Automated Composition in Retrospect: 1956-1986
Author(s): Charles Ames
Source: Leonardo, Vol. 20, No. 2, Special Issue: Visual Art, Sound, Music and Technology (1987),
pp. 169-185
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/1578334
Accessed: 12/09/2008 23:18
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=mitpress.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform that
promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.

The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to Leonardo.

http://www.jstor.org

,Automated

Composition in

Retrospect:

1956-1986
Charles Ames
Abstract-This article chronicles computer programs for automated musical composition over the last 30
years, providingmusical examples from 11 computer-composedworks. The author begins by focusing on
early American efforts to impose stylistic controls through random sampling and testing, then describes
Europeanstatistical approaches used until 1970. The rise of 'interactive'compositional utilities duringthe
1970s is linked to the growing proliferation of on-line computers.The currentdecade has been a period of
eclectic interests: the resurgence of statistical procedures, the introduction of 'top-down' recursivegrammars,the adaptationof problem-solvingtechniquesfrom Artificial Intelligence andthe continuationof
interactive efforts.

1. INTRODUCTION
This article chronicles efforts to harness
the computer as a tool for compositional
decision making, beginning in the mid1950s and working up to the present
decade. Although precedents for automated composition exist throughout
musical history, never have such efforts
posed as great a challenge to what for
many have been fundamentalassumptions
about the nature of creativity and theaesthetic purposes of composition. It istherefore not surprising that these developments have met with continuing-andoften virulent-resistance. Too often,
however, the limitations of one or two
individual approaches have been extrapolated into conclusions that computers
are inherently unsuited to compositional
problem solving. Even more unfortunate
has been the tendency among many
critics to base judgments on ad hoc
aesthetic criteria that are irrelevant towhat practitioners of automated composition have actually been trying toachieve.
A major obstacle to any informed
understandingof automated composition
has been the lack of accessible knowledge
concerning how these composers havegone about realizing their inspirations as
pieces of music. For most readers, only
the well-publicized achievements ofLejaren Hiller [1-5] and Iannis Xenakis[6, 7] come to mind; in fact, there havebeen a number of other composers whose
work has been equally deserving ofrecognition. Although Hiller made someCharles Ames (composer), 49-B Yale Avenue,
Eggertsville, NY 14226, U.S.A.
Manuscript solicited by Anthony Hill.
Received 17 January 1986.

? 1987 ISAST
Pergamon Journals Ltd.
Printed in Great Britain.
$3.00+0.00
0024-094X/87

oI8oi)od4

POS4Be'RFfR)'

IIIIII

MuSiC 8/S'AcK-Ou)COS

D:r,4AreotlLz

2 1,2.,2,?
2.
144ntn-M

?ar

to^

I

a...i

1 IF

'

ct

. t

1

I

1t ijz }a
Ho-a
t

'i

1gF

r'K2m

K

S 1i- 1~-;

CLICK

M-

r-

L.A-sy

&

.

1'Si

"

-

J

(A 4

o
Jof
I

r - -I J

II

,

-

c4fcK

vJ/ird A

.-.

-iA

)

;X ^
1js^

---I

I

Jar roo LA6E-LAW4rAcHALGE
c7
(m7

-

-rI r - T ?
A-COJ-IC
C7
Rv

eJ-?

IC.

r

G40r7~
a?

i sJI

46t?

J.C
c- &4a6
??
z-r4
t

6r
^-4-

ni

I

'1-

- 'ToJ-

11

i

-^

:b

1 j Al? J n4Aia

AJ, OAL- P-TA-riTJ'^ I 7i .:tn

I

EJD ..O.

I I

? SDm

M-, 1

t e4<

I-

r

?

f

P%4?-IL. )T---rTo1JB

E - LCrtIi^
I;^ . . JlJ

i j I _4gDMAJ)EE

I ^-

;

CAL-CO - LArr-?9

I

4y

4*2"

jaI

4o
BOLvr

DR. DOGLQ5

I
7 11
J-

.

