Leonardo

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: 20/09/2011 00:20

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Automated Composition in Retrospect: 1956-1986

Charles Ames

Abstract-This article chronicles computer programs for automated musical composition over the last 30 years, providing musical examples from 11 computer-composed works. The author begins by focusing on early American efforts to impose stylistic controls through random sampling and testing, then describes European statistical approaches used until 1970. The rise of 'interactive'compositional utilities duringthe 1970s is linked to the growing proliferation of on-line computers. The current decade has been a period of eclectic interests: the resurgence of statistical procedures, the introduction of 'top-down' recursive grammars,the adaptationof problem-solvingtechniques from Artificial Intelligence and the continuationof interactive efforts.

1. INTRODUCTION This article chronicles efforts to harness oI the computer as a tool for compositional POS4 I II I Be'RFfR)' decision making, beginning in the mid- 8oi)od4 IIIIIII I IIIIII 1950s and working up to the present L-/RIc 1V MuSiC 8/ decade. Although precedents for auto- S'AcK-Ou)COS D:r,4Areotl mated composition exist throughout s.s.e.st 2 1,2.,2,?2. L z Z (A'I4E MAr,c,^JS musical history, never have such efforts ' TOoo8o Z9 7 ).tAl RS-rtj CLEIt posed as great a challenge to what for 144ntn-M tJd ^&SeXS ^ oa DR. DOGLQ5 BOLvr4o many have been fundamental assumptions to^ ?ar B&6IrL c about the nature of creativity and the I 1 IF T)#". f rM^- I a... i 'i 7 ^ aesthetic purposes of composition. It is ^^5(^SAt U1- d _ j.1w I 11J- J I;^ . . Jl therefore not surprising that these deve- i I _4gDM AJ)EE ' 1 j lopments have met with continuing-and I ^ . t j 1 I ^- t r 6,,. ct ^k gF 4y f Dm? S- 6r^-4- e4< often virulent-resistance. Too often, ~~~~~~~ C' tIi M- 1 ia G40r7~ ; I I , , a? however, the limitations of one or two Ho-a1t ijzI }a jaI 4*2 " I I t I- individual approaches have been extra- CAL-CO - LAr- AJ, OAL- P-TA-riTJ' c4fcK - vJ/ird A polated into conclusions that computers r-?9 r'K2m . :b -^ n i .-. ---I are inherently unsuited to compositional r- i ^ 7- i sJI ) I ;X ^ problem solving. Even more unfortunate K S 1i- 1~-; .:tnI 1js^ has been the tendency among many CLICK M- P%4?-IL. )T---rTo1JB -iA - Jar roo LA6E-LAW4rAcHALGE critics to base on ad hoc judgments & A (m7 c7 aesthetic criteria that are irrelevant to A-sy 1 j Al? n4 - L. 1i A " J I -rI r T ? what practitioners of automated com- 'S - '1- E - LC - 'ToJ- IC. eJ-? -COJ-IC ' ReNAD_ - t - position have actually been trying to 46t? C7Rv A ^ achieve. r r I informed I L A major obstacle to any t ? I11 J ;1 If- p ' I^ understandingof automated composition EJD ..O. J.Cc- &4a6?? o - 7AJi'.- WATC__k^r RO < AJDR-LC_- has been the lack of accessible knowledge z-r4 t Jof DED- M9AJD -AJ6AJ/&_ -E ULAOrJVIN2if JGS- (A 4 I 17f c- " concerning how these composers have - ,i --I 3.-,.1 - . gone about realizing their inspirations as I j i r -I J P. l^n-1 a rT I I1 pieces of music. For most readers, only oL AD CAL -CO - LA-LA - r_ -rf4ts&GAL JA6 Jo EARr oR 8ouL'sEos AL- uJ.i/S 0) - D-'D -,fA l D- /,a_Jsr uf A ireH AD 'c So - the well-publicized achievements of C? .F' n' ,4 .--I r t. __., ,I I Lejaren Hiller [1-5] and [6, 7] come to mind; in fact, there have been a number of other composers whose b.54_-6&r-r'b e--rdfA_ o- - -roO- i-T/7oJ DI-, J/hJE k4e6 .

Manuscript solicited by Anthony Hill. Received 17 January 1986. Fig. 1. Martin Klein and Douglas Bolitho, "Push Button Bertha", 1956. Public domain.

? 1987 ISAST Pergamon Journals Ltd. Printed in Great Britain. LEONARDO, Vol. 20, No. 2, pp. 169-185, 1987 0024-094X/87 $3.00+0.00 progress in correcting this deficiency Ilisac Suite Experiments Summarized through his 1970 comprehensive survey ExperimentOne: Monody, two-part, and four-part writing of early efforts [8], he was able to provide A limited selection of no musical examples and only the barest first-speciescounterpoint rules used for controlling the musical details about how individual pieces were output (a) Monody: cantus firmi 3 to 12 notes in length made. The present article seeks not only (b) cantus firmus settings 3 to 12 notes in length to the of automated Two-part bring history (c) Four-part cantus firmus settings 3 to 12 notes in length composition up to date, but also to clarify (1) what has motivated composers over Experiment Two: Four-part first-species counterpoint the last 30 years to delegate their creative Counterpointrules were added successively to random white-note music as follows: decisions to a machine, and (2) how these (a) Random white-note music composers have gone about programming (b) Skip-stepwise rule; no more than one successive repeat the machine to give them what they (c) Opening C chord; cantus firmtis begins and ends on C; cadence on C: B-F wanted. tritone only in VII; chord; tritone resolves to C-E (d) Octave-range rule (e) Consonant harmonies only except for 6 chords (f) Dissonant melodic intervals (seconds, sevenths, tritones) forbidden II. "PUSH BUTTON BERTHA": 1956 (g) No parallel unisons, octaves, fifths 6 One of the earliest instances of auto- (h) No parallel fourths, no chords, no repeat of climax in highest voice mated composition was a program for composing 'Tin Pan Alley' melodies, ExperimentThree: Experimental music which was created by Martin Klein and Rhythm, dynamics, playing instructions, and simple chromatic writing Douglas Bolitho of Burroughs, Inc. using (a) Basic rhythm, dynamics, and playing-instructionscode a computer called DATATRON. An (b) Random chromatic music anonymously written Burroughs publi- (c) Random chromatic music combined with modified rhythm, dynamics, and cation outlines the operation of the I playing-instructionscode program as follows: (d) Chromatic music controlled by an octave-range rule, a tritone-resolutionrule, and a skip-stepwiserule (e) Controlled chromatic music combined with modified and The operatorinspires DATATRON by rhythm, dynamics, first keying in a 10-digit random playing-instructionscode number.This causes the machineto (/) Interval rows, tone rows, and restricted tone rows generate and store 1000 single digits, each representingone of the eight Experiment Four: Markoff chain music diatonic notes in the scale with two (a) Variation of zeroth-order harmonic function from tonal allowable accidentals. The probability complete program restriction to distribution then motivatesDATATRON to pick "average" successive notes at random, testing (b) Variation of zeroth-order harmonic probability function from random to eachfor melodicacceptability as it goes "average" distribution along [9]. (c) Zeroth-orderharmonic and proximity probability functions and functions com- bined additively One result of this process was the melody (d) First-order harmonic and proximity probability functions and functions com- "Push Button Bertha" (see Fig. 1), which bined additively was first aired on July 15, 1956 [10]. (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, re- spectively, and vice-versa (g) ith-order harmonic function on strong beats, first-orderproximity function on III. THE URBANA SCHOOL: weak beats; extended cadence; simple closed form 1957 TO 1966 Klein and Bolitho's method of random Fig. 2. Illlac SuiteExperiments Summarized. Reproduced from Hiller and Isaacson [5]. Copyright sampling and testing provided what 1959McGraw-Hill Book Company. Used by permissionof the publisher. seemed at the time a viable emulation by computer of traditional compositional Hiller, Isaacson and Baker experiments were collected into an Illiac decision In the same 2 making. fact, During the same years in which Klein Suite for string quartet. Figure details method had been which developed independently and Bolitho were programming DATA- Hiller and Isaacson's procedures, Hiller and Leonard Isaacson by Lejaren TRON, Hiller and Isaacson were under- utilized two basic approaches: at the of University Illinois, taking a series of compositional "experi- 1. Random selection constrained The Urbana/Champaign. publicity gen- ments"* using the ILLIAC computer, by lists of rules, an approach erated Hiller and Isaacson's Illiac that of Klein and by which had been designed and built at resembling Suite the establish- [11], supplemented by Urbana. Many of their results were Bolitho (Experiments 1-3). ment under Hiller of one of the nation's presented in a well-publicized concert 2. Markov chains, also random, earliest attracted likelihood studios, which, coincidentally,also occurredduring in which the relative a number of individuals interested in July 1956. Subsequently, these and later of each option was conditioned merging the new music with the new by one or more immediately technology. Along with Hiller and preceding choices (Experiment Isaacson, these people included Robert *Enclosure of terms in double quotes indicates coined 4). Baker [12], James Tenney [13], Herbert or otherwise idosyncratic terminology drawn from An excerpt from the appears specific sources. Brun [14-17] and John Myhill [18-20]. in Fig. 3.

