Warren Burt: A Fig Tree (1990)

Abstract

"Fig Tree (In a Post-Coltrane Environment 1 / f is Too Highly Correlated) is the final movement of a ten-movement piece called Chaotic Research Music, written in 1989-90, in which I investigated many different ways of applying chaos theory to music. The title of this movement refers to my critique of some musical works which used a kind of random structure called 1/f weighted noise for structuring music. While it may be true that this kind of structure possesses fractal qualities, and some mathematicians have pointed out that the melodic structure of much traditional music resembles that of 1/f weighted noise, these factors alone are not enough to guarantee my musical interest. Since John Coltranes sheets of sound, let alone John Cages or Iannis Xenakiss work, I have wanted melodic material of greater complexity and unpredictability than that which possesses 1/f characteristics. The sound of music structured this way often sounds too predictable, too normal for my ears. For this piece, the Verhulst equation xnext = rx(l-x) was used to generate motives from three to eight notes long. These motives were used as templates to transpose the motives into different tempi, loudnesses and pitch levels so that the motives could be extended into phrases. The phrases were then extended into longer melodies and then assembled into canons using the same principles. All of these canons were then transposed into a set of microtonal scales which I invented in 1987, and the structure of all the harmonics of all the sounds in the piece were determined by the structures of the motives in their various scales. Six of the canons control simple tones made with a technique called additive synthesis, while the other six control samples of the motives themselves, played with their appropriate timbre and tuning. This was my most rigorous application of concepts of self-similarity to date, where every aspect of the piece, from the timbre to the large scale structure of the canons, was derived hierarchically from the same chaos-derived source. In live performance, I select which of the canons is playing at what time, improvisationally controlling both the textural and large scale harmonic motions of the piece. The end result of all these quasi-mathematical workings, however, is a surprisingly gentle piece, made of resonant bell tones, which again and again grows from melodic simplicity into textures of greater complexity, and then returns to its initial, simpler state." -- Warren Burt