,
The Rhythmic Structure of Music, p. 2.
According to Heinrich Schenker, the originator of modern harmonic analysis, music can be
understood on three principal levels: foreground,
middleground, and background. Schenker advocates a universal deep structure for music based on
his formalisms not unlike Chomsky’s. This structure has two components, a fundamental melodic
line and a bass line, which may be discovered
by reeursively removing extraneous musical notes
from a piece to reveal its harmonic and contrapuntal skeleton.
The structure of music is the bridge between the composer and the listener. Music’s various aspects - pitch, intensity, duration, timbre,
texture, and harmony - are interwoven at many
different levels in an architectonic fashion. [Narmour, 1990] Experimental evidence shows that humans retain pitch information in their memories
at different levels of abstraction. [Deutseh, 1982]
Like pitch, the rhythms in a piece of music can be
analyzed on multiple hierarchical levels. [Cooper
& Meyer, 1960] Each note is analyzed in terms of
its contextual tonal hierarchies, [Krumhansl, 1990]
offering the musical stability which leads to emotion and meaning in music. [Meyer, 1956]
Smurph’s hierarchical storing and analysis of patterns is consistent with the multilevel
hierarchical structures in many forms of Western
tonal music. The classical sonata, for example, is
a hierarchy of subunits, and the "subunits in one
branch are generally found in identical or varied
form in other branches. For example, the themes
from the exposition are also heard in the development, recapulation, and coda. but in different
orders, keys, and tonalities. Similarly, the motives from one theme also appear throughout the
movement,but transposed, inverted, stated in retrograde, diminished or augmented, or otherwise
altered. Although the formal structure of a musical composition varies widely from one composer
or style to another, the hierarchical nature of the
form remains nearly universal." [Bateman, 1980]
6 Music as a Language
able at all stages of the compositional process, it
reflects music’s potential ambiguities through its
stochastic generator. Also, rather than having to
rewrite its grammar to create music in another
style, Smurphsimply digests, analyzes, and emulates new input music.
7
"Just as letters are combined into
words, words into sentences, sentences
into paragraphs, and so on, so in music individual tones becomegrouped into
motives, motives into phrases, phrases
into periods, etc. This is a familiar concept in the analysis of harmonic
and melodic structure."
- Grosvenor
Cooper and Leonard Meyer, The Rhythmic Structure of Music, p. 2.
This multilevel hierarchical structure allows music to be viewed as a language. Besides
the more formal approaches to describing music
in terms of languages’ semantics, parts of speech,
transformations,
and musical grammars, [Bernstein, 1976] it is widely acknowledgedthat the hierarchical structure of music lends itself well to
another analogy. Music groups itself into phrases,
motives, and section, just as language is composed
of words, sentences, and paragraphs. Also, like
language, music creates tension and relief through
its use of dissonance and cadences.
As a language, it possesses the same universal deep structure that Chomskydiscusses in
linguistics.
[Chomsky, 1965] Music can be discussed in terms of the abstract expressions of
formal language theory. Lerdahl and Jackendoff concentrate on the hierarchical aspects of music. They employ grouping analysis of musical
sections, phrases, and motives as well as metrical
analysis to break downhierarchies like two 3-note
groups that are part of a larger 6-note group. They
also use time-span reduction and prolongational
reduction to isolate pitch hierarchies. [Lerdahl &
Jackendoff, 1983]
There have been attempts to compose
music based on formal grammars, but one problem with this approach is that it can never be
"adequate to mirror the total ambiguity which is
so important in music, of the boundary between
new figures and variations of an old one." [Lidov
& Gabura, 1973] Smurph captures the essence of
the structure of music without using formal grammars to output music. Since its patterns are avail122
Domain-Independent
Creativity
One of the primary high-level goals of this
research is to explore to what extent creativity can
be achieved in individual domains using principles
that are essentially domain-independent. In the
case of Smurph the goal then is for Smurph to
exhibit the musical characteristics of those that
have formal music training, without explicitly being given music theory as in knowledge-basedcomposition systems. Smurph’s expertise must come
from its experience in "listening to" well-formed
music.
The first primitive version of Smurphwas
based strictly on its hidden Markovmodel. As was
expected, if Smurph used a high order of probabilistic synthesis, redundantrepetition resulted. If
the order of synthesis was too low, the resulting
output note sequences were mostly random and
not typical of the input pieces’ style.
Smurph’sfirst compositions contained coherent phrases, but lacked some of the basic elements which characterize Western tonal music.
Since each note in its compositions was determined
by probability, the overall structure which permeates most music was missing. Repetition, selfreference, and theme and variation occured only
infrequently. The concept of modulating between
keys was completely alien to Smurph. Musical tension and release were rare, and particularly glaring
was the absence of definitive endings.
Rather than encoding music-theoretic
heuristics into the system, Smurphwas directed to
improve its playing through other means. Smurph
now stores the patterns of its compositions in a
separate database, and occasionally consults this
database to develop recurring musical phrases and
create theme and variation.
Smurph produces
endings to its pieces by using the endings of the
pieces it has listened to. Starting from the last
note, usually the tonic or a fifth above it, Snmrph
works backwards to write a bar or two of the final phrase which sometimes combines the tension
and release of the traditional V7-I cadence with
the patterns of the melody.
In giving Smurphthe capability of generating music that follows someof the rules of music
theory, we are actually giving it the potential to
produce creative music based on generalizations
of these qualities. If Smurphcan learn the laws of
traditional music theory then it can break them.
Thus Smurph by judiciously extending the boundaries of Western music may eventually be truly
creative. [Boden, 1990]
8
Prediction
are successful in other related domains. This approach may lead to plausible move generators for
chess, organic synthesis, and automatic theorem
proving, each being an area in which humans have
shown superiority to computers. Finally, mappings of pattern structures across multiple problem domains will be explored, such as in music
composition based on chess patterns.
Our presentation furnishes specific results, including the creative output of the system,
further details on its inner workings, and a critical
analysis of its strengths and weaknesses.
"Prediction is very difficult, especially of the future." - Niels Bohr
10 Acknowledgements
The authors are indepted to David Cope
and Kevin Karplus for valuable discussions and
suggestions.
References
Like speech recognition systems and adaptive coding techniques, Smurphuses the context of
input it has seen so far to predict upcomingpatterns. Humans,whether they realize it or not, also
predict upcomingsections of music as they listen
to it. In fact, the emotional aspect of music is
mainly based on expectancy and surprise [Meyer,
1956] [Narmour, 1990]. Furthermore, experimental evidence shows that even children can predict
whena piece of music is finished [Serafine, 1988].
9
Conclusions
and Ongoing
Research
Smurph creates original motives in the
style of the input compositions. Whereas some
previous experiments in statistical
analysis of
melodies [Olson, 1967] have only calculated zero
through third-order analyses, Smurph produces
higher-order analyses. Part of Smurph’schallenge
is using the right order of synthesis and combining
multiple orders of probabilistic information, and
herein ties part of its creativity and our challenge
as researchers. WhenSmurph sounds good enough
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in a double-blind Turing test. Also, Smurph will
itself be given a test to determine which of two
input pieces is Mozart’s (or another composer’s),
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By creating a computer program which
learns a creative art through experience in another
domain besides chess, the hypothesis that the basis for creativity is domain-independent is being
tested. Webelieve that problem solving and the
arts mayutilize similar mechanismsto recognize,
alter, and combine patterns. Based on this theory, we hope to build intelligent systems which
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