I have been experimenting with writing a program to generate musical compositions algorithmically. The current version is based on papers by Christopher Dobrian, John Fitch and Jeremy Leach.
The program that created the above examples is designed foremost to impose form through repetition at multiple structural levels. Rhythm is created though such repetition and through fairly crude variations of note lengths in relation to a steady pulse. The examples are, I believe, all in C major, but the program makes no attempt to start or end on the tonic or any C major chord tone. It is entirely unaware of any harmonic or tonal considerations beyond which notes constitute the scale. A trivial modification to the program produces works in the twelve-tone chromatic scale which are not appreciably different except for a different "coloration". Some of the examples may in fact be chromatic, I do not recall for certain.
I will not claim that results are great music, but I believe that they are musical, somewhat interesting, and successfully avoid the formless and wandering quality that is found in many algorithmic works. This is in stark contrast to an earlier program based on Schenkerian theory that ignored form (examples in the "schenkerian" subdirectory). The results, which were harmonized, sounded interesting for a very short while, but very soon the lack of repetition became irritating. The result was akin to an aimless wandering improvisation. In the absence of thematic repetition, the Schenkerian linear motions and the harmonic structure were unable to supply a sense of direction or purpose. Your opinion may differ.
The current program also suffers to a lesser extent from the lack of a sense of direction, the bane of all algorithmic music. I believe that this is due to insufficient contrasts between formal sections (to provide, through more change, more of a sense of having gone somewhere) and due to insufficient effort to ensure return in various musical parameters. Currently return is imposed merely by a probabilistic slant towards ABA structures and substructures.
Writing music-composition programs has been an extremely valuable exercise in understanding what makes music work. When writing music oneself, one relies to a large extent on unconscious intuition. A music-composing program has no intuition; it can only work on the explicitly formulated knowledge of music that one has programmed into it. This provides a method to experimentally test musical theories; one uses them to write a program and then sees if the results work.
Sadly, most work on algorithmic composition, indeed most experimental music in general, ignores this last step of "seeing if the results work". Instead the usual tact is to modify ones sense of aesthetics to match the results, which are usually lacking. This applies equally to both pretentious art music and typical hobbyist "fractal music". As a result, we learn nothing about music or ourselves from the experience.
The pursuit of such an experimental method has made me realize that the bulk of traditional and contemporary music theory is severely lacking. Music theory is in general overwhelming obsessed with aspects of pitch. This is true of modern atonal theory and Schenkerian analysis as well as more traditional theory. Simply contrast the number of works on the subject of harmony with the number on the subject of rhythm.
In reality, pitch is a very subordinate aspect of music. Rhythm and form (by which I mean the structure of repetition and change) are the decisive factors. One can write interesting music in a purely percussive idiom. One cannot write interesting music without rhythm or form. Music without rhythm and form would be ametrical at all levels, with change occurring randomly at random times. It would be pointless, wandering, and ultimately boring.
Pitch-obsessed music theory is often in contradiction with the findings of psychology.
Serialism is based on structures of pitch relation which experiments (as well as the personal experiences of many) have repeatedly shown to be "cognitively opaque" (Lerhahl and Jackendoff) and essentially unperceivable. To the extent that such music is interesting, I claim that it is due to rhythmic and formal structure intuitively composed into the music and has little or nothing to do with the tone rows and serial structure which is its supposed basis. Such music can often be understood simply as percussive music performed on pitched instruments. The pitches are for the most part simply irrelevant. Disclaimer: I must admit that I am not enormously knowledgeable or even very interested in this style of music.
Schenkerian theory posits that tonal music derives its sense of goal-directedness from deeply embedded long-range linear pitch motions. Leaving aside the question as to whether or not even a trained listener can hear these motions underneath the multiple layers built on top of them, experiments show that linear pitch motions simply do not create a sense of implication (Schellenberg). Given a partial linear pitch motion the most-implied next tone is a repetition on the final tone, not a continuation of the motion.
Schenkerian and traditional theory also posit that the return to the original key at the end of a large work provides a sense of closure and return. . In shorter works and shorter portions of a large work, this seems valid. However, few people possess absolute pitch and the average untrained person has a sense of relative pitch accurate only to within about a semitone or two, even over short time scales. Also, psychology has repeatedly shown that people have a limited working memory. How then is an average listener with mediocre relative pitch supposed to accurately remember an initial tonic for the twenty minute length of a long piece, despite all of the confusion of multiple modulations to distant keys, and be able to accurately compare it to the final cadence? Clearly, they cannot, and they probably cannot even with intense concentration. Furthermore, I think it is fair to say that the uneducated listener is not even aware that they are supposed to. Instead they typically are aware of thematic repetition, as well as conventional closing formulae.
Dobrian, C. 1995. "Algorithmic Generation of Temporal Forms: Hierarchical Organization of Stasis and Transition." Proceedings of the 1995 International Computer Music Conference.
Fitch J., and Leach J. Summer 1995. "Nature Music and Algorithmic Composition." Computer Music Journal 19(2):23-33.
Fitch J., and Leach J. 1995. "The Application of Differential Equations to the Modeling of Musical Change." ICMC '95: Digital Playgrounds440-443. ICMA and Banf Centre for the Arts.
Leach J. 1995. "Algorithmic Composition as Gene Expression Based on Fundamentals of Human Perception."XI Colloquium on Musical Informatics 7-10. Universita degli Studi di Bologna.
Leach J. 1996. "Making Sense of the World: Temporal & Spatial Perception and the Function of Art." Proceedings of the Second International Symposium - Creativity and Cognition 1996" 176-183. LUTCHI Research Centre.
Leach J. 1996. "Towards a Universal Algorithmic System for Composition of Music and Audio-Visual Works." On the Edge 320-323. ICMA and HKUST.
Lerdahl, F., and Jackendorff, R. 1983. A Generative Theory of Tonal Music. Cambridge, Massachusetts: MIT Press.
Salzer, F. 1962. Structural Hearing: Tonal Coherence in Music. New York, New York: Dover Publications.
Schellenberg, E. Spring 1997 "Simplifying the Implication-Realization Model of Melodic Expectancy." Music Perception14(3):295-318.
Cooper, G., and Meyer, L. 1960. The Rhythmic Structure of Music. Chicago, Illinois: University of Chicago Press.
Cope, D. 1991. Computers and Musical Style. Madison, Wisconsin: A-R Editions.
Cope, D. 1996. Experiments in Musical Intelligence. Madison, Wisconsin: A-R Editions.
Helmholtz, H. 1954. On the Sensations of Tone. New York, New York: Dover Publications.
Lerhdahl, F. 1987 "Timbral Hierarchies" Contemporary Music Review 2:135-160.
Lerhdahl, F. 1988 "Tonal Pitch Space" Music Perception 5(3):315-350.
Rameau, J. 1971. Treatise on Harmony. New York, New York: Dover Publications.
Sethares, W. 1999. Tuning, Timbre, Spectrum, Scale. London, Great Britain: Springer-Verlag.