Composing the neverending song.
May 5, 2006 4:09 AM Subscribe
The mathematics of experimental music - I need some help composing a piece that will give John Cage
a run for his money.
posted by Jimbob to science & nature (19 answers total) 1 user marked this as a favorite
So I have this idea, that I've been experimenting for a while with in Audiomulch. Phrases of melody, of varying lengths, played on top of each other and constantly repeating.
For instance, one phrase might be 7 bars long, another 31 bars, another 53 bars long. All these phrases are playing at the same time, and repeating constantly, giving an ever-changing interplay of tones.
I want to be able to calculate how long it is before the entire composition repeats itself - how long until all the phrases align again like they were at the start. At first glance, it seems that multiplying the repeat lengths might give me an idea (7 x 31 x 53 = 11501 bars), but if any of the repeat lengths share common factors, it seems like this might not work out correctly.
If you like, you can imagine it as a set of wheels with a marker on them, all spinning at a different number of revolutions per minute. How long until all the markers line up at their starting positions again? Is there some formula I can apply to this to work out how long my song will be before it repeats? What is the best way to pick the length of each repeating phrase? Again, intuitively I feel that prime numbers are the way to go, to avoid common factors. Is this correct?