Composing With Computers. A Progress Report by L.Hiller, 1981

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Composing with Computers: A Progress ReportAuthor(s): Lejaren HillerSource: Computer Music Journal, Vol. 5, No. 4 (Winter, 1981), pp. 7-21Published by: The MIT Press

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LejarenHillerDepartment of MusicState University of New York at Buffalo

Buffalo,New York 14214

Composing w i t h

Computers rogress

e p o r t

Computermusic has come to have two different

meanings that are not competitive but complemen-tary.The first, computer-composedmusic, involves

composition, that is, note selection. The second,computer-realized music, involves conversion into

electronic sound of a score that may or may nothave been composed with the aid of a computer.These two operations can be performedin se-

quence, so that a composer's score can be both

composed and realized by means of a computer(Fig. 1).Depending on the computer configurationand the composer's objectives, the boundarybe-tween these two processes can be sharplydefinedorratherfuzzy.

Although computer composition has been goingon since 1956, when LeonardIsaacson and I startedwork on the Illiac Suite for String Quartet, more

efforthas been expended over the years on soundsynthesis. This is because there is a pressingneedfor accurate,reproducibleelectronic sound andformodern tools for acoustic research. Sound synthesishas applications in music education, and the com-mercial possibilities of sound synthesis far tran-scend the concerns of the avant-gardecomposer.Perhapsthe most important reason for greaterem-

phasis on sound synthesis is that computer-assistedcomposition is inherently a more obscure, difficult,and controversial topic. Computer-assistedcom-

positionis difficult to

define,difficult to

limit,and difficult to systematize. As with any kind of

composing, work in this field tends to be highlypersonalized and hence less accessible to others.

Computer composition also requiresthe attentionof a skilled composer who has enough experienceto ask the proper questions. Despite all these barri-

ers, substantial progresshas been made in com-

puter composition over the last 25 years.

Some 12 years ago, I preparedan exhaustive re-view of computer music composition until thattime (Hiller 1970b). Among the composersmen-tioned therein were Pierre Barbaudand lannisXenakis of Paris,Gottfried Michael Koenigof

Utrecht, HerbertBruinof Urbana-Champaign, lli-nois, and JamesTenney,now of Toronto.This listcould be considerablyextended today.In our own

group,JohnMyhill and CharlesAmes areparticu-larly active. Reportsin this issue of ComputerMu-sic Journalof other composers' recent work will fillin the present picture.

Writing compositional algorithms forces me toscrutinize composition as process. I have to beaware of how compositional logic really works andhow compositional priorities arrange hemselves. In

working with computers, musical ideas come to methat I probablywould not otherwise have imagined.This carries over to composing I now do without

computers as well.I shall review here some of my own work, espe-

cially that of recent yearsabout which I have pub-lished relatively little so far. (Insteadof doing much

publishing, I have been slowly but steadily gather-ing all the documentation into a series of techni-cal reports.The relevant reportsare listed in the

References.)The composition list shown in Table 1 providesa

framework for the discussion to follow. The list canbe split into two parts: (1)earliercompositions pro-duced at the University of Illinois and (2)more re-cent works written in Buffalo since 1968. This splitis a logical one, because if I include Algorithms Iwith the latter group,all of these either point to-ward or actually make use of the programmingpackage I currently use.

One striking feature of all this work has beenits pragmatism.I like to get the music performed.Performanceis, without a doubt, the best test ofthe results. Nowadays, for example, I plan a piece

like Algorithms III with my basic system, program

Computer Music Journal,Vol. 5, No. 4, Winter 1981,0148-9267/81/000007-21 $05.00/0C

1981Massachusetts Institute of

Technology.

Hiller 7

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Fig. 1. The computer used synthesis algorithms,as a composing machine, high-level score languagewith facilities for composi- interpreters, and digital-tional algorithms, analog- to-analog conversion into

to-digital conversion of sound.natural sounds, sound

SoundSynthesis

"Natural" Algorithms

Sounds

CompositionAlgorithms Input Output

Analog-to-Digital Digital Digital-to-AnalogiConverter Computer Converter

(Pass2)

Digital OutputComputer Input

(Pass1)Interpreter AudioTape

Recorder

Playback

Input Printed Composer's

Data "Score" OwnScore

OptionofInstrumentalPerformance

PHRASE, n mind, and duringthe compositionalprocess I improve programPHRASEby addingnew

algorithms or improving existing ones.A second feature of my approachto computer

composition has been its emphasis upon probabilityand statistics. My music tends to proceedfrom dis-orderto order. It starts with randomgenerationofmusical elements and proceedswith the impositionof more and more constraints on the elements' ac-

ceptability. I have done this consistently since the

original Illiac Suite. To be sure, I was much influ-

enced by readingsI had done in information theory.

