Mathematically Constructed Music

In another post, I explain a way to use a code to make an infinitely long string of symbols that never repeats. I decided to use this method to make some music. In this post, I explain how you can do the same thing.

  1. First, take the first 6 bars of Twinkle, Twinkle Little Star, in the key of C. This song only has six different notes, C, D, E, F, G and A.
  2. Then, merge the pairs of identical notes into single notes. That way, each bar contains exactly two notes.
  3. Label the bars C, D, E, F, G and A, in any order you like.

Now you have a code – a way of changing a letter into a pair of letters. When I did it, I got this code :

  • C becomes CG, because the first bar (which I labeled it C) contains the two notes C and G.
  • D becomes AG, because the second bar (which I labeled D) contains the two notes A and G.
  • Likewise, E becomes FE, F becomes DC, G becomes GF and A becomes ED.

Actually, practically any way of converting letters to other letters will do. A letter doesn’t have to change into two other letters. You don’t have to get your code from a real song, you could roll dice instead.

Once you have your code,

  1. Choose a starting letter. I chose C.
  2. Encode the letter using your code. For me, that gave CG.
  3. Do this again and again. I got CGGF, then CGGF/GFDC, then CGGF/GFDC/GFDC/AGCG, and so on.
  4. For me, my song got twice as long each time I applied the code. You can hear the results in the Youtube Video below.

In the video, the melody is the first 256 notes of my infinite sing, and the bass is the first 64 notes, played at one quarter of the speed.  The music is kinda catchy. It would be better if the notes were different lengths, but that would be easy to do with a different code.

If you’re musically talented, why don’t you have a go? Even if the result is not the next Gangnam style, it could easily form the base of a more interesting piece.

Or, feel free to start with my piece. I’m making it available under a Creative Commons Attribution Sharealike license, which means you can take it, copy it, modify it, even sell it, as long as you (a) point out that the original is from me (for example, by linking back here), and (b) release your modifications under the same license.

To get you started, you might like to download an mp3 version of this song, or a MIDI version, or the printable sheet music.