^k
~~~~~
C'
~~

^&SeXSf rM^-T)#"j(A'I4E MAr,c,^JS).tAl RS-rtj CLEIt'oa_ j.1w^^5(^SAtU
1- d

I^
6,,.

tJd

^
c

L
B&6Ir

Z
7

Z9

TOoo8oIj

I

L-/RIc 1V
s.s.e.stt

II I III
IIIII

;1

'

k^r
7AJi'.
WATC__---I,i

P. l^n1-E
3.-,.1

"

' I^

I

-rN

At!
PA4W-G LI/L6r
OIL
r<6AJ
WOaroTe--rdfA_

Oo- - -ro

k4e6

RO < AJDR-LC_JGSULAOrJVIN
2if

I -

a rT

i-T/7oJ.<?aAvr
r4is_sar t

r
VLLAID/oou(RiGHr

sd.

-, t,1/--L
4/~AS W/~

I

L

.

I1

'sEos
-LA - r_
-rf4ts&GAL JA6 Jo EARr oR 8ouL
oL AD CAL -CO - LA
So 'cireH ADuf A
AL- uJ.i/S 0) - D-'D -,fA l D- /,a_Jsr
r
n' ,4
.--I
__.,
.F'
t.
,I

b.54_-6&r-r'b

^

p

If-

DM9AJD -AJ6
AJ/&_
DE
c17f

t

ReNAD_ -A

DI-, J/hJE
,?

C?

,

ruj 11IflJE -fLL-

D?i3/q _ /f-

/AJ

C-/

--__

. ---

Fig. 1. Martin Klein and Douglas Bolitho, "Push Button Bertha", 1956. Public domain.

LEONARDO, Vol. 20, No. 2, pp. 169-185, 1987

I

progress in correcting this deficiency
through his 1970 comprehensive surveyof early efforts [8], he was able to provide
no musical examples and only the barest
details about how individual pieces were
made. The present article seeks not only
to bring the history of automatedcomposition up to date, but also to clarify(1) what has motivated composers overthe last 30 years to delegate their creativedecisions to a machine, and (2) how thesecomposers have gone about programming
the machine to give them what theywanted.

II. "PUSH BUTTON BERTHA": 1956
One of the earliest instances of automated composition was a program forcomposing 'Tin Pan Alley' melodies,
which was created by Martin Klein andDouglas Bolitho of Burroughs, Inc. using
a computer called DATATRON. An
anonymously written Burroughs publication outlines the operation of the
program as follows:
TheoperatorinspiresDATATRONby
first keying in a 10-digit random
number.This causes the machineto
generate and store 1000 single digits,

each representingone of the eight
diatonic notes in the scale with twoallowable accidentals. The program
then motivatesDATATRONto picksuccessive notes at random, testing
eachformelodicacceptability
as it goesalong[9].
One result of this process was the melody"Push Button Bertha" (see Fig. 1), which
was first aired on July 15, 1956 [10].

III. THE URBANA SCHOOL:
1957 TO 1966
Klein and Bolitho's method of random
sampling and testing provided what
seemed at the time a viable emulation bycomputer of traditional compositional
decision making. In fact, the same
method had been developedindependently
by Lejaren Hiller and Leonard Isaacsonat the University
of Illinois,
Urbana/Champaign. The publicity generated by Hiller and Isaacson's Illiac
Suite [11], supplemented by the establishment under Hiller of one of the nation's
earliest electronic music studios, attracted
a number of individuals interested inmerging the new music with the newtechnology. Along with Hiller andIsaacson, these people included Robert
Baker [12], James Tenney [13], Herbert
Brun [14-17] and John Myhill [18-20].

170

Ilisac Suite ExperimentsSummarizedExperimentOne: Monody, two-part, and four-part writing
A limited selection of first-speciescounterpoint rules used for controlling the musicaloutput(a) Monody: cantus firmi 3 to 12 notes in length(b) Two-part cantus firmus settings 3 to 12 notes in length(c) Four-part cantus firmus settings 3 to 12 notes in length
ExperimentTwo: Four-part first-species counterpoint
Counterpointrules were added successively to random white-note music as follows:(a) Random white-note music(b) Skip-stepwiserule; no more than one successive repeat(c) Opening C chord; cantus firmtis begins and ends on C; cadence on C: B-F

tritone only in VII; chord; tritone resolves to C-E(d) Octave-rangerule(e) Consonant harmonies only except for 6 chords(f) Dissonant melodic intervals (seconds, sevenths, tritones) forbidden(g) No parallel unisons, octaves, fifths(h) No parallel fourths, no 6 chords, no repeat of climax in highest voice
ExperimentThree: Experimental music
Rhythm, dynamics, playing instructions, and simple chromatic writing(a) Basic rhythm, dynamics, and playing-instructionscode(b) Random chromatic music(c) Random chromatic music combined with modified rhythm, dynamics, andI playing-instructionscode(d) Chromatic music controlled by an octave-range rule, a tritone-resolutionrule,and a skip-stepwiserule(e) Controlled chromatic music combined with modified rhythm, dynamics, andplaying-instructionscode(/) Interval rows, tone rows, and restricted tone rows
Experiment Four: Markoff chain music(a) Variation of zeroth-order harmonic probability function from complete tonal
restriction to "average"distribution(b) Variation of zeroth-order harmonic probability function from random to"average" distribution(c) Zeroth-orderharmonic and proximity probability functions and functions combined additively(d) First-order harmonic and proximity probability functions and functions combined additively(e) Zeroth-order harmonic and proximity functions on strong and weak beats,
respectively, and vice-versa(f) First-order harmonic and proximity functions on strong and weak beats, respectively, and vice-versa(g) ith-order harmonic function on strong beats, first-orderproximity function on
weak beats; extended cadence; simple closed form
fromHillerandIsaacson[5]. Copyright
Summarized.
Reproduced
Fig. 2. Illlac SuiteExperiments
1959McGraw-Hillof thepublisher.
BookCompany.Usedby permission
Hiller, Isaacson and Baker
During the same years in which Klein
and Bolitho were programming DATATRON, Hiller and Isaacson were undertaking a series of compositional "experiments"* using the ILLIAC computer,which had been designed and built at
Urbana. Many of their results were
presented in a well-publicized concert
which, coincidentally,also occurredduring
July 1956. Subsequently, these and later*Enclosure of terms in double quotes indicates coinedor otherwise idosyncratic terminology drawn from
specific sources.

Ames, Automated Composition

experiments were collected into an Illiac
Suite for string quartet. Figure 2 details
Hiller and Isaacson's procedures, which
utilized two basic approaches:
1. Random selection constrainedby lists of rules, an approach
resembling that of Klein and
Bolitho (Experiments 1-3).
2. Markov chains, also random,in which the relative likelihoodof each option was conditionedby one or more immediately
preceding choices (Experiment
4).
An excerpt from the Illiac Suite appears
in Fig. 3.

James Tenney
James Tenney had been drawn to
Urbana as a graduate student by Hiller's
groundbreakingcoursein electronicmusic.
tr0t i9Jhcj^While at Urbana, Tenney pursued studies
J6F
r e De r
Z. j-f
8 Z*_
9'6ZIJ88 #DDD+ D S p S D 7 p S g t p S 2 t }p-cottp
in computer composition. In 1961 he wasinvited to Bell Telephone Laboratories[25] where Max Mathews [26-28] was in
the process of developing his now wellknown digital sound-synthesis programs.
Though unaware of the "stochastic musicprogram" that lannis Xenakis wasdeveloping roughly at the same time [29],Tenney had been inspired by Xenakis's
statistical scores such as Pithoprakta andAchorripsis,which had been described inarticles by Xenakis [30]. Tenney's
programs differ substantially fromXenakis's in Tenney'suse of (1) segmented
line graphscontrollinghow compositionalparameters evolve over time, and (2)hierarchic procedures devised in responseto the Gestalt psychology of Max
Wertheimer.
Most of Tenney's composing programs
generated files of numeric data whichwere then realized digitally by Mathews's
MUSIC4 program. However, one exception admits direct visual examination of
the score: Tenney's 1963 Stochastic String
Quartet. This piece divides into three
sections, which at the indicated tempi last50, 100 and 40 seconds. Sections divide
into intermediate structural units, which
Tenney calls "clangs", and these in turndivide into notes. The profile of eachsection is controlled by graphs of musical* WHOLE-TONESHAKE
attributes,such as clang durations,average
3. Measures
Fig.3. LejarenHillerandLeonardIsaacson,IlliacSuite,1957,excerptfromExperimentperiods between attacks, ranges of pitches,
55-72 show "basic rhythm,dynamics, andplaying-instructionscode"; measures73-80 show "random
dynamics and several aspects of timbre:
chromatic music";measures81-100 show "randomchromaticmusic combinedwith modifiedrhythm,
vibrato, tremolo, "spectrum" (sul tasto,of
Used
Edition.
New
Music
1957
permission
bycode".
Copyright
dynamics, and playing-instructions
ord., sul pont.) and "envelope" (pizz.,
the publisher,TheodorePresser Company, Bryn Mawr, PA 19010, U.S.A.
arco-staccato, arco-legato, arco-marcato,arco-sforzando). Each graph supplies a
into creative activity that interaction withmean value to one or more random
A second early collaborator of Hiller's
a computer can provide. For example,
generators in order to select attributes for
was Robert Baker, who conceived theHiller and Isaacson [23] describe thea specific clang; in turn, the program
composing utility called MUSICOMP
of"those
of
as
a
Suite
these clang attributes into further
Illiacfeeds
aspects
COMstudy
forSimulator
Interpreter(MUsicthe process of composition..." which
random generators in order to selectpositional Procedures). MUSICOMP
can be modeled " ... by applying certain
attributes for a note. The opening of thegreatlyfacilitatedthe processof developingfrom
mathematical
Stochastic String Quartet appears in Fig.
deriving
operations
new composing programs by managing
certainand4.
generalsubroutines
theoryprobabilityoflibraries
compositional
An especially significant feature of theprinciples of analysis incorporated in aand other programming modules which[then] new theory of communication
quartet is Tenney's elaborate procedure
individual composers could link together
called information theory". Hiller andfor notating rhythm. Not content toin a main program designed to meet their
A
Cantata:articleBaker'sandHiller"Computerapproximatehis rhythmsas displacements
own idiosyncratic purposes.
relative to a simple meter such as 4/4,
Study in Compositional Method" expresBaker first utilized MUSICOMP to create
ses a similar attitude:
Tenney exploits bracketed rhythmic
their 1962 ComputerCantata [21], which
proportions directly as a compositional
employed serial methods drawn "almost
Since our primary purpose was toresource. His notational procedure works
Structuresin toto" from Pierre Boulez's
theflexibilityandgenerality
demonstrate
as follows. At the broadest level, theCantata
for two pianos [22] in addition to theof MUSICOMP,the Computerpresents a rather wide variety of
program selects the length of each clang
methods employed to create the Illiac
compositional procedures, some ofin quarter notes. Within a clang, it thenSuite.
whichprovedof greaterestheticvalueaselects an independent "gruppetto" unit
hisandHillercolleagues,
Among
than others,and manyof whichcould
for each instrumental part. Measure 13,
morestrong motivation for automating thebe improved[!] by
sophisticatedfor example, constitutes one clang lasting
logic [24].
compositional process has been the insight
:,,..

fd..

Pp cresc.

map

Ames, Automated Composition

