Algorithmic Composition: Computational Thinking In Music
contributed articlesThe composer still composes but also getsto take a programming-enabled journey ofmusical discovery.By Michael gin MusicIn the West, the layman’s vision of the creative artist islargely bound in romantic notions of inspiration sacredor secular in origin. Images are plentiful; for example, aman standing tall on a cliff top, the wind blowing throughhis long hair, waiting for that particular iconoclastic ideato arrive through the ether.a Tales, some even true, ofgenii penning whole operas in a matter of days, furtherblur the reality of the usually slowly wrought process ofcomposition. Mozart, with his celebrated speed of writing,is a famous example who to some extent fits the cliché,though perhaps not quite as well as legend would have it.ba I’m thinking in particular of Caspar David Friedrich’s painting From the Summit in the HamburgKunsthalle.b Mozart’s compositional process is complex and often misunderstood, complicated by myth, especially regarding his now refuted ability to compose everything in his head15 and his own statements(such as “I must finish now, because I’ve got to write at breakneck speed—everything’s composed—58comm unication s of th e acm j u ly 2 0 1 1 vo l . 5 4 n o. 7Non-specialists may be disappointed that composition includes seemingly arbitrary, uninspired formalmethods and calculation.c What weshall see here is that calculation hasbeen part of the Western compositiontradition for at least 1,000 years, Thisarticle outlines the history of algorithmic composition from the pre- andpost-digital computer age, concentrating, but not exclusively, on how it developed out of the avant-garde Westernclassical tradition in the second half ofthe 20th century. This survey is moreillustrative than all-inclusive, presenting examples of particular techniquesand some of the music that has beenproduced with them.A Brief HistoryModels of musical process are arguably natural to human musical activity. Listening involves both the enjoyment of the sensual sonic experienceand the setting up of expectations andpossibilities of what is to come: musicologist Erik Christensen describedit as follows: “Retention in short-termbut not written yet” in a letter to his father, Dec.30, 1780). Mozart apparently distinguished between composing (at the keyboard, in sketches) and writing (preparing a full and finalscore), hence the confusion about the length oftime taken to write certain pieces of music.c For example, in the realm of pitch: transposition, inversion, retrogradation, intervallicexpansion, compression; and in the realm ofrhythm: augmentation, diminution, addition.key insights M usic composition has alwaysbeen guided by the composer’s owncomputational thinking, sometimeseven more than by traditionalunderstanding of inspiration. F ormalization of compositionaltechnique in software can free the mindfrom musical and cultural clichés andlead to startlingly original results. A lgorithmic composition systemscover all aesthetics and styles,with some open-ended variantsoffering an alternative to the fixed,never-changing compositions that formost of us define the musical limits.Illustratio n by St udio tonnedoi:10.1145/1965724.1965742
credi t t kj u ly 2 0 1 1 vo l . 5 4 n o. 7 c omm u n icatio n s of t he acm59
contributed articlesFigure 1. First part of Mozart’s Musikalisches Würfelspiel (“Musical Dice”): Letters overcolumns refer to eight parts of a waltz; numbers to the left of rows indicate possiblevalues of two thrown dice; and numbers in the matrix refer to bar numbers of four pagesof musical fragments combined to create the algorithmic 38716561135471473312541301010328371065Figure 2. Part of an advertisement for The Geniac Electric Brain, a DIY music-computer kit.memory permits the experience of coherent musical entities, comparisonwith other events in the musical flow,conscious or subconscious comparison with previous musical experiencestored in long-term memory, and thecontinuous formation of expectationsof coming musical events.”9This second active part of musicallistening is what gives rise to the possibility and development of musical form;composer György Ligeti wrote, “Becausewe spontaneously compare any new feature appearing in consciousness withthe features already experienced, andfrom this comparison draw conclusionsabout coming features, we pass throughthe musical edifice as if its construction60comm