Not only does this procedurework, but it seems

philosophically satisfying. The trapin writing a

completely deterministic set of algorithms isthat they reduce the whole process to mere datatransformation.

EarlyCompositions

Because the Illiac Suite (which I now also call

String Quartet No. 4) was the first composition

written with a digital computer, LeonardIsaacson

8 Computer Music Journal







Table 1. Lejaren Hiller: computer music compositions

Illiac Suite for String Quartet (1957)(composed with LeonardIsaacson)

Duration: 18 minPublisher: Theodore Presser

Recording: Heliodor HS25053

"TheFlying Lesson"from Music for "The Birds"

(by Aristophanes) (1958)Duration: 2 minPublisher: None

Recording: Private tape

Computer Cantata (1963)(composed with RobertBaker)


Recording: Heliodor HS25053, reissued on CRI-SD-310

An Avalanche for Pitchman, Prima Donna, PlayerPiano,Percussionist and PrerecordedPlayback (1968)

Text: Frank ParmanDuration: 9-13 minPublisher: Theodore Presser

Recording: Heliodor 2549006

HPSCHDfor 1 to 7 Harpsichordsand 1 to 51 Tapes(1968)(composed with JohnCage)Duration: 20 min to any lengthPublisher: C. F. Peters

Recording: Nonesuch H-71224

Algorithms I for 9 Instruments and Tape(VersionsI to IV) (1968)Duration: 9 min per versionPublisher: Theodore Presser

Recording: Version I: DGG2543005Version II: Private tapeVersion III:Private tapeVersion IV: DGG2543005

ComputerMusic for Percussion and Tape (1968)(composed with G. Allan O'Connor)


Recording: Heliodor 2549006

Algorithms II for 9 Instruments and Tape(VersionsI to IV) (1972)(composed with Ravi Kumra)

Duration: 5 min per versionPublisher: Theodore Presser

Recording: Version I: UnperformedVersion II: UnperformedVersion III: Private tapeVersion IV: Private tape

Hiller 9







Table I. (cont'd)

A Preview of Coming Attractions for Orchestra(1975)Duration: 16 minPublisher: TheodorePresserRecording:Private ape

Electronic Sonata for Four-ChannelTape (1976)Duration: 53 minPublisher: NoneRecording:Private ape

Midnight Carnivalfor an Urban Environment(1976)

Duration: IndeterminatePublisher: NoneRecording:Private ape

Persiflagefor Flute, Oboe and Percussion (1977)Duration: 11minPublisher: WaterlooRecording:Commercial elease n preparation

Algorithms III for 9 Instruments and Tape(VersionsI to IV) (inprogress)Duration: 9 minPublisher:NoneyetRecording:Unperformedunfinished)

and I had to deal with many elementary questionsas to how computer music might be composed.

I had been working since late 1952 as a chemiston a research project sponsored by the UnitedStates Government. Although I had had a bit of ex-

posure to analog computers at Du Pontpriorto

this, it was at the University of Illinois that I firstlearned how to use digital computers, specificallythe Illiac I. This was very much brute force ma-chine

languagework-no

fancy, high-levellan-

guages. My researchdirector,FrederickWall,assigned to me the problem of computing statis-

tically the dimensions of idealized polymer mole-cules in solution. This work introduced me to theMonte Carlo, or Markov, processes of calculationthat became central to my later work.

It occurred to me that, by changing the control-

ling conditions from geometric to contrapuntal,thesame basic programcould be adaptedto writingsome counterpoint exercises. I suggested this ideato LeonardIsaacson, who was also a chemist on thesame

project. He liked the idea as a programming

challenge, even though his knowledge of music was

purely that of a listener. So we started with a fewsmall experiments and, little by little, the projectgrew.Around this time I mentioned the projecttoMilton Babbitt,my former composition teacher,and he was both intrigued and encouraging,partlybecause he himself was beginning to think a lotabout electronic music.