170 Ames, Automated Composition James Tenney :,,.. fd.. Pp cresc. map James Tenney had been drawn to Urbana as a graduate student by Hiller's groundbreakingcourse in electronicmusic. r0t t i9Jh j^ c cottp*_ . j-f While at Urbana, Tenney pursued studies 9'6ZIJ 8 8 #D D D+ D S p S D 7 p S g t p S 2 t }p-J6F 8 Z Z r e D e r in computer composition. In 1961 he was invited to Bell Telephone Laboratories [25] where Mathews [26-28] was in the process of developing his now well- known digital sound-synthesis programs. Though unaware of the " music program" that lannis Xenakis was developing roughly at the same time [29], Tenney had been inspired by Xenakis's statistical scores such as Pithoprakta and Achorripsis, which had been described in articles by Xenakis [30]. Tenney's programs differ substantially from Xenakis's in Tenney's use of (1) segmented line graphs controlling how compositional parameters evolve over time, and (2) hierarchic procedures devised in response to the Gestalt psychology of Max Wertheimer. Most of Tenney's composing programs generated files of numeric data which were then realized digitally by Mathews's MUSIC4 program. However, one excep- tion admits direct visual examination of the score: Tenney's 1963 Stochastic String Quartet. This piece divides into three sections, which at the indicated tempi last 50, 100 and 40 seconds. Sections divide into intermediate structural units, which Tenney calls "clangs", and these in turn divide into notes. The profile of each section is controlled by graphs of musical * WHOLE-TONESHAKE attributes,such as clang durations,average 3. Measures Fig.3. LejarenHiller and Leonard Isaacson, Illiac Suite, 1957, excerpt from Experiment periods between attacks, ranges of pitches, and code"; measures 73-80 show "random 55-72 show "basic rhythm,dynamics, playing-instructions dynamics and several aspects of timbre: chromatic music"; measures 81-100 show "randomchromatic music combinedwith modifiedrhythm, (sul tasto, dynamics, and playing-instructionscode". Copyright 1957 New Music Edition. Used by permissionof vibrato, tremolo, "spectrum" the publisher,Theodore Presser Company, Bryn Mawr, PA 19010, U.S.A. ord., sul pont.) and "envelope" (pizz., arco-staccato, arco-legato, arco-marcato, arco-sforzando). Each graph supplies a A second early collaborator of Hiller's into creative activity that interaction with mean value to one or more random was Robert Baker, who conceived the a computer can provide. For example, generators in order to select attributes for composing utility called MUSICOMP Hiller and Isaacson [23] describe the a specific clang; in turn, the program (MUsic Simulator Interpreter for COM- Illiac Suite as a study of "those aspects of feeds these clang attributes into further positional Procedures). MUSICOMP the process of composition..." which random generators in order to select " greatlyfacilitated the processof developing can be modeled ... by applying certain attributes for a note. The opening of the new composing programs by managing mathematical operations deriving from Stochastic String Quartet appears in Fig. libraries of compositional subroutines probability theory and certain general 4. and other programming modules which principles of analysis incorporated in a An especially significant feature of the individual composers could link together [then] new theory of communication quartet is Tenney's elaborate procedure in a main program designed to meet their called information theory". Hiller and for notating rhythm. Not content to own idiosyncratic purposes. Hiller and Baker's article "Computer Cantata: A approximatehis rhythmsas displacements Baker first utilized MUSICOMP to create Study in Compositional Method" expres- relative to a simple meter such as 4/4, their 1962 ComputerCantata [21], which ses a similar attitude: Tenney exploits bracketed rhythmic drawn "almost as a compositional employed serial methods was to proportions directly Since our primary purpose works in toto" from Pierre Boulez's Structures demonstratethe flexibility and generality resource. His notational procedure for two pianos [22] in addition to the of MUSICOMP,the ComputerCantata as follows. At the broadest level, the methods employed to create the Illiac presents a rather wide variety of program selects the length of each clang Suite. compositional procedures, some of in quarter notes. Within a clang, it then which of estheticvalue and his a proved greater selects an "gruppetto" unit Among Hiller colleagues, than others,and manyof whichcould independent strong motivation for automating the be improved[!] by moresophisticated for each instrumental part. Measure 13, compositional process has been the insight logic [24]. for example, constitutes one clang lasting

Ames, Automated Composition 171 STOCHASTIC STRING QUARTET James Tenney technical notes on Sonoriferous Loops J =60 compiled by Briin, his program advances 9qOf .s Ii I i I --- Vn I - -- ^x e_ .__~-_- -4- x from moment to moment in the score, in effect 3$ - ,___3._, 'scanning' each instrumental (or Vn II synthetic) part to determine whether or not the part is engaged by a note or rest. If Va 37"jj'> not, then the program initiates the sfz=3 _pj , :--==- following steps: -:' - -1. The Vc Y - - 1- , . 1.,mI r- I m- !-i V- Rhythm. program randomly "?.- t"I . .- v-i PAW I t? J i I I I 'j- _ -_p~ J.X; selects "denominators" and 4 "numerators" from 16, 6, 5 and 4; these are applied to a common Vn multiple of 240 to produce a duration. 2. Vn Rest/Play Choice. The program z- s -^ next decides whether to rest or to play a note. The relative activity of each part within a 3-, - - section of music is controlled by ~ J>_ "rest/play probabilities"; in the opening measures, for example, flute rests 26% of the time, double bass Vn I trumpet 32%, 50%, V 7r 4 mallets 68% and unpitched percussion 74%. Vn II IT _- 3. Pitch. Should the program elect to play a note in Step 2, it will Va next select a chromatic degree and a register. The mechanism Vc r^- X for selecting degrees consults a 12-element array which the program randomly shuffles at the beginning of each 12-note Vn cycle. Because this mechanism 4 supplies degrees for all parts Vn simultaneously, the composite texture obeys a uniform distri- bution of degrees. Registers are _,-- selected at random. , Once rhythms and pitches had been - 1J determined his Bruin v=== P tJj?1 by program, manually (fj d/m. -PP intervened to supply tempi, dynamics and "instrumental modes (pizz., mute, stacc., Fig. 4. JamesTenney, Stochastic String Quartet, 1963, measures 1-15. Copyright198 t5 Sonic Art t Editions,2617 Gwynndale Avenue, Baltimore, MD 21207, U.S.A. Used by permission of tbhe publisher. etc.) An excerpt from another computer- composed work of Briiun'sfor ensemble two quarters; the gruppetto units are 5 ... whereasthe human mind, co nscious and tape, Non-Sequitur VI, appears as (violin 1), 2 (violin 2), 3 (viola) and 2 of its conceivedpurpose, appi roaches Fig. 6. Briun'scomments regarding this ('cello). Each gruppetto unit in turn evenan artificialsystem with a selective work evoke Xenakis's investigation in divides randomly into smaller divisions. attitudeand so becomesaware the of Achorripsis[32] of the minimal conditions This fluid metrical preconceivedimplications othe continually structure system,the computerswould sh iow the necessary to create a composition. then provides a notational framework for totalof theavailable content. Re vealing However, Briin imposes the additional the 'floating-point' durations generated farmore than only the tendencie s of the requirement of 'musicality' through the human this nonselective by Tenney's random generators. mind, picture mechanism of random sampling and of themind-created system shou significantimportance [31]. testing: Herbert Briun Briiun'sSonoriferous Loops aldopts the Theprogramming of [Non-SequiturVI] A member of the Urbana composition model of Varese's Deserts by a]Iternating mainly reflectsthe continuoussearch faculty from 1963 to the present, Herbert four digitally synthesized interludes with foranswers to thefollowing: (1) Whatis Brtin the minimal number and power of employed MUSICOMP to create a five short movements for live eemsemble. restrictiverules that will select from number of works including his 1964 The live ensemble employs the five randomgenerated sequences of elements SonoriferousLoopsand 1966Non-Sequitur instrumental parts shown in Fig. 5- that particular variety of element- VI. Like Hiller, Isaacson and Baker, Brun flute, trumpet, double bass, malllets (xylo- concatenationssatisfying the conditions valued composing programs as truly phone and marimba) and I mnpimtched for either recognizableor stipulated 'musical'forms and events? (2) Coulda empirical means for testing formulations percussion-while the interlude-s employ combinationof stochasticchoice rules of compositional procedures: three synthetic voices. Accordiing to the with heuristic, multivalent,decision