171

STOCHASTIC STRING QUARTET

technical notes on Sonoriferous Loops
by Briin, his program advancescompiled
9qi
Of .s IIIi
I
Vn I
-4- -x --^x e_
from moment to moment in the score, in,___3._, effect 'scanning' each instrumental (or$3 Vn II
synthetic) part to determine whether or
not the part is engaged by a note or rest. If'>
not, then the program initiates the
Va
37
"jj
,
sfz=3
_pj
:--==following steps:-:' -1.
rm- !Rhythm.The programrandomly,mIY
Vc-- 1- ,t"I . . 1.
I
i
ViI
PAW I ? J i I
I
"?.t
'j- _
selects "denominators" and
J.
X;
-_p~
"numerators" from 16, 6, 5 and4; these are applied to a common
Vnmultiple of 240 to produce a
duration.
2. Rest/Play Choice. The programVnz- s -^
next decides whether to rest or
to play a note. The relative
activity of each part within asectionof music is controlled by
3-,
~ J>_
"rest/play probabilities"; in the
opening measures, for example,
flute rests 26% of the time,
trumpet 32%, double bass 50%,
Vn I
V 7r 4
mallets 68% and unpitchedpercussion 74%.
Vn II
IT _3. Pitch. Should the program electto play a note in Step 2, it willVa
next select a chromatic degree
and a register. The mechanism
Vc
X
for selecting degrees consults ar^12-element array which theprogram randomly shuffles atthe beginning of each 12-noteVncycle. Because this mechanism
4
supplies degrees for all partsVnsimultaneously, the composite
texture obeys a uniform distribution of degrees. Registers are_,-selected at random.
Once rhythms and pitches had been,
determinedby his program,Bruinmanually
1J- v===tJj?1
P(fj d/m.
-PPintervened to supply tempi, dynamics and"instrumental modes (pizz., mute, stacc.,
4.
James
Stochastic
Fig.
Tenney,tStringQuartet,1963,measures1-15. Copyright198t5SonicArt
Avenue,Baltimore,MD21207,U.S.A.Usedbypermissionof tbhepublisher. etc.)
Editions,2617Gwynndale
An excerpt from another computercomposed work of Briiun'sfor ensemble
two quarters; the gruppetto units are 5
and tape, Non-Sequitur VI, appears as... whereasthehumanmind,conscious(violin 1), 2 (violin 2), 3 (viola) and 2of its conceivedpurpose,appiroaches
Fig. 6. Briun'scomments regarding thisevenanartificialsystemwitha selective('cello). Each gruppetto unit in turnwork evoke Xenakis's investigation in
attitudeand so becomesaware
divides randomly into smaller divisions.
Achorripsis[32] of the minimal conditions
the preconceivedimplicationsof otheThis continually fluid metrical structurenecessary to create a composition.
system,the computerswouldshiow thethen provides a notational framework for
totalof theavailablecontent.Revealing
However, Briin imposes the additional
the 'floating-point' durations generated
farmorethanonlythetendencies of therequirement of 'musicality' through thehumanmind,this nonselectivepicture
by Tenney's random generators.
mechanism of random sampling andof themind-createdsystemshou
testing:significantimportance[31].
James

TenneyJ =60.__~-_-

4.- v-

Herbert Briun
A member of the Urbana composition
faculty from 1963 to the present, Herbert
Brtin employed MUSICOMP to create anumber of works including his 1964
SonoriferousLoopsand 1966Non-Sequitur
VI. Like Hiller, Isaacson and Baker, Brunvalued composing programs as truly
empirical means for testing formulationsof compositional procedures:

172

Briiun'sSonoriferous Loops aldopts themodel of Varese's Deserts by a]Iternating
four digitally synthesized interludes withfive short movements for live eemsemble.
The live ensemble employs the five
instrumental parts shown in Fig. 5flute, trumpet, double bass, malllets (xylophone and marimba) and I mnpimtchedpercussion-while the interlude-s employ
three synthetic voices. Accordiing to theAmes, Automated Composition

Theprogrammingof [Non-SequiturVI]mainlyreflectsthe continuoussearch
foranswersto thefollowing:(1)Whatis
the minimal number and power ofrestrictiverules that will select fromrandomgeneratedof elements
sequencesthat particular variety of elementconcatenations
satisfyingtheconditions
recognizableor stipulatedfor
either'musical'formsandevents?(2) Coulda
combinationof stochasticchoiceruleswith heuristic, multivalent,decision

SONORIFEROUS LOOPS
Brun
HerbertOpus 32 - 1964
J = 1440crosses the corresponding scaledegree.Note durationstherefore
depend on the steepness of thecontour as it passes from one
scale step to the next.
IV. EUROPEAN ALGORITHMIC
MUSIC: 1960-1970
The first-known European composer
to become involved with automatedcompositional procedures was Pierre
Barbaud, who presented computer-composed pieces in Paris as early as 1960.
Many of Barbaud's procedures are
documented in a monograph entitled
Initiation a la compositionmusicale automatique [35]; they include permutational
methods applied to traditionalharmonies,
serial (12-tone) methods and methods ofrandom selection. In his article "Algorithmic Music" he sets forth the aesthetic
philosophy that musical composition"consists in creating what scholastics
called an artifactum, that is to saysomething that nature does not produce".
Barbaud confronts objections that automation removes the 'humanity' fromcomposition by turning the complaint
against itself:

I

I!
2

Musicis generallycalled'human'when
it considers temporary or inherent
tendenciesof the mind,of partor all of
a composer'spersonality.Suchmusicis
based on feelingand since it turnsits
back,in a sense,on pureknowledge,it
mightratherbe called'inhuman',for itcelebrateswhat we have in common
with all the animalsratherthan withwhat is individualto man:his reason.
Algorithmicmusic is thus 'inhuman'
only in one sense of the word, it is'human'in as muchas it is the productof rationalbeings[36].
1964HerbertBriin.Usedby
Loops,1964,measures0-9. CopyrightFig.5. HerbertBriin,Sonoriferous
permissionof the composer.

taking procedures contribute an apparent 'musical' coherence to a chain ofchanges of state in a structured system?
[33]

John Myhill
Although John Myhill came to Urbana
in 1964 as a professor of philosophy andmathematics, he had in fact previously
undertaken formal musical studies withMichael Tippet. An avid supporter ofactivities then in progress at Urbana,
Myhill in 1965 contributed a Scherzo a
Tre Voce for computer-synthesized tapealone. The Scherzo, directly inspired bygraphic methods advocated by Joseph
Schillinger [34], derives melodic contours
for each of its three voices-hence thetitle-from the eight evolving sinusoids
depicted in Fig. 7.

As with Brun's Sonoriferous Loops
program, Myhill's program scans all
three voices from moment to moment;
however, in this case the program determines whether or not each part is ready to
begin a new contour. If ready, theprogram selects a shape from those given
in Fig. 7, an overall duration for the newcontour and one of the following threemodes of performance:
1. Siren-like glissandi.
2. Discrete pitches taken from ascale relative to a rhythmic
pattern: the scale degree inclosest proximity to the contourat the onset of a note determines
the pitch(Schillinger'sapproach).
3. Discrete pitches again takenfrom a scale. Here, each newnote begins when the contour

Ames, Automated Composition

Compositionally, where the Urbana
school tended to focus on local relationships implemented in the form of stylistic
rules, the Europeans emphasized global
qualitiesof musicalpassages, as quantified
by statistical distributions. Technically, it
was Europeans such as lannis Xenakis[37] and Gottfried Michael Koenig [3842] who were the first to conceive of acomposing program as a utility capable ofgenerating many pieces, rather than a
one-shot effort geared toward a specificcompositional goal. Xenakis extolls what
he considers to be the virtues of suchgeneralized utilities in the following
poetic terms:
With the aid of electronic computers
the composer becomes a sort of pilot:
he presses the buttons, introduces
coordinates, and supervisesthe controlsof a cosmic vessel sailing in the space ofsound, across sonic constellations andgalaxies that he could formerly glimpse

173

=92

I
I

I
Fig. 6. Herbert Brun, Non-Sequitur VI, 1966, measures 1-8. Copyright 1966 Herbert Briin. Used by permissionof the composer.

V

Constant deviation from central pitch

Increasing deviation from central pitch

Decreasing deviation from central pitch

o
c

.2
0

*

1-a)
Tia

4)

0

A

A

VV\J\j
/

l

C]

o

ItA
;T.im

JLVV

V

v

Fig. 7. Melodic contoursin John Myhill's Scherzo a Tre Voce,1965. At its maximum(vertical) spread,each contourspans a one-and-one-halfoctave range.

174

Ames, Automated Composition

only as a distant dream. Now he can
explore them at his ease, seated in anarmchair [43].

lannis Xenakis
Perhaps the best-known composer to
employ computers has been lannis
Xenakis. It was Xenakis who had first
introduced statistical methods of composing for live ensembles: Pithoprakta(1956) exploits Gaussian distribution torealize the "temperatures" of massed
glissandi, while Achorripsis (1957) uses
Poisson's distribution of rare events toorganize"clouds"of sound. The aggregate
effect of these statistical scores concerned
Xenakis much more than specific relationships between musical elements; in his
1962 "stochastic music program" [44], hebegan delegating specific decisions to therandom-number generatorof a computer.

Following the model of Achorripsis,thestochastic music program employs statistical procedures to deduce a musical workwith "the greatest possible asymmetry ...
and the minimumof constraints,causalities,
and rules". Xenakis designed his program
to create works for varied ensembles
according to varied input data suppliedby the composer. Among the morefamiliar pieces produced by Xenakis
using this program are ST/10-1,080262
for 10 instruments, ST/48-1,240162 fororchestra (48 instruments) and MorsimaAmorsima ( ST/4-1,030762) for 4 instruments.
One can gain a sense of how Xenakis
worked with his program by examining
the input data -used to create one such
work, Morsima-Amorsima. This work
lasts 17 minutes, 12 seconds at theindicated tempo. Its ensemble consists ofviolin, 'cello, contrabass and piano, andfor these instruments, Xenakis established respective maximum densitiesat 4, 4, 3 and 15 notes per second. These
values result in a combined maximum
density of 26 notes per second, but
Xenakis nudged this value upwardslightly
to 28. He also specified a combined
minimum density of 0.07 notes per
second-approximately one note every
13 seconds. The stochastic music program
converts these "objective" limits to
produce a range of "subjective" (logarithmic) densities from 0 to 6. For each of
the integral points along this range ofsubjective densities (0, 1, ..., 6), theprogram accepts a list of probabilistic
weights by which notes will be drawn
from each of the various timbre classes
available from the ensemble. For
Morsima-Amorsima,Xenakis has defined(Density=5.3)

,.-.

,
Z_

cil

JWtl Density =0.4-

~ ~ ~ ~-~~~0~~~~-0o

--

-

0

.tto

Fig. 8. Chartof orchestrationversussubjectivedensityfor lannis Xenakis's

Theindicatedtimbreclassesare:(1) piano,(2) arco
Morsima-Amorsima.

ponticello, (3) harmonics,(4) arco normale,(5) glissando, (6) tremolo arco