One evening, when we had some results, I

showed them to a composer friend. He said thatwhat we had was all very good but that it wasn't

music, and that he would be more impressedwerethe counterpoint really correct. Isaacsonand I

thought about going on to more complex strict

counterpoint but soon droppedthis idea in favorof

composing some experiments more relatedto con-

temporarymusic. This resulted in the final twomovements of the Suite. When we first performedthe Illiac Suite, or ratherthree movements of it, a

huge amount of publicity was generated(alot of itrathersilly).

The first time I gave a talk on the subject of com-








puter music was in 1956 beforean audience ofabout 2000 computer experts and engineers at a Los

Angeles meeting of the Association of ComputingMachinery.Attitudes towardthis earlywork rangedfrom curious to skeptical to overtly hostile. Rather

interestingly, computer scientists were more openminded than musicians, and musicians were more

open minded than scholars in the humanities,many of whom seemed to regardme as monstrous.

I did not hear a complete performanceof the Il-liac Suite until several years later.I was giving a

talk at a conference, and afterwarda man intro-duced himself to me as Max Mathews. He said hehad a present for me-a tape recordingof the IlliacSuite he had gotten the WQXRStringQuartet tomake. This was aroundthe time he was developingMusic IV.

Since the Computer Cantata has been rather

thoroughly described elsewhere (Hiller 1964; Hillerand Baker 1964), there is little I need say about ithere except that in it Robert Baker and I were con-

centratingagain on basic problem solving, thistime with an emphasis on statistics, stochastic pro-

cesses, and rhythmic complexities more profoundthan those attempted in the Illiac Suite.

Both An Avalanche ... and HPSCHD, thoughcomposed with computer algorithms, are theatrical

compositions and hence differ from the earlier di-dactic works. An Avalanche ... is a satiricalpiecedealing with the state of the performingarts in theUnited States, and HPSCHD is a gigantic multi-media spectacle. HPSCHD involved three sets of

computer programs,one for composing the tapeparts and realizing them in sound by means of digi-tal-to-analog conversion, the second for composingharpsichordparts derivedfrom Mozart'sMusicalDice Game, and the third for creatinga perfor-mance part for the high-fidelity enthusiast sittingat home listening to the collage we prepared or acommercial phonographrecording.Contrarytowhat many critics thought (Will they never learn?),this was not a chaotic piece. The basic note genera-tor was a subroutine called ICHING that recreatedthe Oracle of the Book of Changes. The results ofsubroutine ICHING were not haphazard,but werebased on a polynomial distribution. Also, much ofthe

programmingwas concerned with melodic con-

structions that Cage hoped would express his admi-ration for the melodic writing of Mozart.

RecentCompositions

Both Electronic Sonata and Midnight Carnivalarerealized with computer sound synthesis and have

nothing to do with computer-assisted composition.A Preview... and Persiflagerepresentsuccessive

stages in the development of the substantial libraryof compositional programsand subroutines I cur-

rently use. The Algorithms cycle, consisting of Al-gorithms I, completed in 1968, Algorithms II,completed in 1972, and Algorithms III, currentlybeing composed, arecentral to this development.The structuralplan of the entire Algorithms trip-tych is shown in Table2.

As I write this, the second movement of Al-

gorithms III is done and the first movement well

along toward completion. Debugging, code conver-

sion, and documentation have all been nearly as

time-consuming as the writing of the programs.The Algorithms cycle is actually more complex

than shown in Table2 because each movement ex-ists in four versions, any one of which can bechosen for a given performance.There are 28 move-ments in all. Each version reflects small but im-

portant changes of parametersor data. This planprovides a rather neat method of testing the practi-cal effectiveness of various compositional algo-rithms. Also, varying some components of a systemunder investigation while keeping others constant

is, of course, a standardtype of experimental de-

sign. First, I specify a compositional system inwhich a particular composition is but one examplefrom a class of essentially similar compositions. Ifcertain elements are changedin the matrix of ele-ments making up the system, its details will benew but its gross propertieswill remain essentiallythe same. It is interesting to speculate how muchmust be changed to createa new work. We can testthe effect of variance of controls in relation to the

whole system to gain some insight into this prob-lem. If we use a computer to do this, we retain aprecise recordof how the variance is producedandwhat its limits are. Let us take Algorithms I as thefirst

exampleof the

applicationof this idea.