172 Ames, Automated Composition SONORIFEROUS LOOPS crosses the corresponding scale Herbert Brun degree. Note durations therefore Opus 32 - 1964 J = 144 depend on the steepness of the 0 contour 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 automated compositional procedures was Pierre Barbaud, who presented computer-com- posed pieces in Paris as early as 1960. Many of Barbaud's procedures are documented in a monograph entitled Initiation a la composition musicale auto- matique [35]; they include permutational I methods applied to traditional harmonies, serial (12-tone) methods and methods of I! random selection. In his article "Algo- 2 rithmic Music" he sets forth the aesthetic philosophy that musical composition "consists in creating what scholastics called an artifactum, that is to say something that nature does not produce". Barbaud confronts objections that auto- mation removes the 'humanity' from composition by turning the complaint against itself:

Musicis generallycalled 'human' when it considers temporary or inherent tendenciesof the mind,of partor all of a composer'spersonality. Such music is based on feeling and since it turnsits back,in a sense,on pureknowledge, it mightrather be called'inhuman', for it celebrateswhat we have in common with all the animalsrather than with what 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 product of rationalbeings [36].

Fig.5. HerbertBriin, Sonoriferous Loops, 1964, measures 0-9. Copyright1964 Herbert Briin. Used by Compositionally, where the Urbana permission of the composer. school tended to focus on local relation- ships implemented in the form of stylistic contribute an taking procedures ap- As with Brun's Sonoriferous Loops rules, the Europeans emphasized global parent 'musical' coherence to a chain of scans all changes of state in a structured system? program, Myhill's program qualities of musical passages, as quantified [33] three voices from moment to moment; by statistical distributions. Technically, it however, in this case the program deter- was Europeans such as lannis Xenakis mines whether or not each part is ready to [37] and [38- John Myhill begin a new contour. If ready, the 42] who were the first to conceive of a Although John Myhill came to Urbana program selects a shape from those given composing program as a utility capable of in 1964 as a professor of philosophy and in Fig. 7, an overall duration for the new generating many pieces, rather than a mathematics, he had in fact previously contour and one of the following three one-shot effort geared toward a specific undertaken formal musical studies with modes of performance: compositional goal. Xenakis extolls what Michael Tippet. An avid supporter of 1. Siren-like glissandi. he considers to be the virtues of such activities then in progress at Urbana, 2. Discrete pitches taken from a generalized utilities in the following Myhill in 1965 contributed a Scherzo a scale relative to a rhythmic poetic terms: Tre Voce for computer-synthesized tape pattern: the scale degree in alone. The Scherzo, directly inspired by closest proximity to the contour With the aid of electronic computers graphic methods advocated by Joseph at the onset of a note determines the composer becomes a sort of pilot: derives melodic contours the pitch(Schillinger's approach). he presses the buttons, introduces Schillinger [34], and the controls 3. Discrete taken coordinates, supervises for each of its three voices-hence the pitches again of a cosmic vessel sailing in the space of title-from the eight evolving sinusoids from a scale. Here, each new sound, across sonic constellations and depicted in Fig. 7. note begins when the contour galaxies that he could formerly glimpse

Ames, Automated Composition 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) A A Ti- / l a 4) VV\J\j 0 C]

o ItA ;T.im V v JLVV

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 Following the model of Achorripsis,the violin, 'cello, contrabass and piano, and explore them at his ease, seated in an stochastic music program employs statis- for these instruments, Xenakis esta- armchair [43]. tical procedures to deduce a musical work blished respective maximum densities- with "the greatest possible asymmetry ... at 4, 4, 3 and 15 notes per second. These lannis Xenakis and the minimumof constraints,causalities, values result in a combined maximum Perhaps the best-known composer to and rules". Xenakis designed his program density of 26 notes per second, but employ computers has been lannis to create works for varied ensembles Xenakis nudged this value upward slightly Xenakis. It was Xenakis who had first according to varied input data supplied to 28. He also specified a combined introduced statistical methods of com- by the composer. Among the more minimum density of 0.07 notes per posing for live ensembles: Pithoprakta familiar pieces produced by Xenakis second-approximately one note every (1956) exploits Gaussian distribution to using this program are ST/10-1,080262 13 seconds. The stochastic music program realize the "temperatures" of massed for 10 instruments, ST/48-1,240162 for converts these "objective" limits to glissandi, while Achorripsis (1957) uses orchestra (48 instruments) and Morsima- produce a range of "subjective" (logari- Poisson's distribution of rare events to Amorsima ( ST/4-1,030762) for 4 instru- thmic) densities from 0 to 6. For each of organize "clouds" of sound. The aggregate ments. the integral points along this range of effect of these statistical scores concerned One can gain a sense of how Xenakis subjective densities (0, 1, ..., 6), the Xenakis much more than specific relation- worked with his program by examining program accepts a list of probabilistic ships between musical elements; in his the input data -used to create one such weights by which notes will be drawn 1962 "stochastic music program" [44], he work, Morsima-Amorsima. This work from each of the various timbre classes began delegating specific decisions to the lasts 17 minutes, 12 seconds at the available from the ensemble. For random-number generatorof a computer. indicated tempo. Its ensemble consists of Morsima-Amorsima,Xenakis has defined

(Density=5.3)

,.-. , JWtl Density =0.4

Z_ -

cil ~~ ~ ~ ~ -- -

-~~~0~~~~-0o 0 .tto

Fig. 8. Chart of orchestrationversus subjective density for lannis Xenakis's Fig. 9. lannis Xenakis, Morsima-Amorsima, 1962, measures 136-146. Morsima-Amorsima.The indicated timbre classes are: (1) piano,(2) arco Each 'JW' marksignifies the first complete measure of a section; densities ponticello, (3) harmonics,(4) arco normale, (5) glissando, (6) tremolo arco calculated by the program are presented in their 'objective' forms. The ponticello, (7) pizzicato and (8) frappe col legno. After a diagramprovided abbreviationsin the string parts are: asp-arco sul ponticello; an -arco by the composer. position normale, and fc--frappe col legno. Copyright 1967 Boosey and Hawkes Music PublishersLimited, 295 Regent Street, LondonW1R 8JH, United Kingdom.Reprinted by permissionof the publisher.