unication s of th e acmwere present in its totality. The interaction of association, abstraction, memory, and prediction is the prerequisitefor the formation of the web of relationsthat renders the conception of musicalform possible.”30For centuries, composers have taken advantage of this property of musiccognition to formalize compositionalstructure. We cannot, of course, conflate formal planning with algorithmictechniques, but that the former shouldlead to the latter was, as I argue here,an historical inevitability.Around 1026, Guido d’Arezzo (the inventor of staff notation) developed a formal technique to set a text to music. Apitch was assigned to each vowel so the j u ly 2 0 1 1 vo l . 5 4 n o. 7melody varied according to the vowelsin the text.22 The 14th and 15th centuries saw development of the quasi-algorithmic isorhythmic technique, whererhythmic cycles (talea) are repeated,often with melodic cycles (color) of thesame or differing lengths, potentially,though not generally in practice, leading to very long forms before the beginning of a rhythmic and melodic repeatcoincide. Across ages and cultures, repetition, and therefore memory (of shortmotifs, longer themes, and whole sections) is central to the development ofmusical form. In the Western context,this repetition is seen in various guises,including the Classical rondo (with section structures, such as ABACA); the Baroque fugue; and the Classical sonataform, with its return not just of themesbut to tonality, too.Compositions based on number ratios are also found throughout Westernmusical history; for example, Guillaume Dufay’s (1400–1474) isorhythmicmotet Nuper Rosarum Flores, writtenfor the consecration of Florence Cathedral, March 25, 1436. The temporalstructure of the motet is based on theratios 6:4:2:3, these being the proportions of the nave, the crossing, theapse, and the height of the arch of thecathedral. A subject of much debateis how far the use of proportional systems was conscious on the part of various composers, especially with regardsto Fibonacci numbers and the GoldenSection.d Evidence of Fibonacci relationships haas been found in, for instance, the music of Bach,32 Schubert,19and Bartók,27 as well as in various otherworks of the 20th century.25Mozart is thought to have used algorithmic techniques explicitly at leastonce. His Musikalisches Würfelspiel(“Musical Dice”)e uses musical fragments that are to be combined randomly according to dice throws (see Figure1). Such formalization procedures ared Fibonacci was an Italian mathematician(c.1170–c.1250) for whom the famous number series is named. This is a simple progression where successive numbers are the sumof the previous two: (0), 1, 1, 2, 3, 5, 8, 13, 21.Ascending the sequence, the ratio of two adjacent numbers gets closer to the so-calledGolden Ratio (approximately 1:1.618).e Attributed to Mozart though not officially authenticated despite being designated K. Anh.294d in the Köchel Catalogue of his works.
contributed articlesnot limited to religious or art music.The Quadrille Melodist, sold by Professor J. Clinton of the Royal Conservatoryof Music, London (1865) was marketedas a set of cards that allowed a pianist togenerate quadrille music (similar to asquare dance). The system could apparently make 428 million quadrilles.34Right at the outset of the computerage, algorithmic composition movedstraight into the popular, kit-builder’sdomain. The Geniac Electric Brain allowed customers to build a computerwith which they could generate automatic tunes (see Figure 2).36 Such systems find their modern counterpartin the automatic musical accompaniment software Band-in-a-Box (http://band-in-a-box.com/).The avant-garde. After World WarII, many Western classical music composers continued to develop the serialftechnique invented by Arnold Schönberg (1874–1951) et al. Though generally seen as a radical break with tradition, in light of the earlier historicalexamples just presented, serialism’sdetailed organization can be viewedas no more than a continuation ofthe tradition of formalizing musicalcomposition. Indeed, one of the newgeneration’s criticisms of Schönbergwas that he radicalized only pitchstructure, leaving other parameters(such as rhythm, dynamic, even form)in the 19th century.6 They looked tothe music of Schönberg’s pupil Antonvon Webern for inspiration in organizing these other parameters accordingto serial principles. Hence the rise ofthe