Hiller 11







Table 2. The complete set of Algorithms compositions

Algorithm Duration in minutes

AlgorithmsII. "TheDecayof Information" 2

II. "Icosahedron" 3III."The ncorporationf Constraints" 4

Algorithms IIIV."Campanology" 5

Algorithms IIIV. "Refinements" 4

VI. "Quotations ndPhraseology" 3

VII."Synthesis" 2Total 23

Algorithms I

The first movement of Algorithms I, "TheDecay of

Information,"is a short introductorypiece that re-

capitulates (in very condensed form)the formalstructure of Computer Cantata. In an evolving plan

of stochastic control, transitionprobabilitiesare al-lowed to increase from zero orderto sixth order.These transition probabilitiesare not the same at

any time for the differentinstruments, since someinstruments reach the sixth-order level sooner thanothers. I employed this process to cause the infor-mation level of this movement to dropfrom 100%to approximately 50% from its beginning to its end,hence "The Decay of Information."The four ver-sions of this movement were obtained by varyingthe rest/play ratio assigned to this movement. "Ver-sion 1"is the emptiest and "Version4" is the fullest.

Because more recent work has supersededmostsubroutines from this movement, only three are in

my current libraryof subroutines. These have beenboth translated and updated.One rathersimple sub-routine provides a distribution accordingto Zipf'slaw, which, whether valid or not, is a nice way of

emphasizing some choices at the expense of others

(Pierce 1961). It states that the probabilityof select-

ing an item in a list is inversely proportionaltorankorder,that is,

P,=

P,/i,

where P, is the probabilityof choosing item i and P,is the probabilityof the first item in the list. Theflow chart of the original subroutine is shown inFig. 2, and the results of 10,000 trials of the currentsubroutine IZIPF,with limit n = 12, is shown inFig. 3.

The second movement of Algorithms I, "Ico-sahedron,"was my first extended effort at program-ming a reasonablycomplex serial composition. Themovement consists of 576 notes made up of a 12-tone row, its three permutations, and the 11 trans-positions of these four fundamental forms. Thus,each variant of the row occurs just once. The row,the sequence of its variants, the dynamic plan, andall the rhythmic units were chosen by randompro-cesses. The whole assembly of note occurrenceswas compiled into the triangularplan shown inFig. 4.

Another feature of this movement involved sort-ing out randomly generatedrhythms in such a waythat rhythmic simultaneities would be maximal atthe center of the movement. This was accom-plished by a large subroutine called MATCH(Hil-ler 1969). I used an instrumentation process forthis movement that interchanges instruments, giv-ing the high, wind instruments breathing space.The individual lines can be quite long andtaxingotherwise.

The third movement, "TheIncorporationof Con-

straints,"is a rondo.

Here I addeda numberof








Fig. 2. Theflow chart forimplementing Zipf's law,used for the compositionAlgorithms I.

z X R 1 =R 1

iA = A + 1.

O M L . Z P F

SaveStoreIndices,

Store Random Subroutine

0 in Q,Fraction RAM2B

1. in A, in RRANGEnXR2

B

=1.//A= 1./A + Q

B S

A = A 1 .

S=S-B

IsYes A > RANGE?

Yes Is

Again No PP-R< 0?

Store

Q in S, No

ClearA and

XR1I

I. Initializations and Computations Yes RANGEof 11/j to Limit n SuppliedAs RANG

Input Parameter.No

II. Computation of successivenormalized probabilitiesand Transfertest of each against random XR1 to AC,fraction till one succeeds. Restore

Exit if rangenot exceeded. Indices

Hiller 13







Fig. 3. A graph of a test of10,000 trials using the pro-cedure outlined in Fig.2.