Ames, Automated Composition 175 eight such classes.The relativedistributions in which the stochastic music program AKKORDE employs these timbre classes are graphed / . along the range of subjective densities in ? Fig. 8; an excerpt from Morsima- f Amorsima appears in Fig. 9. Once provided with its basic input data-length of the composition, average length of a section, range of densities and constitution of the ensemble-the sto- 9 7 - b chastic music program is ready to go. The Ut/ program is structured in two loops: an H- ; j , __. outerloop determinesthe duration, density ~'' 9 r jt 2ti J 7 and distribution of timbre classes (the last ^^ ^ by locating the subjective density along ^ 7^ "/ the horizontal scale in Fig. 8, then 9 97- determining weights for each timbre class along the vertical) for each section of the ^O ^ T work, and an inner loop composes the actual notes. Details of these mechanisms if^ may be found in Xenakis's own description . of the program [45] and John Myhill's less mathematically demanding critique [46].

Gottfried Michael Koenig A less well-known but equally signi- ficant contributor has been Gottfried Michael Koenig, who has been associated for many years with the Institute of Sonology in Utrecht both as a teacher and as an administrator. Koenig's work in ~~ 'm 'm I..~ automated composition began in 1964 'PP with a composing program entitled PROJECTI, and this program has been responsible for several of Koenig's compositions including his 1965 Project 1, Version 1 for 14 instruments. Although Koenig's background is serial (he had

worked on as a assistant 6 early composer, ;- and teacher in the Cologne electronic T\ P,^,q tD b music studio), it had become apparent to Koenig by the time he undertook PROJECT1 that "the trouble taken by the composer with series and their TOENE permutations has been in vain; in the end I y19 _ i it is the statistical distribution that Xi-r: I i --r rI r 1l" PP / _--_ p determines the composition" [47]. mp-======ff A more elaborate program from 1969 called PROJECT2 [48] incorporates a I broad palette of statistical procedures 19: rFL f ff P which users can patch together in different mp combinations. Although Koenig deve- loped PROJECT2for pedagogicfunctions, lyI ? 1 - A i11 he has used it himself in one instance to r P f __ create an ambitious Ubung fur Klavier ("Study for Piano", 1970). The score to --5 - - 3 - this work consists of 12 "structures"; - - rip ~~~~, v_;7 " -7 o:' ; r- I I Fig. 10. GottfriedMichael Koenig Ubung fur /il.-;-JI"f,, Klavier,1970, Structure8, Variant1. The 'chords' , (Akkorde) and the 'tones' (Toene) result from - 7~~~~ . 7, independent sets of directives to Koenig's ig I7 1 r. r ; 1 PROJECT2program. Copyright 1969 Gottfried I PP Michael Koenig. Used by permission of the mf composer.

176 Ames, Automated Composition each structureappears in three "variants", register, (3) entry delay, or period between dent of one another; e.g. pitches do not for which the only change in directives to consecutive attacks, (4) duration and (5) directly affect rhythms. However, in a few PROJECT2 is the duration. Koenig dynamic. The harmony parameter is situations such as the restriction upon acknowledges the indeterminate aspects chosen by one of three principles (imple- durations in Structure 8's "groups of of his compositional process by allowing mented as program subroutines) called chords", the user is able to engage a the performerto choose between variants; ROW, CHORD and INTERVAL. For "block", causing PROJECT2 to toss out the fact that such indeterminacy is closely each parameter other than harmony, the unacceptable choices and select new circumscribed is reflected in Koenig's user either must specify a constant value options. instructions that at least one variant of or must provide a supply of options and Like GROUP, Koenig's 'harmonic' each structuremust be played, and that all specify one of six selection features (also principles, CHORD and INTERVAL, 12 structures must be presented in a implemented as subroutines): may be regardedas 'higher-order'selection prescribed order. SEQUENCE, ALEA, SERIES, RATIO, features. Each call to CHORD first An examination of Structure 8 of the GROUP or TENDENCY. Table 1 presents requests a module such as ALEA or Ubung fur Klavier illustrates the a breakdown of the principles, selection SERIES to choose an entry from a table workings of PROJECT2. Variant 1, features and supplies used to compose of chords provided by the user. Koenig's which is the shortest, contains two sets of Structure 8 [50]. table for the "groups of chords" in material: eight 'groups of chords' and Of the selection features employed for Structure 8 is shown here as Fig. 11; in five 'groups of tones' (Fig. 10). Structure 8, ALEA and SERIES are the this instance, the job of selection falls to Koenig provides the following synopsis most fundamental. ALEA samples ele- ALEA. Once it has obtained a chord, of Structure 8 in his instructions to the ments at random with replacement from CHORD again invokes either ALEA or performer, which allow elements of the supply, with uniform likelihood of SERIES to determine a (register-free) performer discretion much like those selection. SERIES also samples elements transposition; ALEA also received this controlling the performance as a whole: at random, but without replacement; i.e. second job in Structure 8. each time SERIES selects an element, it The INTERVAL principle employed A transition:chords and tones alternate. eliminates this element from consideration for the 'groups of tones' implements a Thereare also severalgroups of both until the entire supply has been exhausted : In order to select a current chordsand tones in everyvariant. Not (at this point, the full supply once again interval, INTERVAL begins by consulting all the groups of chords or tones have to becomes The for a such as be played,but those selected must be in available). procedure user-provided logical matrix, the given order.Groups of tones must SERIES is reminiscent of the random the one for Structure 8 shown in Fig. 12. alwaysbe separatedby chords,groups shuffling undertaken by Brin's Sonori- This matrix informs INTERVAL which of chords can join on to one another ferous Loops program. Compared to of the 11 intervals from the minor second over of (withoutjumping groups chords). ALEA, SERIES requires many fewer to the major seventh are acceptable, given A second group of chords then joins on rhythmically where indicated by the calls before its actual choices come to the most recent interval employed by the arrow. Such arrows, when present, reflect the distribution of options inherent program. INTERVAL then requests have no significance if groups of chords in the supply. GROUP is a higher-order SERIES to select from these acceptable alternate with groups of tones. What selection feature which repeats each options. The currentinterval then becomes must be played are: at least three groups of tones in the first variant .... The element a number of times before the most recent interval for the next call to number of groups of chords is left to the resampling the supply; the number of INTERVAL, perpetuating the chain. player, but he should begin with a repetitions and the new supply element Once it has determined a chromatic group of chords [49]. can be selected either by ALEA or by degree using one of Koenig's principles, it SERIES, depending on the user's direc- remains for PROJECT2 to generate Included among the musical "parameters" tives. lower and upper registral limits for this selected by PROJECT2 are (1) harmony, For the most part, the selectionprocesses degree. In Structure 8, Koenig has or degree of the chromatic scale, (2) undertaken by PROJECT2 are indepen- specified constant registral limits. Thus, each pitch within the "groups of chords" Table 1. Breakdownof principles,selection features and suppliesused to compose will be within of the Structure 8 of the Ubungfur Klavier (see Fig. 10) placed randomly any four octaves between C3 (C below middle Parameter Chords Tones C) and B6. Similarly, pitches in the of tones" occur between Harmony CHORD from chord table INTERVAL from intervallic "groups randomly shown in Figure 11. matrix shown in Figure 12. G2 and F#6.

Register Constant: C3- B6 Constant: G2 to F#6 Index Degrees

Entry Delay ALEA from 0.24, 0.30, ALEA from 0.46, 0.58, 1 C# F 2 F# A 0.37, 0.46, 0.58, 0.72, 0.72, 0.89, 1.11, 1.38, 3 Bb C and 0.89 seconds for and 1.72 seconds. 4 F F# entire chord. 5 A Bb 6 C# F F# Duration ALEA from 0.10, 0.12, Same as 7 C# F C entry delay 8 F# A Bb 0.15, 0.19, 0.24, 0.30, 9 F F# A 0.46, 0.58, and 0.72 10 C# Bb C seconds for entire chord; 11 A Bb C duration not exceed 12 C# F F# A may 13 C# F Bb C entry delay. 14 F# A Bb C 15 F F# A Bb Dynamics GROUP: elements by SERIES SERIES from pp, p, mp, 16 C# F F# C from pp, p, mp, mf, f, and mf, f, and ff. 17 C# A Bb C ff; repetitions by SERIES from 3, 4, 5, 6, and 7. Fig. 11. Chordal table for Structure 8 of Koenig's Ubung fur Klavier.

