Music

"Heisenberg" from "God does not play dice!" (1994)
for live-interactive MIDI hyperinstrument

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The theory of quantum mechanics introduced an unavoidable element of unpredictability or randomness into science. In 1922, Albert Einstein was awarded the Noble Prize in physics for his contribution to quantum theory, yet he never accepted the notion that the universe was governed by chance. His feelings were summed up in one of his most famous statements: “God does not play dice!”

"God does not play dice!" (1994) is an experimental multi-movement work that poses the question: Can interesting music can be created from random processes? It explores various implementations of a 1/f algorithm that generates fractal streams of pseudorandom numbers (Bolognesi 1983). When carefully mapped by the composer to musical parameters such as pitch, loudness and duration, these number streams can be used to create surprisingly beautiful musical structures. 1/f noise was first discovered in nature by Benoît Mandelbrot. Since Mandelbrot’s discovery, 1/f noise has been found in the annual flood levels of the Nile river, fluctuations in the stock market, and the flow patterns of traffic on an expressway (Gleick 1987).

More about Heisenberg

1/f distributions can be simulated on a computer using a dice-rolling algorithm suggested by Richard Voss (Voss 1978). My first encounter with the algorithm was through Martin Gardner's famous "Mathematical Recreations" column in Scientific American (Gardner 1992). I used Cycling '74's Max/MSP, a graphical multimedia programming environment for music composition, to implement the algorithm. My implementation of the Gardner/Voss 1/f algorithm is shown in Fig. 1.

Fig. 1. 1/f algorithm implemented in Max/MSP. (Click to load larger image.)

The brief introductory movement of "God does not play dice!" presented here is a traditional theme and variations form based on the "1/f melody" shown below (Fig. 2).

Fig. 2. 1/f melody

The theme above was produced by mapping the output of the four-dice version of the 1/f algorithm to the pitches of the theme. The duration of each note in the theme was held constant. This melody was discovered after numerous "unsuccessful" runs of the algorithm. A dice-inspired algorithm that produces brownian noise (Gardner 1992), a natural random process first described by Einstein, was used to shape the dynamic profile of the theme. The theme is presented at the beginning and end of the work. In between, each variation of the theme is produced in real time by the computer using various dice-inspired random selection techniques. Consequently, this is but one of an infinite number of possible pieces that can rightfully be call "Heisenberg."

References

Tommaso Bolognesi, "Automatic Composition: Experiments with Self-Similar Music," Computer Music Journal (Vol. 7, No. 1, Spring 1983), pp. 25-36.

Martin Gardner, "White, Brown and Fractal Music," in Fractal Music, Hypercards, and More... (New York: W.H. Freeman, 1992), pp. 1-23.

James Gleick, Chaos: Making a New Science (New York: Penguin, 1987).

R.F. Voss and J. Clarke, "'1/f Noise' in Music: Music from 1/f Noise," Journal of the Acoustical Society of America (Vol. 63: 1978), pp. 258-263.

Links

Cycling 74's Max/MSP