4000 IZIPF TESTI IZ

Test of I Iz3000 SubroutineIZIPF 13237IZIPF TEST

(10,000 Samples) I IZIZ2 1570

2000 IZIPF TESTI IZ

3 1034IZIPF TESTI IZ

4 848IZIPFTEST

1000 I I Z5 646

800 IZIPFTESTI IZ

S6 545

600 - IZIPFTEST0 I IZ

500 - 7 479

z I IZIPFTEST400 I I Z

8 400

IZIPF TEST300 I I Z

9 352IZIPF TESTI IZ

200 10 349IZIPFTESTI IZ

11 277IZIPF TESTI IZ

100 I I I 1 1 I1 12 2631 2 3 4 5

67 8 9 101112

Rank Order








Table 3. Structuralplan of the third movement of Algorithms I, "TheIncorporationof Constraints"

Durationin

Section Content Seconds

1A Sixth-ordertochasticmusic 848

1B Chord valuationwithregardo adissonance-consonancendex 402A Combination f the contentof section1Bwithfifth-ordertochasticmusic 16

482B Threecontrapuntal rocesses 323A Combination f the contentofsection2B withfourth-ordertochasticmusic 24

483B Fixedchoirsof rhythms 244A Combination f the contentof section3B with third-andsecond-ordertochasticmusic 32

48

4B Varyinghoirsofrhythms 165A Combination f the contentof section4Bwithfirst-andzero-ordertochasticmusic 40485B Process ora statistical onal cadence 8

Total: 240

Table 4. Basic change-ringingprocess for even-numbered sets of bells

Row 1 (lead-end) 12345678Row 2 21436587Row 3 24163857

Row 4 42618375Row 5 46281735Row 6 64827153Row 7 68472513Row 8 86745231Row 9 87654321Row 10 78563412Row 11 75836142Row 12 57381624Row 13 53718264Row 14 35172846Row 15 31527486Row 16 13254768

Note: Eight bells is a typical number. The lead-end s calledrounds if this is the very start of ringing.

cess with each version, Ravi Kumra and I wrote a

large number of programsand subroutines, themost important of which were RING1, RING2, and

RING3, that dealt with various ways permutationscould be propagatedand broughtto full cycle, re-

turning to the original sequence (rounds).A flowchart showing how the compositional process was

organizedis shown in Fig. 5. Subroutine FLIP ar-ries out the operationshown in Table4.

Program HRASE

All the more recent computer compositions listedin Table 1 have been produced by means of a largemain programcalled PHRASE.The first of these

compositions is the orchestral work A PreviewofComing Attractions. ProgramPHRASE s now

being combined with an ever growing number ofsubroutines that place constraints on choices of thefive note parametersof pitch, dynamics, timbre,playing style, and rhythm. In contrast to earlier al-

gorithms for music composition, programPHRASEcan be used to compose themes, motives, and

phrases, and, even more importantly,to imitate andcombine these phrases in a number of ways. This

system transcends the manipulation of individualmusical elements because it can handle substantial

groupsof elements that can be related to the totalscore.

The importance of this, it seems to me, is the

recognition that hierarchical structure is the funda-mental architecturalprinciple that makes a musicalwork into a coherent whole. In a hierarchicalstruc-

ture, some events in a score aremore significantthan others in the pattern created when a concept

16 ComputerMusic Journal







Fig. 5. The flow chart forchange ringing used in Al-

gorithms II.

Entry

Initialization

Skipthis stepforring2.

thepeal Yes PrintheCompleted? peal.

No

SSelect an operationat random.

Obtain he new lead-end

by applyingthis operation.

Yes this lead-end

u n i q u e

This step only

No for ring 2.

Is

the lengthbetween matched Yes Print the

lead-ends peal. Exitsatisfactory?

No

Select an untried

operation.

H a v e

Ring 1 and ring 2Yes all three Yes Go back

operations 1 node.been tried?

Go back 4 nodes. No Ring 3 only

II (2

Hiller 17







is encoded into music. A message is seldom just alinear string of events like beads on a chain. Rather,the events in a message are tied together by com-

plex network structures that subordinatesomeevents to others.

Notions of this sort arealreadyembodiedin more

sophisticated analytic systems such as that of Hein-rich Schenker (1979). In similar studies of language,the idea of hierarchyforms the basis of the develop-ment of generative grammars.

For a variety of reasons, the concept of hierarchy

was little used in the early development of com-puter music algorithms. Because I felt this lack, Iset about writing the programsI shall now discuss.