Ames, Automated Composition 177 Fig. 13 and in an analogous set of Most Current Interval Recent durations. In order best to "hear" what Interval m2 M2 m3 M3 P4 TT P5 m6 M6 m7 M7 the computer would be doing in real time as he manipulated GROOVE's input m2 yes no no no no no no no no yes yes M2 no yes yes yes no no yes yes no yes yes devices during this initial foray into m3 no yes no no no no yes no yes no no automated composition, Ghent employed M3 no no no no no yes no yes no yes no a set with tonal orientation P4 no no no no no no -yes no yes yes no pitch strong TT no yes no no no yes no yes no no no around Bb. When he had specified both P5 no yes yes no yes no no no no no no pitch and duration sets, he developed a m6 no yes no yes no no no no no yes no M6 no no yes no yes no no no no yes no program to generate 10 "functions" m7 yes yes no yes yes yes no no yes yes no (monodic sequences of notes); these M7 yes yes no no no no no no no no yes functions wereproduced by using weighted randomness to select pitch-set elements Fig. 12. Intervallie matrix for Structure 8 of Koenig's Ubungfur Klavier. and duration-set elements for each note. The resulting functions, denoted by Otto Laske digitally controlled analog synthesis or Ghent using the symbols F 1, F2, . .. F10, A close collaborator of Koenig's has throughsoftware sound-synthesis packages in turn provided all of the material for been Otto Laske [51-57]. As a composer modeled after Mathews's MUSIC4 and Lustrum.Because Ghent's programsrepre- and musical epistemologist, Laske has MUSIC5 programs[74], and later through sented pitches in these functions by their been strongly interested in the impact of digital hardware. position in the set rather than by their computer-aided tools on the way com- location on the keyboard, he was able to posers think. For a number of years implementmotivic operations which acted Ghent and beginning in the early 1970s, Laske has Spiegel indirectly on set positions-operations worked to blend insights from cognitive In particular, an environment such as not unlike the traditional practices of psychology, formal linguisticsand artificial Mathews and Moore's GROOVE (Gener- transforming motifs modally-relative to intelligenceinto an expertsystem "bridging ating Realtime Operations on Voltage- notes of a constituent major or minor the gap between a composer's semantic controlled Equipment) [75] utilizes the scale. In Fig. 14, for example, violin II intuitions and low-level data". In Laske's computer as an intermediary between the plays the original form of F1. The 'cello work, composing programs such as user (working through specialized control plays a derivative of F I which is obtained Xenakis'sand Koenig'sare often employed devices such as keyboards and/or panels by invertingthis original sequence around to create "proto-scores" which Laske will of knobs and switches, along with the 8, the central position in Fig. 13: the freely edit and arrange. usual alphanumeric terminal) and an opening D in violin II lies two positions array of real-time sound-synthesis hard- lower than position 8, so the opening G in UTILITIES IN THE V. INTERACTIVE ware. Such an environment enables a the 'cello lies two positions higher, and so UNITED STATES AND CANADA: composer/performer to deal at a reflex forth. Also appearing in Fig. 14 is F2, 1970-1978 level with sounds and timings, although played in original form by the viola, in The 1970s marked the widespread the price for this is that compositional 'indirect' inversion by trumpet 2, in obsolescence of 'batch-oriented' compu- procedures must be simple enough to run retrogradeby trumpet 1 and in retrograde ters programmed by stacks of punched in real time. Along with random selection, inversion by the bass. Not shown in this cards in favor of 'on-line' systems, either in some of the more familiar procedures excerpt is the operation of indirect the form of single-user computers and falling within this category are traditional transposition, which Ghent calls trans- minicomputers dedicated to real-time motivic operations. The most active users location. Translocation is performed by functions or of large time-shared systems of GROOVE were Emmanuel Ghent adding a constant modulo 15 to each capable of servicing many users simulta- beginning in 1968 [76-78] and Laurie successive position in a function. neously. The new fashion for on-line Spiegel beginning in 1974 [79-81]. Concerning the role of the computer in computing found its musical counterpart The first piece to involve the GROOVE this process, Ghent states: in utilities motivated largely by a desire to facility directly in compositional decision facilitate rapid interaction between making was Ghent's 1974 Lustrum. The of the indirect composer and sound: and Lustrum is scored for a quintet of special use pitchreferencing ... is indeed without electronic instruments technique possible Richard Moore's 1968 GROOVE [58- stringed developed the help of a computerbut the labor 63]; Leland Smith's 1972 SCORE [64] by Mathews (among other things, these involvedin spellingout all mannerof (later converted into a music printing instruments could be set to emulate possiblevariants would be prohibitive. program); Barry Truax's 1973 POD with brassy timbres), for conventional brass Also the more one hears what the is in to its enhancements and for computer-generated tape; computer producing response subsequent [65-68]; quintet one'sown selectiveprocesses, the more Herbert Brun's 1976 SAWDUST [69] the piece also exists in an all-computer ideas suggest themselves as further and William Buxton's 1978 SCED [70- version entitled Brazen. avenuesfor variation[82]. 73]. Such utilities were coupled inevitably Lustrum (or Brazen) has its genesis in with sound synthesis, at first through the 15-element "pitch-set" depicted in Subsequent to Lustrum,Ghent developed compositional algorithms based on the "linearization"of chordal structures [83]. f 2- *4 "'7 *0I- Since he had already employed similar 'I techniques in manually composed works I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 for small ensembles, Ghent regarded his programming as "teaching the computer to think the Fig. 13. Pitch set for Emmanuel Ghent's Lustrum. Redrawn from Ghent, "Real-Time Interactive way [Ghent] thought, CompositionalProcedures" [58]. compositionally"-although Ghent re-

