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The Role of Computer Technology in Music and MusicologyIntroductionTechnology has followed a path parallel to the development of music. From early pipes with cross holes, embouchures and reeds to the fine mechanics of 19th century pianos and wind instruments, passing through medieval carillons and renaissance string instruments, music has never been shy about incorporating the latest developments of technological discoveries. This is especially true for contemporary electronic and computing devices, because, if the computer can be seen as the ultimate instrument capable of reproducing any known sound and of generating new ones, it is also a machine for the manipulation of symbols that can assist a composer or a musicologist in practical activities and in theoretical studies. And while electronic computers are a relatively modern invention, the idea behind algorithmic procedures and programming is probably as old as mathematics and known in the ancient worlds of Egypt, Babylon, Greece. This writing is a collection of examples to show, in a historical progression, how computer technology (like any technology) has already significantly contributed to music and musicology, and supports the thesis that modern applications of programming, artificial intelligence and the like, to music, follow a well established and ancient tradition. Recent times have seen the development of two significant aspects of computing technology: the availability of inexpensive, good quality sound processors and synthesizers, which have bridged the gap between ancient subdivisions of computer music, one preoccupied with sound synthesis, and the other with algorithmic and musicological processes - thus allowing immediate reproduction of computer generated music; and the emergence of standards [reference IEEE CS], such as MIDI and SMDL, that allow easy encoding, reproduction and exchange of musical data. Without these, the examples described below would have hardly been possible. Early contributions: Dice Game
Experimental Music and the Illiac SuiteIt is generally recognized that the first piece of music actually written by an electronic computer is the Illiac Suite in 1956, so titled in honor of the Illinois Automatic Computer, built at the same university at Urbana-Champaign, one the first high-performance computers [reference Hiller]. The Illiac Suite is an experiment to test various algorithms for composition. It can be said that it does not aim to be, in a strict sense, "great" or "beautiful" music, but a clever utilization of a computing machine to see which musical effects a certain rule produces. It consists of four movements, called experiments: the first is about the generation of cantus firmi, the second generates four-voice segments with various rules, the third deals with rhythm, dynamics and playing instructions, and the fourth with various models and probabilities for generative grammars or Markoff Chains. Consider for example Experiment 2. It consists of eight sections, subdivided in two segments each, with random dynamics. Each section introduces a new counterpoint rule, in the following order (reprinted from Hiller):
Listening to the piece confirms the impression of randomness generally associated with computing machinery, notoriously incapable of grasping and conceiving a whole out of local details. Nevertheless, there is some merit in how, slowly, the music converges to something resembling 17th century music. The idea must have seemed fascinating, over forty years ago, that after century of dreams a machine has become available with unlimited possibilities for testing hypotheses. And testing hypotheses, from Bach to Schönberg, is also what music, and especially musicology, is about. Thus again, the Illiac Suite, in spite of its "modernity", "computer age" features, mathematical procedures,is nothing but a continuation of a tradition to which a new technology has been added. Harmonization of the Unfigured BassThe technology of Artificial Intelligence, a discipline of the mid-fifties with the goal of constructing "intelligent" machines, brought about among others the language LISP, one of the first to express in an elegant and concise way operations on symbols - instead of on numbers as in FORTRAN - as well as dynamic data structures of unlimited length for searches the depth of which is not known beforehand. Symbols can be defined as entity with non-numerical quality, such as notes, chords and the like, hence operators can represent construction of intervals, key transposition and the like.
The fundamental idea was that, to overcome the random feeling of typical computer music as in the Illiac Suite, a a contextual framework, at least at some level, is needed by a computing system, such as the one provided by tonal classical harmony. However, harmony is more like a language learnt by examples and rules about what-not-to-do than a procedure, hence it was felt that a formal treatment in the form of algorithms was needed - there is perhaps some parallelism with natural language processing, in spite of serious differences, which has been treated elsewhere [reference Baggi and Negrotti, 1997]. In the same path, modern interactive, window-based computers have allowed completion of projects in which harmonic constraints in symbolic form have become easy to program and to use[reference Cope].