total serialists: Boulez, Stockhausen, Pousseur, Nono, and others inEurope, and Milton Babbitt and hisstudents at Princeton.gSeveral composers, notably Xenakis(1922–2001) and Ligeti (1923–2006),f Serialism is an organizational system in whichpitches (first of all) are organized into so-called12-tone rows, where each pitch in a musicaloctave is present and, ideally, equally distributed throughout the piece. This technique wasdeveloped most famously by Schönberg in theearly 1920s at least in part as a response to thedifficulty of structuring atonal music, musicwith no tonal center or key (such as C major).g Here, we begin to distinguish between piecesthat organize pitch only according to the series(dodecaphony) from those extending organization into music’s other parameters—strictlyspeaking serialism, also known as integral ortotal serialism.Much of theresistance toalgorithmiccomposition thatpersists tothis day stemsfrom the misguidedbias thatthe computer,not the composer,composesthe music.offered criticism of and alternativesto serialism, but, significantly, theirmusic was also often governed by complex, even algorithmic, procedures.hThe complexity of new compositionsystems made their implementationin computer programs ever more attractive. Furthermore, developmentof software algorithms in other disciplines made cross-fertilization rife.Thus some techniques are inspiredby systems outside the realm of music (such as chaos theory (Ligeti, Désordre), neural networks (Gerhard E.Winkler, Hybrid II “Networks”),39 andBrownian motion (Xenakis, Eonta).Computer-BasedAlgorithmic CompositionLejaren Hiller (1924–1994) is widelyrecognized as the first composer tohave applied computer programs toalgorithmic composition. The use ofspecially designed, unique computerhardware was common at U.S. universities in the mid-20th century. Hillerused the Illiac computer at the University of Illinois, Urbana-Champaign, tocreate experimental new music withalgorithms. His collaboration withLeonard Isaacson resulted in 1956in the first known computer-aidedcomposition, The Illiac Suite for StringQuartet, programmed in binary, andusing, among other techniques, Markov Chainsi in “random walk” pitchgeneration algorithms.38Famous for his own random-process-influenced compositions, if nothis work with computers, composerJohn Cage recognized the potentialof Hiller’s systems earlier than most.The two collaborated on HPSCHD,a piece for “7 harpsichords playingrandomly-processed music by Mozart and other composers, 51 tapesof computer-generated sounds, approximately 5,000 slides of abstracth For a very approachable introduction to themusical thought of Ligeti and Xenakis, seeThe Musical Timespace, chapter 2,9 particularlypages 36–39.i First presented in 1906, Markov chains arenamed for the Russian mathematician AndreyMarkov (1856–1922), whose research into random processes led to his eponymous theory,and today are among the most popular algorithmic composition tools. Being stochasticprocesses, where future states are dependenton current and perhaps past states, they areapplicable to, say, pitch selection.j u ly 2 0 1 1 vo l . 5 4 n o. 7 c omm u n icatio n s of t he acm61
contributed articlesdesigns and space exploration, andseveral films.”16 It premiered at theUniversity of Illinois, Urbana-Champaign, in 1969. Summarizing perspicaciously an essential differencebetween traditional and computerassisted composition, Cage said inan interview during the composition of HPSCHD, “Formerly, whenone worked alone, at a given point adecision was made, and one went inone direction rather than another;whereas, in the case of working withanother person and with computerfacilities, the need to work as thoughdecisions were scarce—as though youhad to limit yourself to one idea—isno longer pressing. It’s a change fromthe influences of scarcity or economyto the influences of abundance and—I’d be willing to say—waste.”3Stochastic versus deterministic procedures. A basic historical division inthe world of algorithmic compositionis between indeterminate and determinate models, or those that use stochastic/random procedures (such as Markov chains) and those where resultsare fixed by the algorithms and remainunchanged no matter how often the algorithms are run. Examples of the latter are cellular automata (though theycan be deterministic or stochastic34);Lindenmayer Systems (see the sectionon the deterministic versus stochasticdebate in this context); Charles Ames’sconstrained search algorithms for selecting material properties against aseries of constraints1; and the compositions of David Cope that use hisExperiments in Musical Intelligence system.10 The latter is based on the con-Algorithmiccomposition is oftenviewed as a sidelinein contemporarymusical activity,as opposed to alogical applicationand incorporationof compositionaltechnique intothe digital domain.Figure 3. Simple L-System rules.1 232 133 21Figure 4. Step-by-step generation of resultsfrom simple L-System rules and a seed.Seed: 21323 2113 21 13 2323 21 13 23 23 21 13 2162comm unicati ons o f t he acm j u ly 2 0 1 1 vo l . 