ponticello, (7) pizzicato and (8) frappe col legno. After a diagramprovided
by the composer.

Fig. 9. lannis Xenakis, Morsima-Amorsima, 1962, measures 136-146.
Each 'JW' marksignifies the first complete measureof a section; densities
calculated by the program are presented in their 'objective' forms. The
abbreviationsin the string parts are: asp-arco sul ponticello; an -arco
position normale, and fc--frappe col legno. Copyright 1967 Boosey and
Hawkes Music PublishersLimited, 295 Regent Street, LondonW1R 8JH,
United Kingdom.Reprintedby permissionof the publisher.

Ames, Automated Composition

175

eight suchclasses.The relativedistributions
in which the stochastic music program
employs these timbre classes are graphedalong the range of subjective densities inFig. 8; an excerpt from MorsimaAmorsima appears in Fig. 9.
Once provided with its basic input
data-length of the composition, average
length of a section, range of densities andconstitution of the ensemble-the stochastic music program is ready to go. The
program is structured in two loops: anouterloop determinesthe duration,densityand distribution of timbre classes (the lastby locating the subjective density along
the horizontal scale in Fig. 8, thendetermining weights for each timbre classalong the vertical) for each section of thework, and an inner loop composes theactual notes. Details of these mechanisms
may be found in Xenakis'sown descriptionof the program [45] and John Myhill's
less mathematically demanding critique[46].

AKKORDE

.

/

?
f

9

-

7Ut/

9 r

b

~'' H-

jt

2ti

^

9 "/

J7

^

7^
T

^

if^

, __.

j

^^

97-

^O

;

.

Gottfried Michael Koenig
A less well-known but equally significant contributor has been Gottfried
Michael Koenig, who has been associatedfor many years with the Institute ofSonology in Utrecht both as a teacher andas an administrator. Koenig's work in
automated composition began in 1964
with a composing program entitled
PROJECTI, and this program has been
responsible for several of Koenig's
compositions including his 1965 Project
1, Version1 for 14 instruments. Although
Koenig's background is serial (he had
worked early on as a composer, assistantand teacher in the Cologne electronic
music studio), it had become apparent toKoenig by the time he undertook
PROJECT1 that "the trouble taken by
the composer with series and theirpermutations has been in vain; in the end
it is the statistical distribution that
determines the composition" [47].
A more elaborate program from 1969
called PROJECT2 [48] incorporates abroad palette of statistical procedures
which users can patch together in different
combinations. Although Koenig developed PROJECT2for pedagogicfunctions,
he has used it himself in one instance tocreate an ambitious Ubungfur Klavier("Study for Piano", 1970). The score to
this work consists of 12 "structures";

Klavier,1970, Structure8, Variant1. The 'chords'(Akkorde) and the 'tones' (Toene) result fromindependent sets of directives to Koenig's
PROJECT2program.Copyright1969 Gottfried
Michael Koenig. Used by permission of thecomposer.

176

6

-

; P,^,q

T\

tD

b

TOENE
I

_ Xi-r:
/

y19

PP

p

_--_

I
rFL
ff

19:

f

f

--5

-

-

o:' r ~~~~,;

v_;7

3

A

-

-

r-

I I

"

7~~~~

mf

Ames, Automated Composition

.

-

-7

/il.-;-JI"f,,

- 1
ig I7
I

ir

mp

-P

r

__

rI

ff

P

1

?

lyI

--r

i

I
mp-========

ip

Fig. 10. GottfriedMichaelKoenigUbungfur~~ I..~

m'

'PP

r.

PP

,
7,

r ;1

i11

1l
"

each structureappearsin three "variants",
for which the only change in directives to
PROJECT2 is the duration. Koenig
acknowledges the indeterminate aspectsof his compositional process by allowing
the performerto choose between variants;
the fact that such indeterminacy is closely
circumscribed is reflected in Koenig's
instructions that at least one variant ofeach structuremust be played, and that all
12 structures must be presented in aprescribed order.
An examination of Structure 8 of the
Ubung fur Klavier illustrates theworkings of PROJECT2. Variant 1,
which is the shortest, contains two sets ofmaterial: eight 'groups of chords' andfive'groupsoftones'

(Fig.

10).

Koenig provides the following synopsis
of Structure 8 in his instructions to theperformer, which allow elements ofperformer discretion much like thosecontrolling the performance as a whole:
A transition:
chordsandtonesalternate.
Thereare also severalgroupsof bothchordsand tones in everyvariant.Not
all the groups of chords or tones have tobeplayed,butthoseselectedmustbe in
the givenorder.Groupsof tones must
alwaysbe separatedby chords,groupsof chords can join on to one another(withoutjumping over groupsof chords).
A second group of chords then joins onrhythmically where indicated by thearrow. Such arrows, when present,
have no significance if groups of chords
alternate with groups of tones. What
must be played are: at least three groupsof tones in the first variant .... The
number of groups of chords is left to theplayer, but he should begin with agroup of chords [49].
Included among the musical "parameters"
selected by PROJECT2 are (1) harmony,or degree of the chromatic scale, (2)register,(3) entrydelay, or period between
consecutive attacks, (4) durationand (5)dynamic. The harmony parameter ischosen by one of three principles (implemented as program subroutines) called
ROW, CHORD and INTERVAL. For
each parameter other than harmony, theuser either must specify a constant value
or must provide a supply of options andspecify one of six selection features (alsoas subroutines):
implemented
SEQUENCE, ALEA, SERIES, RATIO,GROUP or TENDENCY. Table 1presents
a breakdown of the principles, selection
features and supplies used to compose
Structure 8 [50].
Of the selection features employed for
Structure 8, ALEA and SERIES are themost fundamental. ALEA samples elements at random with replacement fromthe supply, with uniform likelihood of
selection. SERIES also samples elements
at random, but without replacement;i.e.
each time SERIES selects an element, iteliminatesthis element from consideration
until the entire supply has been exhausted(at this point, the full supply once again
becomesavailable).

The procedure for

SERIES is reminiscent of the random
shuffling undertaken by Brin's Sonoriferous Loops program. Compared to
ALEA, SERIES requires many fewer
calls before its actual choices come toreflect the distribution of options inherent
in the supply. GROUP is a higher-orderselection feature which repeats eachelement a number of times before
resampling the supply; the number ofrepetitions and the new supply element
can be selected either by ALEA or by
SERIES, depending on the user's directives.
For the most part,the selectionprocesses
undertaken by PROJECT2 are indepen-

Table1. Breakdownof principles,selectionfeaturesand suppliesusedto compose
Structure 8 of the Ubungfur Klavier(see Fig. 10)

dent of one another; e.g. pitches do notdirectly affect rhythms. However, in a few
situations such as the restriction upon
durations in Structure 8's "groups ofchords", the user is able to engage a"block", causing PROJECT2 to toss out
unacceptable choices and select new
options.
Like GROUP, Koenig's 'harmonic'
principles, CHORD and INTERVAL,
may be regardedas 'higher-order'selection
features. Each call to CHORD first
requests a module such as ALEA or
SERIES to choose an entry from a tableof chords provided by the user. Koenig's
table for the "groups of chords" inStructure 8 is shown here as Fig. 11; inthis instance, the job of selection falls to
ALEA. Once it has obtained a chord,
CHORD again invokes either ALEA or
SERIES to determine a (register-free)transposition; ALEA also received thissecond job in Structure 8.
The INTERVAL principle employed
for the 'groups of tones' implements a
Markov chain: In order to select a current
interval,INTERVAL begins by consulting
a user-provided logical matrix, such as
the one for Structure 8 shown in Fig. 12.
This matrix informs INTERVAL whichof the 11 intervals from the minor second
to the major seventh are acceptable, given
the most recent interval employed by the
program. INTERVAL then requests
SERIES to select from these acceptableoptions. The currentintervalthen becomesthe most recent interval for the next call to
INTERVAL, perpetuating the chain.
Once it has determined a chromatic
degree using one of Koenig's principles, itremains for PROJECT2 to generate
lower and upper registral limits for thisdegree. In Structure 8, Koenig has
specified constant registral limits. Thus,
each pitch within the "groups of chords"
will be placed randomly within any of thefour octaves between C3 (C below middleC) and B6. Similarly, pitches in the"groupsof tones" occur randomlybetween
G2 and F#6.

Parameter

ChordsTones

Harmony

CHORD from chord tableshown in Figure 11.

INTERVAL from intervallic
matrix shown in Figure 12.

RegisterConstant: C3-

Constant: G2 to F#6

Index

ALEA from 0.24, 0.30,
0.37, 0.46, 0.58, 0.72,
and 0.89 seconds for
entire chord.

ALEA from 0.46, 0.58,
0.72, 0.89, 1.11, 1.38,
and 1.72 seconds.

ALEA from 0.10, 0.12,
0.15, 0.19, 0.24, 0.30,
0.46, 0.58, and 0.72
seconds for entire chord;duration may not exceed
entry delay.

Same as entry delay

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

Entry Delay

Duration

Dynamics

B6

GROUP: elements by SERIES
from pp, p, mp, mf, f, andff; repetitions by SERIES
from 3, 4, 5, 6, and 7.

SERIES from pp, p, mp,
mf, f, and ff.

Ames, Automated Composition

Degrees
C#

F
F#

A
Bb

F
C#
C#

F
F
F

A

Bb

F#
F#

A
A

Bb

F#

A
A

F#
C

Bb
Bb

C
C

A
A

Bb
Bb
Bb

C
C

A

Bb

C#
C#
C#

C#
C#

F
F
F
F

C

F#

F#
F#
F#

C
C

Fig. 11. Chordal table for Structure 8 of
Koenig's Ubungfur Klavier.

177

Current

Interval

Most
RecentInterval

m2

M2

m3

M3

P4

TT

P5

m6

M6

m7

M7

m2
M2
m3
M3
P4
TT
P5
m6
M6
m7
M7

yes
no
no
no
no
no
no
no
no
yes
yes

no
yes
yes
no
no
yes
yes
yes
no
yes
yes

no
yes
no
no
no
no
yes
no
yes
no
no

no
yes
no
no
no
no
no
yes
no
yes
no

no
no
no
no
no
no
yes
no
yes
yes
no

no
no
no
yes
no
yes
no
no
no
yes
no

no
yes
yes
no
-yes
no
no
no
no
no
no

no
yes
no
yes
no
yes
no
no
no
no
no

no
no
yes
no
yes
no
no
no
no
yes
no

yes
yes
no
yes
yes
no
no
yes
yes
yes
no

yes
yes
no
no
no
no
no
no
no
no
yes

Fig. 12. Intervallie matrix for Structure 8 of Koenig's Ubungfur Klavier.

Otto Laske
A close collaborator of Koenig's has
been Otto Laske [51-57]. As a composer
and musical epistemologist, Laske has
been strongly interested in the impact ofcomputer-aided tools on the way composers think. For a number of years
beginning in the early 1970s, Laske has
worked to blend insights from cognitive
psychology,formal linguisticsand artificial
intelligenceinto an expertsystem"bridging
the gap between a composer's semantic
intuitions and low-level data". In Laske's
work, composing programs such as
Xenakis'sand Koenig'sareoften employed
to create "proto-scores" which Laske will
freely edit and arrange.
V. INTERACTIVEUTILITIES IN THE
UNITED STATES AND CANADA:
1970-1978
The 1970s marked the widespreadobsolescence of 'batch-oriented' computers programmed by stacks of punchedcardsin favor of 'on-line' systems, eitherin
