mathematics as a basis for music

or .. mathematics as a basis for art (part 2)
I’m a little late to the party.

I was researching natural number sequences to create number generators when I came across the OEIS (online encyclopedia of integer sequences). It has a whole bunch of sequences, and I had only created a few (fibonacci, padovan, perrin, lucas and feigenbaum). Not only that, it lets you listen to the sequences by deriving pitch and duration from the sequences via midi files.
It uses another site to generate the midi files, the Musical Algorithms site.

Man, that site is loaded. Besides number sequences, the site lets you input all kinds of algorithms and sequences including DNA sequences (ATGC), constants, powers etc.. and listen to them by tweaking pitch and duration (derived by scaling or mapping).

Oh well..
So, I’m gonna have to take a slightly different tack, probably filtering sequences based on criteria (such as some described in the book “This is your brain on music“), transforming them (like adding syncopations) and combining them..

Stay tuned…


mathematics as a basis for art

Last evening, during one of our coffee-shop meanderings, I started thinking about generating patterns from a string of numbers, and see if a more complex “artlike” graphic comes out of it. Granted “artlike” is subjective, in this case, I’m taking it to mean if more than 50% of the people who view it will think it was deliberately created by a human artist using pen/brush strokes.

There’s been a lot of work around pattern generation using cellular automata, and also sound/noise generation using string of numbers.. This is my attempt to mimic that process from the grounds up.

To generate these larger patterns, we can start with three basic grouping of things.. numbers, glyphs and the length or width of the finished graphic.

For the numbers, one could programmatically come up with a “number generator” that can spit out a list of numbers following some algorithm that’s replicable.. (like a fibonacci series, or pascals triangle or some fractal function)

For the glyphs, one would have to come up with a basic set of graphic representations for the numbers.
One simple way would be to re-represent the individual numbers by some other thing like “-” for 1, “|” for 2, etc. the problem with that is multiple digit numbers will end up producing larger numbers of glyphs that may affect the length/width of the end graphic.

One could take that further by creating a transformation function, that takes a number from the number_generator and tranforms it to a glyph of fixed width based on some algorithm.

Then one would have to have a lenth/width generator that spits out the length (in repetions, how many glyphs) and the width of the graphic. one could also just generate one dimension either the length or the width, and keep the other open, so you could keep adding glyphs row by row or column by column. The length width generator could also depend on different inputs, like the max number of numbers generated by the number generator (or say, the weather pattern currently like the ambient temperature of one’s location)

Some fun things to try would be what we see in the real world..
for number generators, we could use the human genome, gene sequences mapped to numeric representations.. one could try base 4 (ATGC) and convert it to base 10 etc..

For glyph transformers one could use image thumbnails, say, map flickr images to numbers,

One could do the same with music (or sound -depending on what you call music). instead of glyphs, one would have a note generator, and instead of length/width, one could have length and scale or something like that.. then one could truly listen to the sound of nature

Lots of stuff out there on the net on this, just search for “algorithmic art” or “alorithmic music” or something like that..
There were even two links about it in today’s boing boing:
mathematical art
pi as music