In designing programPHRASE,I defined three

processes that might occur during composing.These are

1. Free flow2. Phraseassembly3. Imitation

Freeflow is used for musical textures that are not

phrase oriented. Phrase assembly producesthe ma-

terial that is imitated. If codified relationshipsdonot exist among notes, as is the case in free flow,then there is nothing to imitate; thus the need for

phrases. Imitation is the most complex set of oper-ations in programPHRASE.It is here that we "do

something" with the raw material provided byphrase assembly. By imitation, I mean the manyways a phraseor groupof notes can be imitated,placed into new contexts, transformed,developed,and modified. This applies not just to traditionaltonal music but to innovative patterns as well.

To codify these imitation processes into a man-

ageable form, I limited processes of imitation to thefollowing options:

1. Transposition2. Choice of voice3. Permutation4. Strict or free rhythmic imitation5. Optional phrase-imitation overlap

To summarize, programPHRASEdoes not in it-self define a musical style; rather, t provides threealternative paths for producingand extending a mu-sical

texture. These paths are shown in Fig.6, as are

some of the subroutines that programPHRASEre-

quires to operateproperly.Forexample, subroutineREADL is used to readin the stochastic orderstobe used in making note parameterchoices and theavailable choices for the five parametersof pitch,dynamics, timbre, playing style, and rhythm. Sub-routine BRANCH governs many of the actualchoice operations;for example, whether assemblyof a phrase should be continued or terminated,whether rest or play should be chosen, or which

phrase should be imitated. SubroutineFILLdoes

the actual choosing of note parametersby calling inturn other subroutines. One line of developmentthat demonstrates hierarchyis as follows: programPHRASE s the master program;subroutineFILL ssubordinate to it; subroutines such as PITCH andTIMBREare subordinate to FILL;and still other

subroutines, such as MODE andGOAL,aresubor-dinate to PITCH.

Figure 7 is a sketch of subroutine FILL.Theboxes with dotted lines indicate subroutines thatare incomplete at the time of this writing.

If the diagramof programPHRASE s now re-

called (Fig.6), it is easy to see how a musical struc-ture is set up. Whenevercomposers wish to obtaina change in texture, they simply set a limit ex-

pressed in /32 notes. This is tested at the end ofthe big loop in programPHRASEeach time a noteis generatedfor each voice of the score. When allvoices have reached this limit, the large loop re-

turning to the very beginning of the program s

entered, and fresh data are readfor whateveraddi-tion is desired, such as new themes to be quoted,new probabilities to be supplied to subroutine

BRANCH, and so on. One type of refinementI add

bit by bit in programming s reduction of theamount of such data that must be specified by the

composer. My general attitude is that the moresuch data areinternally generated,including long-rangevariance of such data, the more effective and

interesting the entire process becomes.

Persiflagerequired20 sets of data.These imposeda gradualchange of texture by changingthe amountof phrase assembly, amount of imitation, types ofrhythms, loudness levels, and so on. Other con-trols, mainly those concerned with pitch choices,more or less took care of themselves. Furtherde-

18 ComputerMusic Journal







Fig. 7. A simplified block

diagram of the subroutineFILLcalled by the programPHRASE.

Mode

Entry

StyleChoose PitchPitch

IRIG Goal

Choose

andICHING Edit - Dynamics I \ MLRL1

Dynamics

t M L R L

Stochastic Choose TimbreIZIPF Sequence Timbre

SOther Routines I

ChooseREIHE Playing Style

Style

ChooseOtherRoutinesRhythmoose

Rhythm

Exit

SubroutineFILL CompositionalModules

tails concerning Persiflage appear elsewhere (Hiller

1978; 1980).

Algorithms III

At present, I am much involved in programmingthe first movement of Algorithms III.The secondmovement is alreadydone. Although quite a bit ofnew

programmingwas neededfor

the second move-

ment, the thorough reorganizationand refinement

contemplated for the first movement was notneeded. The title of the first movement, "Refine-

ment," means just that. The final movement willbe a synthesis of just about all the programmingwritten for the whole cycle.

The second movement, "QuotationsandPhrase-

ology,"is partitionedinto blocks, some of whichare assigned the function of "phraseassembly"or

"theme quotation," dependingon the version; some








of which are assigned the production of "free flow"or "imitation"; and some of which are assigned anew process, "double imitation," which is an at-

tempt to imitate whole blocks of material, not justsingle lines. The parameters controlling all this arenow assigned to individual voices, so it is possibleto assign different textures to different portions ofthe performing body at the same point in the score.