178 Ames, Automated Composition = 105

trumpet-like

- - - . ~Iv * v710-_ "Fl- _ -v-_ -- v_=vw ff -tpl -I-

Fig. 14. EmmanuelGhent, Lustrum,1974, measures208-212. Copyright1978 PersimmonPress, 131 Prince Street, New York, NY 10012, U.S.A. Used by permissionof the publisher. served the option to modify what the percent, or anywhere in between, by the 'new generation' of composers seeking computer produced. turning a knob while listening to the creative assistance from computers are music evolve of the knob A variety of comments by Spiegel [the position , Claudio Baffioni at each moment would be recorded by [87], illustrateshow a composer might typically GROOVE for later playback]; or I Clarence Barlow [88-90], Tommaso interact in real time with GROOVE. To could throw a switch to change over to Bolognesi [91], Lelio Camilleri, Joel create her 1974 composition Patchwork, an entirely different set of rules [85]. Chadabe, Thomas DeLio, for example, Spiegel developed programs [92], David Feldman, Christopher Fry that monitored GROOVE's input devices [93], Peter Gena [94], Francesco Guerra Truax and Buxton in order to "derive from [them] much [95], Christos Hatzis [96], Steven more complex music than [Spiegel] Two Canadians who had studied under Holtzman [97,98], Kevin Jones [99], Gary actually played". Spiegel has commented Koenig and Laske, Barry Truax and Kendall [100], Shirish Korde, Petr Kotik, as follows: William Buxton, have since organized Ron Kuivila, LauraTedeschini Lalli [101], studios respectively in David Levitt [102], Denis Lorrain [103], The programI wrote for [Patchwork] Vancouver and Toronto. In addition to Leonard Manzara [104], Larry Polansky, had all Bach's favorite [motivic] developing real-time performance systems, CurtisRoads [105-108], David Rothenberg manipulations-retrograde,inversion, both Truax and Buxton have developed [109], Andrew Schloss, William augmentation,diminution, transposi- non-real-time environments which permit Schottstaedt [110], Sever Tipei [111], tion-available on switches, knobs, users to with little or no Horacio Charles pushbuttons,and keys, so that I could get by pro- Vaggione, Wourinen, manipulatethe 4 simplemelodic and 4 gramming. These environments enable David Zicarelli and myself [ 112-120].The rhythmic patterns with them in the users to monitor results closely as a extent of this new activity has been far too sameway that a playerof an instrument composition takes shape. They minimize great to continue with a detailed survey of manipulatesindividual tones. (I did delays in non-real-time interaction by pieces, so I shall limit my remaining edit it a lot, too.) [84] providing a menu of precompiled "macros" examplesto significantworks that have not The melodic patterns mentioned by (Buxton's term) and by incorporating been describedpreviously in the literature. Spiegel were representedby her programs facilities for rapidly evaluating musical Further details may be obtained from the as "relative (intervallic) distances" from a products, specifically: real-time digital works cited in the References and Notes. "pitch reference point" which Spiegel synthesis augmented visually by graphic could control in real time from her displays. Laske [86] has documented how Thomas DeLio keyboard. Elsewhere Spiegel describes he built up his 1980 composition some of the 'higher-level' methods of Terpsichore as a succession of increasingly Thomas DeLio's 1976 Serenade for controlling the musical evolution of her elaborate "subscores", using macros solo piano is an elaborate work for which 1975MusicforDance through GROOVE's supplied by Buxton's SCED (SCore the form was composed manually while input devices: EDiting) utility. the details were selected automatically. The Serenade has three parts, each BecauseI could hearthe music consisting of 10 sections; markedcontrasts played VI. NEW APPROACHES: 1976-1986 while computationwas in progress,I and occasional long silences between couldchoose which musical decisions I Recent efforts have shown a new many of these sections give the Serenade to the rest to wanted make, leaving sophistication toward automated deci- an episodic quality congenial to its title. follow the I had coded .... For logic sion with increased machine The work is built from a number example,I couldset the probability that making along up of a certain pitch would be played on participation in decisions affecting large- primary rhythmic patterns and chromatic strong beats at zero percent, at 100 scale compositional form. Included among cells. Part I introduces these ideas in

Ames, Automated Composition 179 __

"embryonic states"; they emerge "fully Rhythm. Over the first 17 quarters, the one from one quarter to the next. This formed" in Part II, which also serves a rhythm coalesces from a sparse, irregular process resulted in the following chain: developmental purpose; Part III extra- texture to a consistent 7:4 pattern. DeLio polates several of the ideas from earlier accomplished this evolution by treating 566777878899 10 10 10 10 10 10... parts into "broad sweeping guestures". each quarter as a statistical frame whose Figure 15 reproduces Part I, Section 10 elements are the 29 unequal rhythmic Once these numbers have been deter- of the Serenade.The basic ideas employed units obtained by interfering septuplet mined, DeLio's program locates these in this section are a 7:4 polyrhythm and thirty-secondsagainst duple sixty-fourths. attacks within each quarter by selecting two chromatic cells: G# B C D and its A graphic depiction of the resulting without replacement from the units reflection, G# A# B D. Registers are pattern appears in Fig. 16. In this section depicted in Fig. 16. Initially, each unit distributed uniformly over the range of the Serenade, only one note may attack receives equal weight; as the rhythm from middle C upward. The section at a time; the number of attacks per evolves, the off-beat thirty-seconds and consists of two gradual evolutions, each quarter results from a "first-order sixty-fourths receive less and less weight lasting 17 quarters. The following transition prQcess"(i.e. a Markov chain) until only the 7:4 pattern remains. This breakdown of methods for handling in which the number of attacks may either pattern holds consistently through the rhythm and pitch is based upon a letter stay the same, increase by one or (with remaining 17 quarters. from DeLio to the author: relatively small probability) decrease by Pitch. At the beginning of Section 10, = 60n"N , j 7 -nI 7 I DeLio's selects r . -r r3 _- 7 ~ Z -- z program degreesuniformly with replacement from G#, B, C and D. J m- 7 -T Through the first 17 quarters the likeli- Q=i. = IAi--= _ -- -- - ( I - 4 7 X 7 ' F' a hood of selecting C decreases gradually while the likelihood of selecting A# so that t r, r , -r 7x,r gradually increases, G#, A#, B and D receive uniform weight at the mid- &~dXBy * point 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 The effectiveness of composing pro- gramshas been improvedradically through the introduction in recent years of recursive programming techniques; the first major area of activity relying heavily on such techniqueshas been the application of Noam Chomsky's phrase-structure grammarsto composition. This approach enables a composer to describe musical forms economically, by first providing a general archetype (or axiom) of the form and by further listing a set of productions for deriving details from generalities. The full power of such an approach can be attained only if the productions are capable of acting upon their own results (i.e. capable of recursion). Although had already described an elaborate left-to-right composing program called PROCES- S/ING as early as 1975 [121, 122], his advocacyof top-downChomskian methods [123] has achieved the most influence. I Roads's emphasisupon productions classi- fied by Chromsky as context-free was quickly extended to embrace other Chomskian ideas such as context-sensitive productions and simple transformationsin Steven Holtzman's 1980 "A Generative Grammar Definitional Language for Music" [124]. In Kevin Jones's 1981 "stochasticweb grammars"[125], context- free productions are to carve Fig. 15. Thomas DeLio, Serenade, 1976, Part I, Section 10. Copyright1976 ThomasDeLio. Reprinted employed by permissionof the composer. up a region of musical space (described in