The Paul Glass MethodThe theoryIn his study in dodecaphony, composer Paul Glass hit the series c - b - c# - b which has some remarkable properties: it is invariant under retrogression sounding the same if played backwards, and it contains all decaphonic intervals from 1 to 6 (semitones), from one note to its next, exactly twice. It is therefore the candidate for a composition with the least possible reference to diatonic intervals and tonal centers. Moreover, and this is the basis of his new system of composition, each note of the series can be seen as the tonic of a diatonic scale (e.g., a major scale with seven notes and no alterations) such that, by proper choice of the order of the notes, the sequence of these twelve 7-note keys becomes at the same time a sequence of seven 12-note dodecaphonic series.
Paul Glass proved therefore by construction that there is at least one series of 12 keys that satisfies these constraints. Obviously its inversion, namely c - c# - b - d - b satisfies them too and enjoys the same properties of invariance and completeness of intervals. It less obvious to see that the chromatic scale, namely c - c# - d - d# - e - f - f# - g - g# - a - a# - b also gives rise to a Glass sequence of 84 notes like the above (tough it contains only one interval, the semitone, throughout, from a note to the next). Hence, counting also the inversion of the chromatic scale, there exist at least four Glass sequences. Even less obvious is the fact that, at any point where there is a choice of keys, some choices do not generate a complete sequence. For instance, in the case described in detail above, starting with C-major one could in theory choose F# as he next key, since it contains all five sharps, however the process pretty soon stops and it is necessary to go back and choose either the key of B or of C# - a process known in computer science as backtracking, which means taking another upper branch for the depth search. Hence the question by Glass was: are there any other series of this kind? If so, which ones, and how many? And are there some with properties such as symmetry and completeness of intervals (at least once)? To answer such questions, a program in the language LISP has been written by this author in 1985, with primitives such as key computation from given notes, knowledge of the chromatic scale, of intervals and the like (it is easy to define such operators in LISP, which then work like built-in operators for arithmetic operations in other languages, but operate on symbols, in this case musical notes, instead of on numbers). The main algorithm is a loop to find all twelve keys in a sequence that satisfy all constraints, that backtracks in case of failure, and this for all possible sequences. The interesting, and somewhat unexpected, result is the following:
It is remarkable that such numbers are made only of the first primes, 2,3,5 and 7, suggesting that there is some deep numerological, or geometric explanation for the method. As the type of key to work upon - e.g., the musical mode is an input to the algorithm, the search has been made for other modes, with any number of notes, and has yielded the following interesting result: Glass sequences exist only for the seven Greek modes, Ionian, Dorian, Phrygian, Lydian, Mixolydian, Eolian, and Locrian (in other words, for 7-note sequences obtained by playing only the white keys of piano, from any key) - of which Dorian is the "king" mode closed under the operation of inversion and retrogression; and the sequencs are the same no matter which mode one chooses! Obviously this is in agreement with the rules of Glass sequences that, within a key, any order for the notes can be chosen. Hence there is no convergence (no Glass sequence) for any altered scale, such as the harmonic minor mode, the ascending melodic minor, nor for any mode with a number of notes different from 7. It seems that Glass sequences, used to construct dodecaphonic sequences, curiously underline an important property of diatonic scales - e.g, only scales with one sequence of two tones and one with three tones, separated by one semitone, can be used to generate Glass sequences. Glass sequences in compositionThe existence of Glass sequences, it is claimed, has important consequences for a composer, because they allow definition and concatenation of dodecaphonic series that smoothly blend from one to the next. Namely, as Schenker's theory for tonality, it provides a method for composing and consistently plan the overall structure of an atonal piece. Prior to the discovery of all possible series by computer, Paul Glass had already used the series of above as the scheme in various compositions - the series is now labeled as no. 866 in the Baggi-Glass catalog. Here follows a list, by no means complete, of examples of compositions by Paul Glass based on this method, together with the associated series:
