MusiNum - The Music in the Numbers

lkindermann [ at ]


Music and mathematics always had a close relationship. Since Pythagoras it is known that tonal harmony is closely related to the numerical relation of the frequencies. In the last years a new field of science and mathematics boomed. Chaos, fractals and self-similarity are topics which caught public interest not at least because of the beautiful pictures which can be generated with them. Hardly anybody does not know the colorful psychedelic pictures of the Mandelbrot-set and even people never heard of complex numbers before bought mathematical books on this topics now. Experiments which tried to extend the beauty of the fractal-art-pictures to the acoustical sense sometimes gave interesting results but usually the sound is quite strange. I think this difficulty arises from the fact that chaos theory usually works with real numbers. But our traditional music is based on discrete frequencies and simple combinations of frequencies, and the mathematical discipline which is employed with the simple numbers is number-theory. Perhaps the most fundamental entities in mathematics are the natural numbers: 1,2,3,4,5... They are something universal: It is a hard thing to imagine a mind which would count in a different way. But the style we write them down can vary: The decimal system based on the digits 0-9 is by no way the only or natural method to present numbers. It has just been arbitrarily chosen some time ago in history. The simplest notation is the binary notation which only uses the digits 0 and 1. Computers always calculate in binary notation because it can be easily mapped to electrical devices: The presence of current means 1 and no current means 0.

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Kindermann, L. (2001): MusiNum - The Music in the Numbers , In: E.R. Miranda, Composing with Computers. Music Technology Series, Focal Press, Oxford. .

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