the form of single-user computers andminicomputers dedicated to real-timefunctions or of large time-shared systems
capable of servicing many users simultaneously. The new fashion for on-line
computing found its musical counterpart
in utilities motivated largely by a desire tofacilitate rapid interaction between
composer and sound: Max Mathews andRichard Moore's 1968 GROOVE [5863]; Leland Smith's 1972 SCORE [64](later converted into a music printing
program); Barry Truax's 1973 POD with
its subsequent enhancements [65-68];
Herbert Brun's 1976 SAWDUST [69]and William Buxton's 1978 SCED [7073]. Such utilities were coupled inevitably
with sound synthesis, at first through

f

2'I

I

2

digitally controlled analog synthesis or
throughsoftwaresound-synthesispackages
modeled after Mathews's MUSIC4 andMUSIC5 programs[74], and laterthroughdigital hardware.
Ghent and Spiegel
In particular, an environment such as
Mathews and Moore's GROOVE (Generating Realtime Operations on Voltagecontrolled Equipment) [75] utilizes thecomputer as an intermediarybetween theuser (working through specialized control
devices such as keyboards and/or panelsof knobs and switches, along with theusual alphanumeric terminal) and anarray of real-time sound-synthesis hardware. Such an environment enables acomposer/performer to deal at a reflex
level with sounds and timings, although
the price for this is that compositional
procedures must be simple enough to run
in real time. Along with random selection,some of the more familiar procedures
falling within this category are traditional
motivic operations. The most active usersof GROOVE were Emmanuel Ghent
beginning in 1968 [76-78] and Laurie
Spiegel beginning in 1974 [79-81].
The first piece to involve the GROOVE
facility directly in compositional decision
making was Ghent's 1974 Lustrum.
Lustrumis scored for a quintet of special
electronic stringedinstrumentsdevelopedby Mathews (among other things, these
instruments could be set to emulatebrassy timbres), for conventional brassquintet and for computer-generatedtape;
the piece also exists in an all-computerversion entitled Brazen.
Lustrum (or Brazen) has its genesis in
the 15-element "pitch-set" depicted in"'7 *0I-

*4
3

4

5

6

7

8

9

10

11

12

13

14

15

Fig. 13. Pitch set for Emmanuel Ghent's Lustrum. Redrawn from Ghent, "Real-Time Interactive
CompositionalProcedures"[58].

178

Ames, Automated Composition

Fig. 13 and in an analogous set of
durations. In order best to "hear" what
the computer would be doing in real time
as he manipulated GROOVE's input
devices during this initial foray into
automated composition, Ghent employeda pitch set with strong tonal orientation
around Bb. When he had specified both
pitch and duration sets, he developed aprogram to generate 10 "functions"(monodic sequences of notes); thesefunctions wereproducedby usingweighted
randomness to select pitch-set elements
and duration-set elements for each note.
The resulting functions, denoted by
Ghent using the symbols F 1, F2, . .. F10,
in turn provided all of the material for
Lustrum.BecauseGhent'sprogramsrepresented pitches in these functions by theirposition in the set rather than by theirlocation on the keyboard, he was able toimplementmotivic operations which acted
indirectly on set positions-operations
not unlike the traditional practices oftransforming motifs modally-relative tonotes of a constituent major or minor
scale. In Fig. 14, for example, violin II
plays the original form of F1. The 'celloplays a derivative of F I which is obtainedby invertingthis original sequence around8, the central position in Fig. 13: theopening D in violin II lies two positions
lower than position 8, so the opening G in
the 'cello lies two positions higher,and soforth. Also appearing in Fig. 14 is F2,
played in original form by the viola, in'indirect' inversion by trumpet 2, inretrogradeby trumpet 1 and in retrograde
inversion by the bass. Not shown in thisexcerpt is the operation of indirecttransposition, which Ghent calls translocation. Translocation is performed byadding a constant modulo 15 to eachsuccessive position in a function.
Concerning the role of the computer inthis process, Ghent states:
Theuseof theindirectpitchreferencing
technique ... is indeed possible without

the help of a computerbut the labor
involvedin spellingout all mannerof
possiblevariantswouldbe prohibitive.
Also the more one hears what thecomputeris producingin responseto
one'sownselectiveprocesses,the moreideas suggest themselves as further
avenuesfor variation[82].
Subsequent to Lustrum,Ghent developed
compositional algorithms based on the"linearization"of chordal structures[83].
Since he had already employed similar
techniques in manually composed works
for small ensembles, Ghent regarded his
programming as "teaching the computer
to think the way [Ghent] thought,
compositionally"-although Ghent re-

= 105trumpet-like

~Iv
ff

-

*
-tpl

-

v710-_"Fl-I-

_

.

-v-_

--

w
v_=v

Fig. 14. EmmanuelGhent, Lustrum,1974, measures208-212. Copyright1978 PersimmonPress, 131 Prince Street, New York, NY 10012, U.S.A. Used bypermissionof the publisher.

served the option to modify what thecomputer produced.
A variety of comments by Spiegel
illustrateshow a composer might typicallyinteract in real time with GROOVE. To
create her 1974 composition Patchwork,for example, Spiegel developed programs
that monitored GROOVE's input devices
in order to "derive from [them] much
more complex music than [Spiegel]actually played". Spiegel has commented
as follows:
The programI wrote for [Patchwork]
had all Bach's favorite [motivic]
manipulations-retrograde,inversion,
augmentation,diminution,transposition-available on switches, knobs,
pushbuttons,and keys, so that I could
manipulatethe 4 simplemelodicand 4
rhythmicpatterns with them in thesamewaythata playerof aninstrument
manipulatesindividualtones. (I did
edit it a lot, too.) [84]The melodic patterns mentioned by
Spiegel were representedby her programs
as "relative (intervallic) distances" from a"pitch reference point" which Spiegel
could control in real time from her
keyboard. Elsewhere Spiegel describes
some of the 'higher-level' methods ofcontrolling the musical evolution of her
1975MusicforDance through GROOVE's
input devices:
BecauseI couldhearthe musicplayed
while computationwas in progress,I
couldchoosewhichmusicaldecisionsIwanted to make, leaving the rest tofollow the logic I had coded ....

For

example,I couldsettheprobabilitythata certain pitch would be played onstrong beats at zero percent, at 100

percent, or anywhere in between, by
turning a knob while listening to themusic evolve [the position of the knob
at each moment would be recorded by
GROOVE for later playback]; or I
could throw a switch to change over toan entirely different set of rules [85].

Truax and Buxton
Two Canadians who had studied under
Koenig and Laske, Barry Truax andWilliam Buxton, have since organizedcomputer music studios respectively in
Vancouver and Toronto. In addition todeveloping real-time performance systems,
both Truax and Buxton have developed
non-real-time environments which permit
users to get by with little or no programming. These environments enable
users to monitor results closely as acomposition takes shape. They minimize
interaction bydelays in non-real-time
providing a menu of precompiled "macros"(Buxton's term) and by incorporating
facilities for rapidly evaluating musicalproducts, specifically: real-time digitalsynthesis augmented visually by graphic
displays. Laske [86] has documented how
he built up his 1980 composition
Terpsichore as a succession of increasingly
elaborate "subscores",using macros
supplied by Buxton's SCED (SCore
EDiting) utility.

VI. NEW APPROACHES:

1976-1986

Recent efforts have shown a new
sophistication toward automated decision making along with increased machine
participation in decisions affecting largescale compositional form. Included amongAmes, Automated Composition

the 'new generation' of composers seeking
creative assistance from computers are
Larry Austin, Claudio Baffioni [87],Clarence Barlow [88-90], Tommaso
Bolognesi [91], Lelio Camilleri, Joel
Chadabe, Thomas DeLio, Charles Dodge[92], David Feldman, Christopher Fry[93], Peter Gena [94], Francesco Guerra[95], Christos Hatzis [96], Steven
Holtzman [97,98], Kevin Jones [99], Gary
Kendall [100], Shirish Korde, Petr Kotik,
Ron Kuivila, LauraTedeschini Lalli [101],David Levitt [102], Denis Lorrain [103],
Leonard Manzara [104], Larry Polansky,
CurtisRoads [105-108], David Rothenberg
William[109], Andrew Schloss,
Schottstaedt [110], Sever Tipei [111],
Horacio Vaggione, Charles Wourinen,
David Zicarelliand myself [ 112-120].The
extent of this new activity has been far too
great to continue with a detailed survey ofpieces, so I shall limit my remaining
examplesto significantworksthat have notbeen describedpreviously in the literature.
Further details may be obtained from theworks cited in the References and Notes.
Thomas DeLio
Thomas DeLio's 1976 Serenade forsolo piano is an elaborate work for which
the form was composed manually while
the details were selected automatically.
The Serenade has three parts, eachconsisting of 10sections;markedcontrasts
and occasional long silences between
many of these sections give the Serenade
an episodic quality congenial to its title.
The work is built up from a number ofprimary rhythmicpatterns and chromatic
cells. Part I introduces these ideas in

179

__

"embryonic states"; they emerge "fully
formed" in Part II, which also serves adevelopmental purpose; Part III extrapolates several of the ideas from earlier
parts into "broad sweeping guestures".
Figure 15 reproduces Part I, Section 10of the Serenade.The basic ideas employedin this section are a 7:4 polyrhythm andtwo chromatic cells: G# B C D and its
reflection, G# A# B D. Registers are
distributed uniformly over the range
from middle C upward. The section
consists of two gradual evolutions, eachlasting 17 quarters. The following
breakdown of methods for handlingrhythm and pitch is based upon a letterfrom DeLio to the author:"Nj = 60n

r

~

,
7

.

r3

-r

J

-

( I

r,

-nI
7

_-

m-

7

Q=
i. =

IAi--=

47t&~dXBy7

Rhythm. Over the first 17 quarters, therhythm coalesces from a sparse, irregular
texture to a consistent 7:4 pattern. DeLio
accomplished this evolution by treatingeach quarter as a statistical frame whose
elements are the 29 unequal rhythmic
units obtained by interfering septuplet
thirty-secondsagainst duple sixty-fourths.
A graphic depiction of the resulting
pattern appears in Fig. 16. In this sectionof the Serenade,only one note may attack
at a time; the number of attacks perquarter results from a "first-ordertransition prQcess"(i.e. a Markov chain)
in which the number of attacks may either
stay the same, increase by one or (withrelatively small probability) decrease by

X

7

r

-- z

Z

I

-T
_

,

-

--' F'

-r

a

7x,r

*

one from one quarter to the next. This
process resulted in the following chain:
566777878899