This example, unlike the preceding and the following ones, is not just a theoretical study in musicology, but a project which has actually helped a real composer to define his methodology and apply the results in his pieces. NeurSwing, an automatic Jazz rhythm sectionThis is another example of synthetic musicology, namely the investigation of a musicological problem thanks to a machine constructed for that purpose. Unlike classical music, the musical merit of a piece of Afro-american Jazz is not really contained in its harmony - relatively simple - , in its melody - often improvised -, in its rhythmic variety - jazz pieces come often only in 4/4 and segments of four measures, sometimes in 6/8, rarely in 5/4 or 7/4 - or in the "purity" of instrumental and vocal sounds - more often than not, these are distorted and personalized on purpose -, but in how well all these elements contribute to the generation of swing. Swing is the blood of jazz, its real medium, through which the jazzman, rather than "making music", "tells a story": as such, it expresses both intellectual elements - the artistic quality of the story - and physical ones, as the push on rhythm - that which makes people want to dance, move or tap their feet, for instance. This is why the score, from which in theory a piece of classical music can be reconstructed (or at least the intention of the composer can be understood at some level) has little meaning in jazz, as swing cannot be annotated: only recordings, from the first acoustical records of 1917 to modern digital recording, can capture swing and allow the establishment of a jazz musicology. While swing is close to impossible to define, as it evolves and changes throughout jazz history - sometimes taking the form of heavy rhythm accents, sometimes the exact opposite - there are technicalities that can be isolated within a given stylistic period: for instance, the constant opposition of a reference pulsation, often irregular, generated by the rhythm section consisting of, say, piano, bass and drums, and the free floating, improvised line by a soloist, say a saxophonist. It is possible, therefore, to isolate accents and rhythmic embellishments at the melodic level, to use rhythmic and harmonic patterns in putting down piano chords, appoggiaturas by the bass and drum rolls, accents and emphasis on the afterbeat by the drums, to generate swing.
The musicological study can be performed at various levels of machine interaction: first, by changing the setting of the stylistic knobs, which allow possibilities in the order of {infinite to the third power}; second, by altering the stylistic net, namely the dependencies, or membership constants of the stylistic elements that belong to corresponding fuzzy sets; third, by changing the substitution tables for harmony and the tables of the rhythmic patterns. This way, a deeper understanding of the technical elements of swing is possible, or at least, as in the case of the Illiac Suite, an analysis of what effect does a rule cause. At the practical level, the machine can be used as a training tool by a would-be jazz performer. Learning alone is not efficient, as one tends to speed up at easier passages and slow down at difficult ones, while swing requires perfect mastery of tempo - more so than in classical music. Learning with a metronome does not allow the interaction provided by a dynamically changing rhythm section, and learning from records of rhythm sections is repetitive and inflexible, as no change of tempo and of key, nor any repetition of isolated and difficult passages, are possible. NeurSwing has been used to learn improvisation of jazz pieces, first with full as-is parameter and slow tempos, then with a higher free value and further with higher hot values, when pianist and bassist push forward with denser structures and the drummer accelerates. It can be used therefore as a teaching machine, as it can tirelessly simulate the operation of a rhythm section, with adequate performance to make a serious study possible. ConclusionsThe examples of above represent by no means an exhaustive list of contributions of computer technology to music and musicology. They have been chosen because they illustrate various aspects of interdisciplinary endeavors: from the early studies of Mozart and Haydn to the "ancient" - in regard to history of computing - Illiac Suite, to three projects by this writer of symbol manipulation dealing, respectively, with tonal harmony, dodecaphony and elements of jazz style. No doubt other examples could have been chosen, as a quick examination of the specialized literature would easily show, including studies promoted by the IEEE CS Technical