When I started learning about computer music in 1984, I became interested in the challenge of trying to program the computer to compose music. My first piece of computer music was an experiment in algorithmic composition focusing on automated composition of metric modulations. Since a metric modulation is essentially a mathematical operation, it seemed reasonable that a computer could calculate and perform such tempo changes more readily than humans. So I set out to write a computer program that would compose and synthesize music that included metric modulations.

The problem that I immediately confronted, though, is how to establish a clear sense of tempo and beat for the listener that would be musically interesting. It’s one thing to use standard Western notation to compose metric modulations on paper, but when there’s no paper or notation involved, and no human performers to add inflection to the music, it’s another thing to figure out exactly how to make the beat evident to the listener so that the metric modulation would be clearly audible.

I was obliged to answer the question, usually taken for granted by musicians, “What are the factors that give us a sense of beat?” The most obvious one is that things happen periodically at a regular rate somewhere roughly in the range of walking/running speed, say from 48 to 144 beats per minute. But music consists of more than simply a single constant rhythm, it contains a wide variety of rhythms. So how do we derive the beat? We use other factors that exhibit regularity such as dynamic accent (loudness), timbral accent (choice of instrument, brightness), melodic contour (a repeating shape), harmonic rhythm (implied chord changes), and harmonically-related beat divisions (triplets, sixteenths, quintuplets, etc.), and we take all of those into consideration simultaneously to figure out rates of repetition that might be considered the beat. (There are also stylistic considerations; we may be familiar with a body of works that all belong to the same style or genre, so that we have established cultural cues about where the beat is considered to be in that type of music.)

So I wrote a program in C that composed phrases of music, and that made probabilistic decisions along the way about how to modulate to a new harmonically-related tempo using beat divisions of the same speed in each tempo. It used factors of melodic contour, dynamic accent, and timbral accent to provide a sense of periodicity. (It incidentally also used continuously changing pitch ranges and continuously changing tuning systems, so that the music has a unique inharmonic character.) The program produced a type of musical score for each phrase of music, a time-tagged list of notes that would be used in the Cmusic sound synthesis language to synthesize the notes on a VAX 11/780 (Unix) computer and store the results in a sound file. (The sampling rate was a mere 16 kHz, but that was barely adequate for the sounds being synthesized.)

The composition was titled Degueudoudeloupe (1985), a nonsense word I thought was evocative of the kinds of sounds and rhythms in the piece. The sounds in the piece are string-like, drum-like, and bell-like sounds synthesized using two methods:  Karplus-Strong synthesis and Frequency Modulation synthesis.

In another composition several years later I again used probabilistic computer decision making to compose time-tagged lists of notes, this time intended to be transmitted as MIDI note data to a Yamaha Disklavier computer-controlled piano. The program was written in the C language, and the MIDI data that that program produced was saved as a MIDI file on a Macintosh Plus computer and transmitted to the Disklavier.

The piece is titled Entropy (1991), and was largely inspired by the following passage from The Open Work by Umberto Eco:

Consider the chaotic effect (resulting from a sudden imposition of uniformity) of a strong wind on the innumerable grains of sand that compose a beach: amid this confusion, the action of a human foot on the surface of the beach constitutes a complex interaction of events that leads to the statistically very improbable configuration of a footprint. The organization of events that has produced this configuration, this form, is only temporary: the footprint will soon be swept away by the wind. In other words, a deviation from the general entropy curve (consisting of a decrease in entropy and the establishment of improbable order) will generally tend to be reabsorbed into the universal curve of increasing entropy. And yet, for a moment, the elemental chaos of this system has made room for the appearance of an order…

The composition was conceived as a vehicle with which to explore ideas of information theory and stochasticism in an artistic way. It explores the perception of randomness and order (entropy and negentropy) in musical structure, and demonstrates the use of stochasticism not only as a model for the distribution of sounds in time, but also as a method of variation of a harmonic “order”.

The notes of this piece were all chosen by a computer algorithm written by the composer. The algorithm takes as its input a description of some beginning and ending characteristics of a musical phrase, and outputs the note information necessary to realize a continuous transformation from the beginning to the ending state. Such a transformation can take place over any period of time desired by the composer (in this piece anywhere from 3 to 90 seconds). The input description is stated in terms of relative probabilities of different musical occurrences, thus allowing the composer to describe music which ranges between totally predictable (negentropic) and totally unpredictable (entropic), and which can transform gradually or suddenly from one to the other.