180 Ames, Automated Composition of I x L xIx l lx x l l x modeling [130] compositional process I Ix I in two-part sixteenth-century counter- x x l x x point. Ebcioglu's was the first program I I I I I I I II since Gill's to implement a fully rigorous constrained search with scheduling and Ix 11 I I I l 11 H I xlx 11 IIxl I lxl I backtracking. He has since employed such methods with success in Fig. 16. Interferencesresulting from a 7:4polyrhythm. X's indicate'primary' units. great simulating J.S. Bach's procedures for Jones's simplest examples by boundaries Fractal C and Charles Dodge's 1984 harmonizingchorales [131]; similar success for time and pitch coordinates) into pro- Profile [127]. in chorale harmonization has been docu- gressively smaller chunks until specific mented by Marilyn Thomas [132]. descriptions of notes have been obtained. Artificial Intelligence I employed comparative searches to create my own 1981 Protocol for piano None of the speculations by Roads, An especially potent approach that [133]; but since that time I have created a Holtzman or Jones resulted, to my know- also relies on recursive programming number of original compositions using ledge, in more than a few brief, illustrative techniques has drawn from Artificial constrained searches [134]. In particular, musical examples. Ironically,my own 1980 Intelligence in order to implement for orchestra resulted my method of 'statistical feedback' [135] Crystals string [126] decision-making processes that employ from has provided a determinate strategy for top-down productions similar to searches to discriminate actively between reconciling long-term statistical distri- Jones's. However, my methods were multiple options. Such searches typically butions with short-term stylistic and derived in response to the Gestalt incorporate one or moreprioritizations- idiomaticconstraints. The set of composing hierarchies of James Tenney-only after- functions that measure in numeric terms ward I programs I developed for the U.S. did discover what Roads, Holtzman (positive or negative, depending on the and pavilion at Expo '85 in Tsukuba, Japan Jones had done. application) how each option available to himself has resumed involve- [136], and the programs for my 1986 solo Tenney a decision will contribute to the resulting violin piece, Concurrence[137], employ ment with composing programs after a musical context. In the author's ter- hiatus. In his 1983/1984 'linked' data structures, such as 'lists', 20-year Bridge minology [128], search-based programs 'trees' and 'networks', to represent th; for two retuned pianos, eight hands, divide into two classes: Tenney fuses hierarchic ideas from his complex interrelationships between ele- period with a slightly more 1. Comparativesearches systemati- ments both of the musical scores recentinterest in the harmonic possibilities cally enumerate every possible themselves and of the musical 'knowledge of just intonation. Bridge consists of three configurationof decisions, evalu- base' consulted by the programs as they sections lasting approximately 8, 13 and ating each configurationin order fabricate these scores. 21 minutes. The initial section presents a to determine the 'best' possible Many of the more recent developments wholly random environment evocative of solution to a problem. in automated composition would probably the compositional world of John Cage; 2. Constrained searches improve not have been possible without supporting the final section realizes a Gestalt dramatically upon the random- advances in computer technology. Back- hierarchy in which individual notes sampling-and-testing approach tracking has been known for decades, but combine into "elements" (chords), ele- of Hiller and Isaacson's Illiac it simply was not practical without either ments combine into "clangs", clangs Suite. Each time such a program liberal grants of computer time or combine into "sequences", which ulti- initiatesa decision, a constrained dedicated systems that could be left mately combine into the section as a searchprioritizes all the available running for many hours (often overnight, whole; the middle section effects a options from most to least in my own experience). The newest home "bridge" from Cage's world to Tenney's. desirable and organizes these computers have changed all that. A An excerpt from the final section appears options into a schedule. It then second important factor has been the in Fig. 17. The notated pitches are methodically works through this dramatic rise in ceilings on both modified by the tuning system shown in schedule until it finds an option 'random-access' and 'mass-storage' Fig. 18. that passes all the constraints. memory, coupled with the introduction A third independent path to recur- Should everyoption in a schedule of 'virtual' operating systems which allow sive compositional procedures has prove unacceptable, the pro- a program to utilize more random-access beenfractal geometry.Although popularly gram then backtracks, revises memory than might physically be present associated with Benoit Mandelbrot, one or more earlier decisions in the computer. Where the original fractals are grounded, in fact, in recursive and tries again. ILLIAC employed by Hiller and Isaacson notions which were well understood by Although computer scientists have em- was limited to 1024 words of random- turn-of-the-century mathematicians such ployed recursivesearches in chess-playing access memory for both composing as Georg Cantor (inventor of the "Cantor and theorem-proving programs since the program and data, modern home com- Set") and Giuseppe Peano (inventor of mid-1950s-and despite Stanley Gill's puterscan access megabytesof information the "Peano Curve").Mandelbrot's writings demonstration with his 1963 computer- rapidly. Only the barest fraction of this proved a source of inspiration to Charles composed Variationson a Themeby Berg potential has been exploited to date. Wourinen, who has explored fractals [129] that backtracking could be an both in a set of short computer-composed effective tool in composing programs- studies realized around 1980 and in more the approach has mostly been ignored Interactive Utilities of the 1980s recentmanually composed works. Fractals until very recently. This pattern was The tradition of 'interactive' com- have since provided the impetus for broken by Larry Polansky's 1975 Four- positional utilities has been extended into several computer-composed pieces in- Voice Canons, composed by a program the 1980s with work undertaken by Curtis cluding Larry Austin's 1981 Canadian with non-rigorous backtracking, and Roads and David Levitt at the Coastlines, Horacio Vaggione's 1984 independently by Kemal Ebcioglu's 1980 Massachusetts Institute of Technology.

Ames, Automated Composition 181 o Roads's 1982 IOS [138] is a utility for "interactive orchestration based on score (pt)0 analysis", in which parsing and pattern- L II I1 are to 8I~ 1" L P matching algorithms employed isolate musical "objects" for user modi- fication. (Although Roads has cited IOS as a musical application of Artificial Intelligence, his descriptions of this program 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 to patch together icons representing ele- mentary operations on streams of note data into real-time networks. Included among the most elementary of Levitt's operationsmight be inputfrom a keyboard, irb " , t-i L -P- button or slider (physical or virtual), output to a , generators such 'MP p '" as clocks or units analogous to the . .- _____o "selection features" of Koenig's (PP) P P P P 2-^L PROJECT2 and modifiers such as adders 3) P; PPi__ _ P and delay lines for loops. Users may define their own higher-order icons by patching together simpler units.

VII. CONCLUSIONS For most of the composers discussed in this article, composition has not been a vehicle of 'expression' or 'affect' in the usual senses of these words. Rather, these listeners to judge their ; i P composers expect musical "artifacts", as Barbaud called them, on the basis of more abstract aesthetic qualities such as balance, clarity, depth (in the hierarchic sense) and so ,y ,%"~ ,r'T. forth. They have used computers to create these artifacts because they believe that such qualities are quantifiable-at least within the scope of a particular work-and they have concluded from experience that there are many com- wp positional problems that computers are better equipped than humans to solve. Considered individually, many of the earlier efforts described in this article have been quite simple. This simplicity has been due partially to limits imposed by technology and partially to the spirit of the 1960s and 1970s, when economy of musical process was itself considered a 8 P virtue. Today, a one-pass, self-contained :c- a , 79'o"D 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 Barlow and St by DeLio, [141] myself [142] has been to divide the overall com- P X- positional process into multiple phases, 8 each undertaken by a separate program. 17. James Tenney,Excerpt from Bridge, 1984, for two pianos. The elapsedtime from the beginning Fig. the of the performanceis indicated in minutes and seconds at the end of each system of staves. Notated Taken collectively, compositions pitches are modified by the tuning system shown in Fig. 18. The rhythmic notation shows relative surveyed here present a rich diversity of attack-pointsby their horizontalplacement on the page. Unbeamed,solid noteheadsindicate staccato; techniques for programming computers the next stem or to the end of the beam; open noteheads employ pedal. beamed notes last either up to to compose music. Practically all the Copyright 1985 Sonic Art Editions, 2617 GwynndaleAvenue, Baltimore, MD 21207, U.S.A. Used by permissionof the publisher.