10 10 10 10 10 10...

Once these numbers have been determined, DeLio's program locates these
attacks within each quarter by selecting
without replacement from the units
depicted in Fig. 16. Initially, each unit
receives equal weight; as the rhythm
evolves, the off-beat thirty-seconds andsixty-fourths receive less and less weight
until only the 7:4 pattern remains. Thispattern holds consistently through theremaining 17 quarters.
Pitch. At the beginning of Section 10,
DeLio's programselectsdegreesuniformly
with replacement from G#, B, C and D.
Through the first 17 quarters the likelihood of selecting C decreases graduallywhile the likelihood of selecting A#
gradually increases, so that G#, A#, B
and D receive uniform weight at the midpoint of the section. Over the remaining
17 quarters, the weights for G#, B and D
decrease gradually until only A# remains
at the end of the section.
Grammars

I

Fig. 15. ThomasDeLio, Serenade, 1976, Part I, Section 10. Copyright1976 ThomasDeLio. Reprinted
by permissionof the composer.

180

Ames, Automated Composition

The effectiveness of composing programshas beenimprovedradicallythroughthe introduction in recent years ofrecursive programming techniques; thefirst major area of activity relying heavily
on such techniqueshas beenthe applicationof Noam Chomsky's phrase-structure
grammarsto composition. This approachenables a composer to describe musicalforms economically, by first providing ageneral archetype (or axiom) of the formand by further listing a set of productions
for deriving details from generalities. The
full power of such an approach can beattained only if the productions arecapable of acting upon their own results(i.e. capable of recursion).
Although Curtis Roads had alreadydescribed an elaborate left-to-rightcomposing program called PROCESS/ING as early as 1975 [121, 122], his
advocacyof top-downChomskianmethods[123] has achieved the most influence.
Roads'semphasisupon productionsclassified by Chromsky as context-free wasquickly extended to embrace otherChomskian ideas such as context-sensitive
productions and simple transformationsin
Steven Holtzman's 1980 "A Generative
Grammar Definitional Language forMusic" [124]. In Kevin Jones's 1981
"stochasticweb grammars"[125], contextfree productions are employed to carve
up a region of musical space (described inI x L

x
xI

l

lx

xI

I

xl

I I

Ix 11 I

Ix

x

Ix l

I I x

l x

I

I II

I I l 11 H I xlx 11 IIxl I lxl

I

X'sindicate'primary'units.
Fig. 16. Interferences
resultingfroma 7:4polyrhythm.
Jones's simplest examples by boundaries
for time and pitch coordinates) into progressively smaller chunks until specificdescriptions of notes have been obtained.
None of the speculations by Roads,
Holtzman or Jones resulted, to my knowledge, in more than a few brief, illustrative
musicalexamples. Ironically,my own 1980
Crystalsfor string orchestra[126] resulted
from top-down productions similar toJones's. However, my methods were
derived in response to the Gestalt
hierarchies of James Tenney-only afterwarddid I discoverwhat Roads, Holtzman
and Jones had done.
Tenney himself has resumed involvement with composing programs after a
20-year hiatus. In his 1983/1984 Bridge
for two retuned pianos, eight hands,
Tenney fuses hierarchic ideas from his
Bell Labs period with a slightly more
recentinterestin the harmonicpossibilities
of just intonation. Bridge consists of three
sections lasting approximately 8, 13 and21 minutes. The initial section presents awholly random environment evocative of
the compositional world of John Cage;
the final section realizes a Gestalt
hierarchy in which individual notes
combine into "elements" (chords), elements combine into "clangs", clangs
combine into "sequences", which ultimately combine into the section as awhole; the middle section effects a"bridge" from Cage's world to Tenney's.
An excerpt from the final section appears
in Fig. 17. The notated pitches are
modified by the tuning system shown in
Fig. 18.
A third independent path to recursive compositional procedures has
beenfractal geometry.Although popularly
associated with Benoit Mandelbrot,
fractals are grounded, in fact, in recursive
notions which were well understood byturn-of-the-century mathematicians suchas Georg Cantor (inventor of the "Cantor
Set") and Giuseppe Peano (inventor ofthe "Peano Curve").Mandelbrot'swritings
proved a source of inspiration to Charles
Wourinen, who has explored fractals
both in a set of short computer-composed
studies realized around 1980 and in more
recentmanuallycomposed works. Fractals
have since provided the impetus forseveral computer-composed pieces including Larry Austin's 1981 Canadian
Coastlines, Horacio Vaggione's 1984

Fractal C and Charles Dodge's 1984
Profile [127].
Artificial Intelligence
An especially potent approach that
also relies on recursive programming
techniques has drawn from Artificial
Intelligence in order to implement
decision-making processes that employ
searches to discriminate actively between
multiple options. Such searches typicallyincorporate one or moreprioritizationsfunctions that measure in numeric terms(positive or negative, depending on theapplication) how each option available toa decision will contribute to the resulting
musical context. In the author's terminology [128], search-based programs
divide into two classes:
1.

Comparativesearchessystematically enumerate every possible
configurationof decisions,evaluating each configurationin orderto determine the 'best' possible
solution to a problem.
2. Constrained searches improvedramatically upon the randomsampling-and-testing approachof Hiller and Isaacson's Illiac
Suite. Each time such a program
initiatesa decision, a constrained
searchprioritizesall the available
options from most to least
desirable and organizes these
options into a schedule. It thenmethodicallyworks through thisschedule until it finds an optionthat passes all the constraints.
Shouldeveryoption in a schedule
prove unacceptable, the program then backtracks, revises
one or more earlier decisions
and tries again.
Although computer scientists have employed recursivesearches in chess-playing
and theorem-proving programs since themid-1950s-and despite Stanley Gill's
demonstration with his 1963 computercomposed Variationson a Themeby Berg[129] that backtracking could be aneffective tool in composing programsthe approach has mostly been ignored
until very recently. This pattern was
broken by Larry Polansky's 1975 FourVoice Canons, composed by a programwith non-rigorous backtracking, andindependently by Kemal Ebcioglu's 1980

Ames, Automated Composition

modeling [130] of compositional process
in two-part sixteenth-century counterpoint. Ebcioglu's was the first program
since Gill's to implement a fully rigorous
constrained search with scheduling andbacktracking. He has since employedsuch methods with great success insimulating J.S. Bach's procedures forharmonizingchorales[131];similarsuccessin chorale harmonization has been documented by Marilyn Thomas [132].
I employed comparative searches tocreate my own 1981 Protocol for piano[133]; but since that time I have created anumber of original compositions using
constrained searches [134]. In particular,
my method of 'statistical feedback' [135]has provided a determinate strategy forreconciling long-term statistical distributions with short-term stylistic andidiomaticconstraints.The set of composing
programs I developed for the U.S.
pavilion at Expo '85 in Tsukuba, Japan[136], and the programs for my 1986 solo
violin piece, Concurrence[137], employ'linked' data structures, such as 'lists','trees' and 'networks', to represent th;complex interrelationships between elements both of the musical scoresthemselves and of the musical 'knowledge
base' consulted by the programs as they
fabricate these scores.
Many of the more recent developments
in automatedcomposition would probably
not have been possible without supporting
advances in computer technology. Backtracking has been known for decades, but
it simply was not practical without either
liberal grants of computer time or
dedicated systems that could be left
running for many hours (often overnight,
in my own experience). The newest homecomputers have changed all that. A
second important factor has been thedramatic rise in ceilings on both'random-access' and 'mass-storage'
memory, coupled with the introductionof 'virtual' operating systems which allow
a program to utilize more random-accessmemory than might physically be present
in the computer. Where the original
ILLIAC employed by Hiller and Isaacson
was limited to 1024 words of randomaccess memory for both composing
program and data, modern home computerscan accessmegabytesof information
rapidly. Only the barest fraction of thispotential has been exploited to date.

Interactive Utilities of the 1980s
The tradition of 'interactive' compositional utilities has been extended into
the 1980s with work undertaken by Curtis
Roads and David Levitt at theMassachusetts Institute of Technology.

181

o

(pt)0

8I~

1"

L

L

,

irb "
'MP
. .-

(PP)

3)

II

I1

P

-P-

t-i L

'"

p

_____o

P;

;

P
P P
PPi__

_ P

2-^L

P

i

,y

P

"~
,%

,r'T.

a

,

wp

:c-

P

8

D
79'o"

St
P X-

8
Fig. 17. James Tenney,Excerptfrom Bridge, 1984, for two pianos.The elapsedtime fromthe beginningof the performanceis indicated in minutes and seconds at the end of each system of staves. Notatedpitches are modified by the tuning system shown in Fig. 18. The rhythmic notation shows relative
attack-pointsby their horizontalplacementon the page. Unbeamed,solid noteheadsindicatestaccato;beamed notes last either up to the next stem or to the end of the beam; open noteheads employ pedal.
Copyright 1985 Sonic Art Editions, 2617 GwynndaleAvenue,Baltimore, MD 21207, U.S.A. Used bypermissionof the publisher.

182

Ames, Automated Composition

Roads's 1982 IOS [138] is a utility for"interactive orchestration based on scoreanalysis", in which parsing and patternmatching algorithms are employed toisolate musical "objects" for user modification. (Although Roads has cited IOS
as a musical application of Artificial
Intelligence, his descriptions of thisprogram indicate that IOS makes few
decisions on its own and that the program
makes no use whatsoever of recursive
searches.) David Levitt's 1986 KIT [139]is a graphic editor that enables users topatch together icons representing elementary operations on streams of notedata into real-time networks. Included
among the most elementary of Levitt's
operationsmightbe inputfroma keyboard,
button or slider (physical or virtual),
output to a synthesizer, generators suchas clocks or units analogous to thefeatures" of Koenig's"selection
PROJECT2 and modifiers such as adders
and delay lines for loops. Users may
define their own higher-order icons by
patching together simpler units.

VII. CONCLUSIONSFor most of the composers discussed inthis article, composition has not been avehicle of 'expression' or 'affect' in theusual senses of these words. Rather, thesecomposers expect listeners to judge theirmusical "artifacts", as Barbaud called
