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Hearing the rhythms of the primes #62

Open MarcTheSpark opened 2 years ago

MarcTheSpark commented 2 years ago

Portfolio

I'm a composer, programmer, and the author of the SCAMP libraries for computer-assisted music in Python. You can see much of my work on my website,

Target topic categories

I'm really interested in the relationship between prime numbers and rhythm. Here's a little demonstration of what I'm talking about. It's a sonification of the prime factorization of the integers; the multiples of each prime creates a repeating rhythm at a different pitch, all of which are layered on top of one another.

Although I'm certainly a math enthusiast, I'm not a mathematician, so I'm curious what a mathematician hears in this.

Target medium

I'm not sure what the best format would be. I think a video that animates the music and explains some interesting properties of it would be cool. But it could also be a piece of writing with musical examples, or perhaps an interactive webpage. If it involves visuals, we would need an animator!

Contact details

E-mail: marc [at] marcevanstein [dot] com ...or just reply to this thread

MarcTheSpark commented 2 years ago

Another possibility, turning functions directly into melodies. I think this is a really interesting approach, because we so often think of functions in terms of their graphs, but music allows you to experience functions through time. Also, it doesn't just have to be a function from R->R; a multidimensional output could be encoded by other sonic dimensions besides pitch, such as timbre/tone color. There's probably something that could be done with a multidimensional input as well, though I'd have to think about it.

kajus-park commented 2 years ago

There are several interesting properties of primes that come to mind that have some effect on how the melody is perceived.

  1. New Rhythms are added one by one.
  2. New Rhythms are added slower. (Prime number theorem). These two properties allow the listener to get used to the patterns made by the current rhythms.
  3. Existence of twin primes (Twin Prime conjecture) Twin primes make a nice and somewhat repeating pattern of down _ down
  4. A locally somewhat constant density of primes gives the song a sense of direction. I don't have too much time but if you want to bounce around some Ideas then I'd be up for a chat.
twtww commented 2 years ago

I listened to your youtube video. Very interesting and I couldn't get the idea out of my head. :-) (So I suppose this should be strong encouragement to make the video)

Some random thoughts. Have you tried inverting the scale? I mean use the even numbers as the bass line, then then use higher pitches for the other primes. If you just use a chromatic scale I would guess it would sound a bit cacophonic, but you can separate the steps sizes to get pleasing chords for the decompositions of non-primes.

Octaves are a regularity in music that you'd ignore in the approach from the video. It would be nice to leverage this somehow, too. Like if 2 is C then 4,8,16 are also C but higher octaves.

Good luck.