182 Ames, Automated Composition 20. J. Myhill,"Controlled Indeterminacy: A First Step towards a Semi-Stochastic Music Language", Computer Music Journal3, No. 3 (1979). Reprintedin Foundationsof ComputerMusic, C. Roads and J. Strawn, eds. (Cambridge,MA: M.I.T.Press, 1985). An upgradedformula for 'controlledindeterminacy' appears in Hillerand Ames[2]. 21. Hillerand Baker[3]. 22. GyorgyLigeti, "Pierre Boulez: Entschei- in der Structure Eb Bb dung und Automatik -7AFt \C \Gt -16.77 ( ) --/ 5/3 5/4 15/8- - 7/5 - 21/20 Ia", Die Reihe IV: Junge Komponisten,K. -1.11 -3.0 -5.0o +0.8-1.28 . Stockhausenand H. Eimert,eds. (Vienna: 33.Translated \ Piano\.. 2\ \ . \ \ UniversityEdition, 1958)p. \ \c \ by Leo Black, under the title "Pierre -33.3f (i )- 14/9- 7/6 7/4 Boulez: Decision and Automatismin V.+1.8 -0.2t +2.1# Structure Ia", Die Reihe IV: Young Composers(Bryn Mawr, PA: Theodore Presser,1960) p. 36. Fig. 18. Tuningsystem for JamesTenney's Bridge. 23. Hillerand Isaacson[5]. 24. Hillerand Baker[3]. approaches employed today have pre- 25. For a discussionof Tenney'sactivities as REFERENCES AND NOTES the first in what came to be a series of cedents in the groundbreaking years from 1. L. Hiller, the I composersin residenceat Bell Labs,see 1956to 1976:constrained decision "Programming Ching making Oracle", ComputerStudies in the Humani- Tenney[13]. (Klein and Bolitho, Hiller and Isaacson), ties and VerbalBehavior 3, 130 (1970). 26. M. Mathews,with L. Rosler,"Graphical conditional or Markov randomness(Hiller 2. L. Hiller and C. Ames, "Automated Languagefor the Scores of Computer Generated Sounds", New and Isaacson, Hiller and Baker, Koenig's Composition:An Installationat the 1985 Perspectives of International in Tsukuba, Music6, No. 2, 92 (1968). INTERVAL feature), statistical pro- Exposition Japan", Perspectives of New Music 23, 27. M. Mathews,with J. Miller,F.R. Moore, cedures (Xenakis, Brimn,Koenig), evolu- No. 2, 196(1985). J.R.Pierce and J.C. Risset, The Technology tions (Tenney, Myhill, Koenig's 3. L. Hiller and R. Baker, "Computer of Computer Music (Cambridge, MA: M.I.T.Press, TENDENCY feature [143], DeLio), Cantata: A Study of Compositional 1969). New Music 28. M.Mathews and F.R. Moore, "GROOVE: hierarchic, (grammatic) structures Method", Perspectives of 3, No. 1, 62 (1964). A Programto Compose,Store, and Edit (Tenney), motivic transformations 4. L. Hiller and R. Kumra,"Composing Functions of Time", Communicationsof Barbaud, Hiller and Baker, Ghent, Algorithms II by Means of Change the Associationfor ComputingMachinery Spiegel), backtracking (Gill). Although Ringing",Interface 8, No. 3, 129(1979). 13, No. 12, 715 (1970). a number of the early computer- 5. L. Hillerand L. Isaacson,Experimental 29. See Myhill[6] and Xenakis[7]. York: 30. 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Although how 11. Hillerand Isaacson[5]. Music Reports 1, No. 2, 32 (1970). 12. Hillerand Baker 40. G.M. Koenig, "PROJECT2:A Pro- deeply the computer will penetrate into [3]. 13. J. Tenney,"Computer Music Experiences, gramme for Musical Composition", such traditionally 'human' domains is yet 1961-1964", Electronic Music Reports 1, Electronic Music Reports 1, No. 3 (1970). to be gauged, it is clear already that No. 1, 23 (1969). 41. G.M. Koenig, "Protocol", Sonological automated composition is an established 14. T. Blum, "HerbertBrun: Project SAW- Reports4 (Utrecht:Institute of Sonology, reality of our time. DUST" (review), ComputerMusic Journal 1979). 3, No. 1, 6 (1979). 42. 0. Laske, "Composition Theory in Acknowledgements-Specialacknowledgement 15. H. 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184 Ames, Automated Composition 137. Ames [120]. was able to represent them as algebraic insightful character. For instance, a paradigm 138. Roads [108]. manipulations-hence the qualification, in a discussion involving several basic premises 139. Yavelow [102]. "formal". would be an example that reveals the interplay 140. Ebcioglu [131]. between most or all of these premises. 141. Barlow [89]. frame-a 'frozen' moment of time; the analogy 142. Ames [113-117, 120]. is drawn from cinematography. An important Peano Curve-derived by infinite recursion, 143. Koenig [40]. instance within the context of this article is the the Peano Curve is a geometric abstraction statistical frame, which denotes a segment of which defies many of our most basic intuitions music over which a 'momentary' statistical concerning how a 'curve' should behave. It has distributionis realizedby a composing program. the following properties: every point in the curve resides at the corner of a and GLOSSARY right angle, Gestalt psychology-the study of the perceptual the 'loops' of the curve are infinitely dense in algorithm-a computational procedure which, factors affecting how elements of the environ- any region (no matter how small) where the after a finite (but possibly very large) number ment are combined mentally into larger forms curve is defined. Yet the Peano Curve never of steps, always returns either a correct ('gestalts'). An outgrowth of commonsense crosses itself! Cf. E. Kramer, The Nature and solution or the answer that such a solution observations made in Wertheimer's 1921 Growth of Modern Mathematics (Princeton, does not exist. article "Laws of Organization in Perceptual NJ: Princeton University Press, 1982) pp. 528- Forms", and a precursor to the modern 529. Artificial Intelligence-emulation by computer discipllineof cognitive psychology. of human problem-solving activities. An prioritization-a procedure that ranks a set of outgrowth of automatic chess-playing pro- heurism (or heuristic)-a computational pro- objects or tasks in order of preference or cedures proposed by Shannon in 1950 and of cedure which "proceeds along empirical lines, urgency. theorem-proving programs developed shortly using rules of thumb, to find solutions or thereafter by Simon, Newell and Shaw in answers" (from Webster's Dictionary). random-refers to a process the outcomes of response to Shannon's proposals. Heurisms are less precise than algorithms, but which are unpredictable or patternless over the they sometimes have the advantage of being short term. automated composition-any use of computer usable under less-than-optimal conditions: programs that undertake decisions affecting where an algorithm must always either return a recursion-the ability of a process to act upon the content of a musical composition. correct solution or fail, a heurism can return a its own results. Recursive techniques make it solution which is mostly correct, but which possible to implement computational processes Cantor Set-invented in the course of Cantor's might deviate occasionally from a few less- that are able, in effect, to propagate 'copies' of mathematical investigations of infinity, a than-critical specifications. themselves. Such processes can spawn multiple Cantor Set may be derived from an unbroken sub-processes; these in turn can spawn sub- segment of the real-number line as follows: hierarchy-a structure in which the inter- sub-processes, and so on to arbitrary levels of divide the segment into three equal portions, relationships resemble the chain of authority complexity. exclude the middle portion, and apply the among priests in an organized religion (hieros same of division and exclusion means each in a procedure 'sacred'); entity hierarchy may statistical distribution-the relative amounts recursively to each remaining portion. One have any number of 'inferiors' but only one by which differing types occur within a might surmise intuitively that such a set would direct 'superior'. Hierarchies are often referred population of elements. dwindle away to nothing; however, Cantor to by computer scientists as tree structures. proved intuition wrong: his set in fact contains a unique counterpart for every number on the left-to-right-refers to a strategy of handling stochastic-literally synonymous with infinite real-number line. Cf. R. Courant and tasks as they arise, as contrasted with top- 'random'; however, discussions of 'stochastic' H. Robbins, What Is Mathematics? 4th Ed. down and other strategies that might defer less processes (as in Xenakis's 1971 book [7]) (New York: Oxford University Press, 1947) pp. urgent tasks. typically reflect a concern for the large-scale 248-249. distributions of outcomes. list-a structure in which each element has at formal grammar-refers to the theory of most one 'predecessor' and one 'successor'. top-down-refers to a process that deals first "linguistic competence" developed during the with generalitiesand which utilizes the 'insights' 1950sby Chomsky. Chomsky divides grammars Markov chain-a 'left-to-right' chain of events gained thereby to cope with more specific into two main classes: "phrase-structure in which the outcome of each individual event tasks. grammars", which are sets of top-down rules is conditioned by the outcome of its immediate determining how the whole of a statement predecessor. with replacement/withoutreplacement-a favo- relates to its parts (its phrases, clauses, etc.), rite paradigm among probability theorists is and "transformational grammars", which are network-a structure in which each element that of blindly drawing colored balls from an sets of procedures for modifying phrase can have any number of direct relationships to urn, where the probabilities are determined by structures in order to produce well-defined any number of other elements. Networks are the proportions of balls of particular colors to changes in 'meaning' (e.g. mild transfor- also known among computer scientists as the total number of balls. Such selection is said mations from active voice to passive, from first directed grap/s. A good example of a network to occur with replacement if balls are returned person to third, from present tense to past, or is the structuredeveloped by Roget for his 1852 directly to the urn after each draw and without more radical transformations such as negation, Thesaurus. replacement if newly drawn balls are set aside. logical inference, and so on). Because such Obviously, the distribution of colors is reflected rules and procedures are typically independent paradigm-a pattern, example or model, much more accurately over the short term by of the specific content of a statement, Chomsky typically of a 'classic', 'shining' or particularly the latter method.

Ames, Automated Composition 185