them, on the basis of more abstract
aesthetic qualities such as balance, clarity,
depth (in the hierarchic sense) and soforth. They have used computers tocreate these artifacts because they believethat such qualities are quantifiable-at
least within the scope of a particular
work-and they have concluded fromexperience that there are many compositional problems that computers are
better equipped than humans to solve.
Considered individually, many of theearlier efforts described in this article
have been quite simple. This simplicity
has been due partially to limits imposedby technology and partially to the spiritof the 1960s and 1970s, when economy ofmusical process was itself considered avirtue. Today, a one-pass, self-contained
composing program such as Ebcioglu's
Bach simulator [140] might involve as
many as 7,000 lines of highly concise
code. An alternative approach employed
by DeLio, Barlow [141] and myself [142]has been to divide the overall compositional process into multiple phases,
each undertaken by a separate program.
Taken collectively, the compositions
surveyed here present a rich diversity oftechniques for programming computers
to compose music. Practically all theA
20. J. Myhill,"ControlledIndeterminacy:First Step towards a Semi-Stochastic
Music Language",

Computer Music

Journal3, No. 3 (1979). ReprintedinFoundationsof ComputerMusic, C. Roads-16.77 (

) --/

-7
AFt

\C

\

\
-33.3f (i )-

\Gt

5/4
-3.0

5/3
1
-1.1

Piano\..2\

15/8-5.0o

\.
14/9-

V.+1.8\\c
7/6

and J. Strawn,eds. (Cambridge,MA:
M.I.T.Press,1985).Anupgradedformulafor'controlledindeterminacy'
appearsin
Hillerand Ames[2].
21. Hillerand Baker[3].
22. GyorgyLigeti,"PierreBoulez:Entscheidung und Automatikin der Structure

Bb

Eb

Ia", Die Reihe IV: JungeKomponisten,K.

21/20
7/5 +0.8-1.28 .

Stockhausen
andH. Eimert,eds.(Vienna:
Edition,1958)p.33.Translated
University
by Leo Black, under the title "Pierre
Boulez: Decision and Automatismin

\\

-0.2t

7/4
+2.1#

Structure Ia", Die Reihe IV: Young

Fig. 18. TuningsystemforJamesTenney'sBridge.
approaches employed today have precedents in the groundbreakingyears from
1956to 1976:constraineddecision making(Klein and Bolitho, Hiller and Isaacson),conditional or Markovrandomness(Hiller
and Isaacson, Hiller and Baker, Koenig's
INTERVAL feature), statistical procedures (Xenakis, Brimn,Koenig), evolutions (Tenney, Myhill, Koenig's
TENDENCY feature [143], DeLio),
structureshierarchic,(grammatic)transformations
motivic(Tenney),
Barbaud, Hiller and Baker, Ghent,
Spiegel), backtracking (Gill). Althougha number of the early computercomposed pieces might seem coarse incomparison to direct human efforts, themore recent introduction of recursion,
linked data structures and prioritized
decision making now enable composing
programs to be 'fine tuned' until theirresults equal or surpass what humans canachieve by hand.
With the musical industry becoming
increasingly 'high-tech', and with today's
teenageracquiringprogrammingexpertiseonce reserved for veterans of university
graduate programs, the notion of acomposer/programmer is no longer
anathema.Growingnumbersof composers
are coming to regard computers not only
as legitimate creative tools but aseffective tools at that. Although how
deeply the computer will penetrate intosuch traditionally 'human' domains is yet
to be gauged, it is clear already that
automated composition is an establishedreality of our time.
acknowledgement
Acknowledgements-Special
is due to LejarenHillerfor allowingme freeaccessto his extensivefiles on earlycomputercompositionand to the late John Myhillfor
critiquingthismanuscript.I wouldalsoliketo
thank the following people for documents,
scores and analytic insights:HerbertBriin,
WilliamBuxton,ThomasDeLio, EmmanuelGhent,GottfriedMichaelKoenig,OttoLaske,
LarryPolansky,CurtisRoads,LaurieSpiegel,JamesTenney,BarryTruaxandIannisXenakis.

REFERENCES AND NOTES
1. L. Hiller, "Programmingthe I Ching
Oracle", ComputerStudies in theHumanities and VerbalBehavior3, 130 (1970).

2. L. Hiller and C. Ames, "AutomatedComposition:An Installationat the 1985
InternationalExposition in Tsukuba,
Japan", Perspectives of New Music 23,

No. 2, 196(1985).
3. L. Hiller and R. Baker, "Computer
Cantata: A Study of Compositional
Method", Perspectives of New Music 3,

No. 1, 62 (1964).
4. L. Hiller and R. Kumra,"Composing
Algorithms II by Means of Change

Ringing",Interface8, No. 3, 129(1979).
5. L. Hillerand L. Isaacson,Experimental
Music(New York:McGraw-Hill,1959).
Reprinted1979,GreenwoodPress.
6. J. Myhill, "Some Simplificationsand
Improvementsin the StochasticMusic
Program", Proceedings of the 1978
InternationalComputerMusic Conference(ComputerMusicAssociation,1978).
7. I. Xenakis, Formalized Music: Thought
and Mathematicsin Composition(Indiana

UniversityPress,1971).
8. L. Hiller, "Music Composed with
Computers-AHistoricalSurvey",Chap.
4 in The Computer and Music, Harry

Lincoln, ed. (Ithaca, NY: Cornell
UniversityPress,1970).
9. Anon., "Syncopationby Automation",
Data from ElectroData,

Aug. 1956(Pasadena,CA: Electro-DataDivisionof Burroughs,Inc.).
10. It was aired over KABC-TV, Los
Angeles,CA.
11. Hillerand Isaacson[5].
12. Hillerand Baker[3].
MusicExperiences,
13. J. Tenney,"Computer
1961-1964", Electronic Music Reports 1,

No. 1, 23 (1969).
14. T. Blum,"HerbertBrun:ProjectSAWDUST" (review), ComputerMusicJournal

3, No. 1, 6 (1979).
15. H. Brin, "From Musical Ideas toComputersand Back",Chap. 2 in The
Computerand Music [8].
16. H. Brin, Uber Musik und zum Computer

G. Braun,1971).
(Karlsruhe:
17. H. Briin,"HerbertBrin Compositions",
bookletaccompanyingthe recordalbumof the samename,non-sequiturrecords
1-3, Champaign,IL, 1983.
18. Hillerand Ames[2].
19. Myhill[6].

Ames, Automated Composition

Composers(BrynMawr, PA: Theodore
Presser,1960)p. 36.
23. Hillerand Isaacson[5].
24. Hillerand Baker[3].
25. Fora discussionof Tenney'sactivitiesas
the first in what came to be a seriesof
composersin residenceat Bell Labs,seeTenney[13].
26. M. Mathews,withL. Rosler,"Graphical
Languagefor the Scores of Computer
Generated Sounds", Perspectives of New

Music6, No. 2, 92 (1968).
27. M. Mathews,withJ. Miller,F.R. Moore,
J.R.PierceandJ.C.Risset,TheTechnology
of Computer Music (Cambridge, MA:

M.I.T.Press,1969).
28. M.MathewsandF.R.Moore,"GROOVE:A Programto Compose,Store,and Edit
Functions of Time", Communicationsof
the Associationfor ComputingMachinery

13, No. 12,715 (1970).
29. See Myhill[6] and Xenakis[7].
30. These Gravesaner Blitter articles werelater collected into the 1971 book
FormalizedMusic; see Xenakis [7].

31. Brin [15].
32. Xenakis[7].
33. Briin[17].
34. J. Schillinger, The Schillinger System ofMusical Composition, 2 volumes (NewYork:CarlFischer,1941).
35. P. Barbaud, Initiation a la composition
musicale automatique (Paris: Dunod,1966).
36. P. Barbaud,"AlgorithmicMusic",froma tradepublication(Paris:SystemsBull,
1969).
37. See Myhill[6] and Xenakis[7].
38. G.M. Koenig, Performancenotes and"Analytical Appendix" to the Ubung
furKlavier(Utrecht:Instituteof Sonology,1969).
39. G.M. Koenig, "Project 1", Electronic
Music Reports 1, No. 2, 32 (1970).

40. G.M. Koenig, "PROJECT2:A Programme for Musical Composition",
Electronic Music Reports 1, No. 3 (1970).

41. G.M. Koenig, "Protocol",Sonological
Reports4 (Utrecht:Instituteof Sonology,1979).
42. 0. Laske, "Composition Theory in
Koenig'sProjectOneandProjectTwo",
Computer Music Journal 5, No. 4, 54(1981).
43. Xenakis[7].
44. See Myhill[6] and Xenakis[7].
45. Xenakis[7].
46. Myhill[6].
47. Koenig[39].
48. Koenig[40].
49. Koenig[38], "AnalyticalAppendix",p.
25.

183

50. Koenig [38].
51. 0. Laske, "Towards a Musical Intelligence System: OBSERVER", NumusWest No. 3, 11 (1973).
52. 0. Laske, "The Information-Processing
Approach to Musical Cognition", Interface 3, No. 2, 109 (1974).
53. 0. Laske, "Toward a Theory of MusicalCognition", Interface 4, No. 2, 147(1975).
54. 0. Laske, Music, Memory, and Mind:
Explorations in Cognitive Musicology(University Microfilms, 1977).
55. 0. Laske, "Subscore Manipulation as aTool for Compositional and Sonic
Design", Proceedings of the 1980 International Computer Music Conference(Computer Music Association, 1980).
56. 0. Laske, Music and Mind: An Artificial
Intelligence Perspective (Needham, MA:
self-publication, 1980).
57. Laske [42].
58. E. Ghent, "Real-Time Interactive Compositional Procedures", Proceedings of
the American Society of University
Composers9/10 (1975-1976).
59. E. Ghent, "Interactive Compositional
Algorithms", Proceedings of the 1977
InternationalComputerMusic Conference(Computer Music Association, 1977).
60. E. Ghent, "Further Studies in Compositional Algorithms", Proceedings ofthe 1978 International Computer Music
Conference(ComputerMusicAssociation,1978).
61. Mathews and Moore [28].
62. L. Spiegel, Liner notes to The Expanding
Universe(Philo Records, no. 9003, 1980).
63. L. Spiegel, Program Notes for Musicfor
Dance, New York PhilharmonicHorizons'84 concert, 3 June 1984.
64. L. Smith, "SCORE: A Musician's
Approach to Computer Music", Journalof the Audio Engineering Society 20, No.
1, 7 (1972: reprinted 1973 in NumusWest No. 4); SCORE Manual, Newversion (Computer printout, Stanford
University, Palo Alto, CA, 1974).
65. W. Buxton, Manualfor the POD Systems(Utrecht: Institute of Sonology, 1975).
66. B. Truax,"ComputerMusicComposition:
The Polyphonic POD System", IEEE
Computer(Aug. 1978).
67. B. Truax, "The Inverse Relation between
Generality and Strength in Computer
Music Programs", Interface 9, No. 2, 49(1979).
68. B. Truax,"The PODX System:Interactive
Compositional Software for the DMX1000", ComputerMusicJournal11, No. 1,
29 (1985).
69. Blum [14].
70. W. Buxton, DesignIssuesin theFoundationof a Computer-Based Tool for Music
Composition (Technical report CSRG97, Computer Systems Research Group,
University of Toronto, 1978).
71. W. Buxton, R. Sniderman, W. Reeves, S.
Patel and R. Baecker, "The Evolution of
the SSSP Score Editing Tools", Computer
Music Journal3, No. 4, 14 (1979).
72. W. Buxton, MusicSoftware User'sManual(Computer Systems Research Group,
University of Toronto, 1980).
73. Laske [55].
74. Mathews et al. [271.
75. Mathews and Moore [28]. GROOVE
represents yet another computer music
innovation from Bell Labs.
76. Ghent [58].

184

77. Ghent [59].
78. Ghent [60].
79. Spiegel [62].
80. L. Spiegel, "Sonic Set Theory: A Tonal
Music Theory for Computers", Proceedings of the Second Annual Symposium
on Small Computersand the Arts (1982).
81. Spiegel [63].
82. Ghent [58].
83. Ghent [60].
84. Spiegel [62].
85. Spiegel [63].
86. Laske [55].
87. Claudio Baffioni, Francesco Guerra andLaura Tedeschini Lalli, "The Theory of
Stochastic Processes and Dynamical
Systems as a Basis for Models of Musical
Structures", Musical Grammars andComputer Analysis, M. Baroni and L.
Callegari, eds. (Florence: Olschki, 1984).
88. C. Abbot,"Clarence
Barlow:(~6gluotobfisisletmesi" (review), Computer Music Journal 7, No. 4, 66 (1983).
89. C. Barlow, "Bus Journey to Parmetron",Feedback Papers, Nos. 21-23 (1980).
90. Stephen Kaske, "A Conversation withClarenceBarlow",ComputerMusicJournal