5 4 n o. 7cept of “recombinacy,” where new music is created from existing works, thusallowing the recreation of music in thestyle of various classical composers, tothe shock and delight of many.Xenakis. Known primarily for his instrumental compositions but also as anengineer and architect, Iannis Xenakiswas a pioneer of algorithmic composition and computer music. Using language typical of the sci-fi age, he wrote,“With the aid of electronic computers,the composer becomes a sort of pilot:he presses buttons, introduces coordinates, and supervises the controls ofa cosmic vessel sailing in the space ofsound, across sonic constellations andgalaxies that he could formerly glimpseonly in a distant dream.”40Xenakis’s approach, which led to theStochastic Music Programme (henceforthSMP) and radically new pieces (such asPithoprakta, 1956), used formulae originally developed by scientists to explainthe behavior of gas particles (Maxwell’sand Boltzmann’s Kinetic Theory ofGases).31 He saw his stochastic compositions as clouds of sound, with individual notesj as the analogue of gasparticles. The choice and distributionof notes was determined by proceduresinvolving random choice, probabilitytables weighing the occurrence of specific events against those of others. Xenakis created several works with SMP,often more than one with the output ofa single computer batch process,k probably due to limited access to the IBM7090 he used. His Eonta (1963–1964) fortwo trumpets, three tenor trombones,and piano was composed with SMP. Theprogram was applied in particular to thecreation of the massively complex opening piano solo.Like another algorithmic composition and computer-music pioneer,Gottfried Michael Koenig (1926–), Xenakis had no compunction adaptingthe output of his algorithms as he sawfit. Regarding Atrées (1962), Xenakis’sbiographer Nouritza Matossian claimsXenakis used “75% computer material,jNotes are a combination of pitch and duration, rather than just pitch.k Matossian wrote, “With a single 45-minuteprogram on the IBM 7090, he [Xenakis] succeeded in producing not only eight compositions that stand up as integral works but alsoin leading the development of computer-aidedcomposition.”31
contributed articlescomposing the remainder himself.”31At least in Koenig’s Projekt 1 (1964)l Koenig saw transcription (from computeroutput to musical score) as an important part of the process of algorithmiccomposition, writing, “Neither the histograms nor the connection algorithmcontains any hints about the envisaged,‘unfolded’ score, which consists of instructions for dividing the labor of theproduction changes mode, that is, thedivision into performance parts. Thehistogram, unfolded to reveal the individual time and parameter values, hasto be split up into voices.”24Hiller, on the other hand, believedthat if the output of the algorithm isdeemed insufficient, then the programshould be modified and the outputregenerated.34 Several programs thatfacilitate algorithmic composition include direct connection to their ownor to third-party computer sound generation.m This connection obviates theneed for transcription and even hinders this arguably fruitful intervention.Furthermore, such systems allow thetraditional or even conceptual score tobe redundant. Thus algorithmic composition techniques allow a fluid andunified relationship between macrostructural musical form and microstructural sound synthesis/processing,as evidenced again by Xenakis in hisDynamic Stochastic Synthesis programGendy3 (1992).40More current examples. Contemporary (late 20th century) techniquestend to be hybrids of deterministicand stochastic approaches. Systemsusing techniques from artificial intelligence (AI) and/or linguistics are thegenerative-grammarn-based system BolProcessor software4 and