Committee on Computer Generated Music [reference IEEE CS]. What however seems to be common to all these efforts is that computer technology, far from being the "villain" and "soulless", "cold" monster of popular mythology, has already assisted music and musicology and will continue to do so for a long time to come. This project at the Scala is one of the best illustrations of what has been referred to as Computer Generated Music, an interdisciplinary approach that contains the vast area spanning from artistic music obtained with the help of computers to audio signal processing, with the extremes included. The projects deals with material science for the restoration and preservation of tapes, such as cleaning, baking, strengthening the support; with signal processing for the audio treatment, removal of noise and hiss and recreation of the spectral balance; with esthetic criteria, to decide how to restore false starts, missing musical material, removal of pops, clicks and hum; with musicological criteria, to classify and order all the material; with computing techniques, for the construction of the data base and of its access keys, including musical keys obtained from whistling and humming a few notes to find a matching music piece; and also with legal matters, such as who is the rightful owner of a recorded piece, the performer, the theater, or who recorded it, who restored it, and the like; and certainly other disciplines not mentioned above. In conclusive words, these are projects that require as much love for technology as is needed for music. They clearly illustrate the common bond between technology and music and will help spread the message of how the deep relationship between science and art is beneficial to both, as it was in the Renaissance and as it is more and more so today. ReferencesBaggi, Denis L., Realization of the Unfigured Bass by Digital Computer, Ph.D. Thesis, University of California, Berkeley. Published by Xerox University Microfilms, Ann Arbor, Michigan, 1974. Baggi, Denis L., Neurswing: An Intelligent Workbench for the Investigation of Swing in Jazz, in Readings in Computer Generated Music, D.Baggi, Editor, IEEE CS Press, Los Alamitos, 1992. Baggi, Denis L. and M. Negrotti, Musica, linguaggio matematico e intelligenza artificiale, invited paper in Convegno Musica: le ragioni delle emozioni, Conference of the Associazione Nuova Civiltà delle Macchine, May 28, 1997, reprinted in Display, Dipartimento dell'istruzione e dalla cultura, divisione della scuola, centro didattico cantonale, Bellinzona, Switzerland, Feb. 10, 1998.
Cope, David, Recombinant Music: Using Computer to Explore Musical Style, IEEE Computer, July 1991, pp. 22-28. Haydn, Joseph, Giuoco Filarmonico, ossia maniera facile comporre minuetti, G.Ricordi & C., Milan, Italy, N.108202. Hiller, Lejaren A., and Leonard M. Isaacson, Experimental Music: Composition With an Electronic Computer, McGraw-Hill, New York, 1959.
IEEE CS, Technical Committee on Computer Generated Music of the Computer Society of the Institute of Electric and Electronic Engineers (IEEE CS TC on CGM), see http://www.computer.org/tab/cgm/tc_cgm.htm and in particular the CD-ROM Standards in Computer Generated Music. Mozart, Wolfgang A., Musikalisches Würfelspiel, K.Anh. 294d, Mainz, Schott's Söhne, Edition 4474. Pedron, Carlo, Nuova serie di esercizi per lo Studio Progressivo del Basso senza numeri, Carish, Milan, Italy, N.14847. Rothgeb, John E., Harmonizing the Unfigured Bass: A Computational Study, Ph.D. Thesis, Yale University. Published by Xerox University Microfilms, Ann Arbor, Michigan, 1968. Slagle, James R., A Heuristic Program That Solves Symbolic Integration Problems in Freshman Calculus, in Feigenbaum, Edward A., and Julian Feldmann, Computers and Thought, McGraw-Hill, New York, 1963, pp.191-203. Also in Slagle, J.R., Artificial Intelligence: The Heuristic Programming Approach, McGraw-Hill, New York, 1971, pp.53-57. ***************************************************************** Denis L. Baggi December 9, 1998 |
The harmonization of the unfigured bass
is an example of the use of early LISP in batch mode [
- d - a - e
The figure illustrates how that works, by
grouping, above, the twelve notes of each series and below those
of each key. Let us start with the key of C-major, which contains
the notes c-d-e-f-g-a-b. To complete the dodecaphonic series,
one needs the extra five notes c#, d#, f#, g# and a#, which are
contained in the keys of B, C# and F#. Assume we choose the key
of B to complete series 1. Then there are two extra notes, namely
e and b, which spill into series 2. Hence series 2 must be made,
among others, of a key which does not already contain e and b:
C# is such a key. This gives nine notes for series 2, which now
needs notes d, g and a to be complete: B