A modulating scheme is also imposed. "Version1" does not modulate, but each voice has its own

transposition scheme. "Version 2" is built on a tone

row, and its modulation scheme depends on thisrow. "Version 3" makes use of a cycle of fifths, and"Version 4" incorporates a simple representation ofthe tonal scheme of a traditional sonata formstructure.

The first movement, "Refinements," will bemade up of 10 sections, as is the third movement of

Algorithms I. However, the addition of composi-tional options makes it vastly more complex. As I

program successive sections of this movement, Ialso steadily tighten up and make more clear and

logical all that is going on. This is rather slow goingbecause so many operations interlock and dependon one another that it is very easy when institutingchanges to cause the whole system to jam up. De-

bugging is slow and costly. A typical run now isabout 5 min of machine time on the CYBER 173, a

very fast computer.Three sections of the movement are done, and in

these I have introduced quite a number of new sub-routines involving, for example, a fully realized

stochastic choice generator, subroutines for timbreand style controls, and a subroutine (REIHE)con-

taining all current tone row operations. The next

step is the introduction-at last-of vertical con-trols such as harmonic rules.

References

Hiller, L. 1964. "Informationstheorieund Computer-musik." In Darmstddter Beitraige ur Neuen Musik 8.Mainz: B. Schott's Sohne.

Hiller, L. 1967. "Programminga Computerfor Musical

Composition." In ComputerApplications in Music, ed.G. Lefkoff.Morgantown:West Virginia University Li-

brary,pp. 65-88.

Hiller, L. 1969. "SomeCompositional TechniquesInvolv-

ing the Use of Computers."In Music by Computers,ed. H. von Foerster and J.W.Beauchamp.New York:

JohnWiley, pp. 71-83.

Hiller, L. 1970a. "Programminghe I-ChingOracle,"ComputerStudies in the Humanities and VerbalBe-havior 3:130-143.

Hiller, L. 1970b. "Music Composedwith Computers-AHistorical Survey." n The Computerand Music, ed.H. B. Lincoln. Ithaca, New York:Cornell UniversityPress, pp. 42-96.

Hiller, L. 1972. "ComputerProgramsUsed to Producethe

Composition HPSCHD."Technical report4. Buffalo,New York:SUNY, Department of Music.

Hiller, L. 1978. "PhraseGenerationin ComputerMusic

Composition.".Technical report 10. Buffalo,New York:SUNY, Department of Music.

Hiller, L. 1979. "PhraseStructure n ComputerMusic."In Proceedings of the 1978 International ComputerMusic Conference,vol. 1, ed. C. Roads.Evanston,Illi-nois: Northwestern University Press,pp. 192-213.

Hiller, L. 1980. "Composingthe Second Movement of

Algorithms III."Technical report12. Buffalo,NewYork:SUNY, Department of Music.

Hiller, L. 1981. "Computer ProgramsUsed to Produce the

Composition Algorithms I."Technical report13. Buf-falo, New York:SUNY, Departmentof Music.

Hiller, L., and R. A. Baker. 1962. "ComputerMusic."In

ComputerApplications in the Behavioral Sciences, ed.H. Borko.EnglewoodCliffs, New Jersey:Prentice-Hall,pp. 424-451.

Hiller, L., and R. A. Baker.1964. "ComputerCantata:An

Investigation of Compositional Procedure."Perspec-tives of New Music 3:62-90.

Hiller, L., and J.Cage. 1968. "HPSCHD:An InterviewbyLarryAustin." Source2(2):10-19.

Hiller, L., and L. M. Isaacson. 1959. ExperimentalMusic.New York:McGraw-Hill. (Recently reprintedbyGreenwood Press, Westport,Connecticut.)

Hiller, L., and R. Kumra.1979. "ComposingAlgorithmsII by Means of Change-Ringing." nterface 8: 129-168.

Kumra,R. 1973. "The Composition of Algorithms II witha Digital Computer."Technical report6. Buffalo,NewYork:SUNY, Department of Music.

Pierce, J.R. 1961. Symbols, Signals and Noise. NewYork:Harper,pp. 238-249.

Schenker,H. 1979. Free Composition, trans. and ed. E.

Oster. New York:Longman.

Hiller 21

Composing With Computers. A Progress Report by L.Hiller, 1981

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