expert systems(such as Kemal Ebcioglu’s CHORAL11).Other statistical approaches that use,say, Hidden Markov Models (as in Jordanous and Smaill20), tend to need asignificant amount of data to train thesystem; they therefore rely on and generate pastiche copies of the music of aparticular composer (that must be codilWritten to test the rules of serial music but involving random decisions.23m Especially modern examples (such as Common Music, Pure Data, and SuperCollider).n Such systems are generally inspired by Chomsky’s grammar models8 and Lerdahl’s andJackendorff’s applications of such approachesto generative music theory.28Figure 5. Larger result set from simple L-System 12311323fied in machine-readable form) or historical style. While naturally significantto AI research, linguistics, and computer science, such systems tend to beof limited use to composers writing music in a modern and personal style thatperhaps resists codification becauseof its notational and sonic complexityand, more simply, its lack of sufficientand stylistically consistent data—theso-called sparse-data problem. But thisis also to some extent indicative of thegeneral difficulty of modeling languageand human cognition; the softwarecodification of the workings of a spokenlanguage understood by many and reasonably standardized is one thing; thecodification of the quickly developingand widely divergent field of contemporary music is another thing altogether.Thus we can witness a division betweencomposers concerned with creatingnew music with personalized systemsand researchers interested in developing systems for machine learning andAI. The latter may quite understandablyfind it more useful to generate musicin well-known styles not only becausethere is extant data but also becausefamiliarity of material simplifies someaspects of the assessment of results.Naturally though, mor
Algorithmic Composition Lejaren Hiller (1924–1994) is widely recognized as the first composer to have applied computer programs to algorithmic composition. The use of specially designed, unique computer hardware was common at U.S.
What problems have beginners in learning algorithms/programming? Give some examples why algorithmic thinking is useful in other subjects/daily life Try to give a definition of Algorithmic Thinking : Title: Learning Algorithmic Thinking with Tangible Objects Eases Transition to Computer Programming
Computational thinking is thinking like a computer scientist, the kind of thinking absolutely required to formulate computational solutions to algorithmic problems. Aristotle wrote, “For things we have to learn before we can do them, we learn by doing . 1.3 Algorithmic Thinking is a Subset of Computation
about it is based on the following 5 themes1: algorithmic thinking, evaluation, generalisation, abstraction and decomposition. Let’s look at each area in turn and at the sub-skills and techniques that they comprise of. Algorithmic thinking Algorithmic thin
Mostly, algorithmic composition is a field that combines computer science and music. However, in general algorithmic composition is an example of generative art. Instead of music, one can create text, images, videos, anything using a similar approa
“algorithmic” from “software” has been also reflected in media studies. [2] “Drawing on contemporary media art practices and on studies of visual and algorithmic cultures, I would like to develop the idea of algorithmic superstructuring as a reading of aest
Algorithmic Trading Table: Proportions of trading volume contributed by di erent category of algorithmic and non-algorithmic traders in the NSE spot and equity derivatives segment (for the period Jan-Dec 2015) Custodian Proprietary NCNP Total Spot Market Algo 21.34% 13.18% 7.76% 42.28% Non-
aforementioned model. Thus, the Triangulation Algorithmic Model is provided and defined to aid in understanding the process of measurement instrument construction and research design. The Triangulation Algorithmic Model for the Tri-Squared Test The Algorithmic Model of Triangulation is of the form (Figure 2). Where,
Introduction to Literary Criticism. Definition and Use “Literary criticism” is the name given to works written by experts who critique—analyze—an author’s work. It does NOT mean “to criticize” as in complain or disapprove. Literary criticism is often referred to as a “secondary source”. Literary Criticism and Theory Any piece of text can be read with a number of different .