9, No. 1, 19 (1985).
91. T. Bolognesi, "Automatic Composition:
Experiments with Self-Similar Music",
Computer Music Journal 7, No. 1, 25(1983).
92. Charles Dodge, "Profile, A Musical
Fractal", Proceedings of the 1986 Symposium on the Arts and Technology atConnecticut College (Shoestring Press,
in press).
93. C. Fry, "Computer Improvisation",
Computer Music Journal 4, No. 3, 48(1980); "Flavors Band: A Language forSpecifying Musical Style", Computer
Music Journal 8, No. 4, 20 (1984).
94. P. Gena, MUSICOL Manual, Version 1(Technical report no. 7, Experimental
Music Studio, State University of New
York at Buffalo, 1973).
95. Baffioni et al. [87].
96. C. Hatzis, "Chronochroma", Interface
8, No. 2, 73 (1979); "Towards an
EndogenousAutomated Music",Interface
9, No. 2, 83 (1980).
97. S. Holtzman, "Musicas System",Interface
7, No. 4, 173 (1978).
98. S. Holtzman, "A Generative Grammar
Definitional Language for Music",
Interface 9, No. 1, 1 (1980).
99. K. Jones, "Compositional Applicationsof Stochastic Processes", ComputerMusic
Journal 5, No. 2, 45 (1981).
100. G. Kendall, "Composing from a Geometric Model: FiveLeafRose", Computer
Music Journal 5, No. 4, 66 (1981).
101. Baffioni et al. [87].
102. See Christopher Yavelow, "MIDI and
the Apple Macintosh", ComputerMusic
Journal 10, No. 3, 11 (1986), which
includes a brief description of Levitt's
KIT.
103. D. Lorrain, "A Panoply of Stochastic'Cannons' ", ComputerMusic Journal 4,
No. 1, 53 (1980).
104. Hiller and Ames [2].
105. C. Roads, prototype (University ofCalifornia at San Diego, 1975).
106. C. Roads, A Systems Approach toComposition (Honors thesis, Universityof California at San Diego, 1976).
107. C. Roads, Composing Grammars, 2nd
Ed. (Computer Music Association, 1978).
108. C. Roads, "Interactive Orchestration

Ames, Automated Composition

Based on Score Analysis", Proceedingsof the 1982 InternationalComputerMusic
Conference(ComputerMusicAssociation,1982).
109. D. Rothenberg, "A Nonprocedural
Language for Musical Composition",
Proceedings of the Second Annual Music
ComputationConference(1975).
110. W. Schottstaedt, "PLA: A Composer's
Idea of a Language", Computer Music
Journal 7, No. 1, 11 (1983).
111. S. Tipei, "MP1-A Computer Programfor Music Composition", Proceedings of
the SecondMusic ComputationConference(1975); "Solving Specific Compositional
Problems with MP ", Proceedingsof the1981 International Computer Music
Conference(ComputerMusicAssociation,1981); "Maiden Voyages-A Score Produced with MP1", Proceedings of the1985 International Computer Music
Conference(ComputerMusicAssociation,1985).
112. C. Ames, "Crystals:Recursive Structuresin Automated Composition", Computer
Music Journal 6, No. 3, 46 (1982).
113. C. Ames, "Protocol: Motivation, Design,
and Production of a Composition for
Solo Piano", Interface 11 , No. 4, 213(1982).
114. C. Ames, "Stylistic Automata in Gradient", ComputerMusic Journal7, No.4,
45 (1983).
115. C. Ames, "Notes on Undulant",Interface
12, No. 3, 505 (1983).
116. C. Ames, "Applications of Linked Data
Structuresto Automated Composition",
Proceedings of the 1985 International
ComputerMusic Conference (Computer
Music Association, 1985).
117. C. Ames, "Two Pieces for Amplified
Guitar", Interface 15, No. 1, 35 (1986).
118. C. Ames, "A.I. in Music", Encyclopediaof Artificial Intelligence, Stuart Shapiro,ed. (New York: John Wiley and Sons, inpress).
119. Hiller and Ames [2].
120. C. Ames, "Concurrence", Interface (inpress).
121. Roads [105].
122. Roads [106].
123. Roads [107].
124. Holtzman [98].
125. Jones [99].
126. Ames [112].
127. Dodge [92].
128. Ames [114].
129. S. Gill, "A Techniquefor the Compositionof Music in a Computer", The Computer
Journal6, No. 2, 129 (1963).
130. K. Ebcioglu, "Computer Counterpoint",
Proceedings of the 1980 International
Computer Music Conference (Computer
Music Association, 1980).
131. K. Ebcioglu, "An Expert System for
Schenkerian Synthesis of Chorales in the
Style of J.S. Bach", Proceedings of the1984 International Computer Music
Conference(ComputerMusicAssociation,1984).
132. M.T. Thomas, "VIVACE: A RuleBased A.I. System for Composition",
Proceedings of the 1985 International
ComputerMusic Conference (Computer
Music Association, 1985).
133. Ames [113].
134. Ames [114-118, 120]; Hiller and Ames
[2].
135. Ames [118, 120]; Hiller and Ames [2].
136. Ames [117]; Hiller and Ames [2].

137. Ames [120].
138. Roads [108].
139. Yavelow [102].
140. Ebcioglu [131].
141. Barlow [89].
142. Ames [113-117, 120].
143. Koenig [40].

GLOSSARY
algorithm-a computational procedure which,after a finite (but possibly very large) numberof steps, always returns either a correct
solution or the answer that such a solution
does not exist.
Artificial Intelligence-emulation by computerof human problem-solving activities. An
outgrowth of automatic chess-playing procedures proposed by Shannon in 1950 and oftheorem-proving programs developed shortly
thereafter by Simon, Newell and Shaw inresponse to Shannon's proposals.
automated composition-any use of computer
programs that undertake decisions affecting
the content of a musical composition.
Cantor Set-invented in the course of Cantor'smathematical investigations of infinity, aCantor Set may be derived from an unbroken
segment of the real-number line as follows:
divide the segment into three equal portions,exclude the middle portion, and apply thesame procedure of division and exclusion
recursively to each remaining portion. One
might surmise intuitively that such a set would
dwindle away to nothing; however, Cantor
proved intuition wrong: his set in fact contains
a unique counterpart for every number on theinfinite real-number line. Cf. R. Courant andH. Robbins, What Is Mathematics? 4th Ed.
(New York: Oxford University Press, 1947)pp.
248-249.
formal grammar-refers to the theory of"linguistic competence" developed during the1950sby Chomsky. Chomsky divides grammars
into two main classes: "phrase-structure
grammars", which are sets of top-down rules
determining how the whole of a statement
relates to its parts (its phrases, clauses, etc.),
and "transformational grammars", which aresets of procedures for modifying phrase
structures in order to produce well-definedchanges in 'meaning' (e.g. mild transformations from active voice to passive, from first
person to third, from present tense to past, ormore radicaltransformations such as negation,
logical inference, and so on). Because suchrules and procedures are typically independentof the specific content of a statement, Chomsky

was able to represent them as algebraic
the qualification,
manipulations-hence"formal".
frame-a 'frozen' moment of time; the analogy
is drawn from cinematography. An important
instance within the context of this article is thestatistical frame, which denotes a segment ofmusic over which a 'momentary' statistical
distributionis realizedby a composing program.
Gestalt psychology-the study of the perceptual
factors affecting how elements of the environment are combined mentally into larger forms('gestalts'). An outgrowth of commonsense
observations made in Wertheimer's 1921
article "Laws of Organization in PerceptualForms", and a precursor to the modern
discipllineof cognitive psychology.
heurism (or heuristic)-a computational procedure which "proceeds along empirical lines,
using rules of thumb, to find solutions or
answers" (from Webster's Dictionary).
Heurisms are less precise than algorithms,but
they sometimes have the advantage of being
usable under less-than-optimal conditions:where an algorithm must always either returna
correct solution or fail, a heurism can return asolution which is mostly correct, but whichmight deviate occasionally from a few lessthan-critical specifications.
hierarchy-a structure in which the interrelationships resemble the chain of authority
among priests in an organized religion (hieros
means 'sacred'); each entity in a hierarchy may
have any number of 'inferiors' but only one
direct 'superior'. Hierarchiesare often referred
to by computer scientists as tree structures.
left-to-right-refers to a strategy of handlingtasks as they arise, as contrasted with topdown and other strategies that might defer lessurgent tasks.
list-a structure in which each element has at
most one 'predecessor' and one 'successor'.
Markov chain-a 'left-to-right' chain of eventsin which the outcome of each individual event
is conditioned by the outcome of its immediate
predecessor.
network-a structure in which each element
can have any number of direct relationships toany number of other elements. Networks arealso known among computer scientists asdirectedgrap/s. A good example of a networkis the structuredeveloped by Roget for his 1852
Thesaurus.
paradigm-a pattern, example or model,
typically of a 'classic', 'shining' or particularly

Ames, Automated Composition

insightful character. For instance, a paradigm
in a discussion involving several basic premises
would be an example that reveals the interplay
between most or all of these premises.
Peano Curve-derived by infinite recursion,
the Peano Curve is a geometric abstraction
which defies many of our most basic intuitions
concerning how a 'curve' should behave. It has
the following properties: every point in the
curve resides at the corner of a right angle, andthe 'loops' of the curve are infinitely dense in
any region (no matter how small) where thecurve is defined. Yet the Peano Curve nevercrosses itself! Cf. E. Kramer, The Nature and
Growth of Modern Mathematics (Princeton,
NJ: Princeton University Press, 1982) pp. 528529.
prioritization-a procedure that ranks a set ofobjects or tasks in order of preference orurgency.
random-refers to a process the outcomes ofwhich are unpredictable or patternless over the
short term.
recursion-the ability of a process to act uponits own results. Recursive techniques make itpossible to implement computational processes
that are able, in effect, to propagate 'copies' ofthemselves. Such processes can spawn multiple
sub-processes; these in turn can spawn subsub-processes, and so on to arbitrary levels ofcomplexity.
statistical distribution-the relative amounts
by which differing types occur within apopulation of elements.
withstochastic-literally
synonymous'random'; however, discussions of 'stochastic'
processes (as in Xenakis's 1971 book [7])typically reflect a concern for the large-scale
distributions of outcomes.
top-down-refers to a process that deals firstwith generalitiesand which utilizes the 'insights'
gained thereby to cope with more specifictasks.
withreplacement/withoutreplacement-a favorite paradigm among probability theorists isthat of blindly drawing colored balls from anurn, where the probabilities are determined by
the proportions of balls of particular colors to
the total number of balls. Such selection is said
to occur with replacementif balls are returned
directly to the urn after each draw and without
replacementif newly drawn balls are set aside.
Obviously, the distributionof colors is reflectedmuch more accurately over the short term by
the latter method.

185