Musique, mathématiques et philosophie

Samedi 13 janvier 2001

Tom JOHNSON (compositeur) : Objets (mathématiques) trouvés

Un objet trouvé, une chose qu'on prend comme elle est. Pas d'art, pas de technique, pas de fiction. Essayer d'être modeste et honnête, comme Marcel Duchamps. Accepter ce qu'on trouve, comme John Cage a accepté les choix des dés.

Bien. C'est simple. Mais si l'objet trouvé est un objet mathématique....

Begin with a very simple automaton :

N > n, n+1, n

This makes the following fixed point sequence

01012101012123212101012101012123212123234323212123...

and that is all a mathematician needs to know in order to go wherever he or she wants to go. But if we really want to see what is happening, it is better to show it like this :

0

010
010121010
010121010121232121010121010

One can sort of see how the sequence multiplies itself by three at each step, but the structure we are making is more clear if we go to a regular-spaced courrier typeface and write :

0

010
010 121 010
010 121 010 121 232 121 010 121 010

and this can be even more clear if we write it as music :

and let me take that just one step further, as I did when I wrote this piece, which is Rational Melody No. 14 :

You may feel that I am now far away from the simple rule n > n, n+1, n, but at every step the goal has been not to decorate or to take off from the basic rule, but rather to show the structure of the basic rule, to enter into this mathematical object, to be able to see and hear it as well as we possibly can. Of course, I am making subjective musical choices here as I select intervals and measure the lengths of the punctuations/rests, but I am making them in order to make the mathematics more clearly audible, not to mystify or to transform the mathematics into something purely esthetic.