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## Insta-Reich

Tonematrix by André Michelle is a function defined on the two-dimensional vector space over the field $\mathbb{Z}_{17}$. And yet, it’s so much more; though self-explanatory, it might save you three seconds to know that the axes correspond to time and pitch, with the latter staggered non-linearly to prevent dissonance. It seems possible that Tokyo / Vermont Counterpoint could be produced directly from this tool if the latter were extended further in time.

A more interesting challenge would be to create a devolution from the audio to tonematrix form. I claim such reverse engineering, followed by a Fourier transform to draw out the particular periodicities in frequency and time, can be used to generate an infinte family of pleasant sounding meanderings of arbitrary length. I would also like to consider the possibility of randomly placing and removing structures on the map at different positions: most of the early random and fractal music was interesting but sounded very much like garbage, whereas by forcing tonality on the output, tonematrix minimises the potential for something awful.

### 3 Responses

1. I wonder what it would sound like if you evolved the matrix according to the rules of The Game of Life* after a certain number of repetitions (1?)

*Or perhaps some other automatum [is that even a word?] that is more forgiving of single points.

2. Yes, excellent. I had also noticed the similarity (in appearance) to the Game of Life. Cellular automata provide exactly the balance of order and randomness one needs. It’s a big shame the source code for tonematrix is not available. In the future, perhaps.

3. on June 11, 2009 at 2:15 am | Reply Tim McKenzie

From a reversal of tonematrix, it’ll only be a few short steps until we discover that Bach’s unfinished Die Kunst der Fuge was actually an unfinished proof of Goldbach’s conjecture.