Sheet music here - http://www.theancientmelodies.com
I arranged this melodic timing and chords to the chromatic "notes" of pi. Instead of the standard decimal (base 10) number, I used base 12 counting, where there are 12 digits in the counting system (A = the 10th digit ; B = the 11th digit), and lined those digits up with the chromatic scale, which is all 12 musical tones in an octave.
What was revealed is amazing. The sequence of melody notes contain as much harmonic structure as those a composer would deliberately choose. I recognized this and made it into this song by timing the notes and adding the chord progression based on the implied structure and context of the notes. The song goes up to the 330th digit.
The final note is the only melody note I added. Since the song begins in the key of "4", playing a "4" at the end of the phrase (instead of "5") brings resolution.
3 | 1 | 848 | 0 | 949 | 3B9 | 186 | 6 | 4 ~4~ |
So the song could end (or go back to the beginning) when any section resolves to the key of "4". In the version in this video, within my arrangement of 330 digits, there are four places to end/repeat the song.
There are many places in the raw notes that contain the mind of a composer. There are many conventional interval structures in the notes that all fit together very neatly and flow in time while simultaneously establishing conventional harmonic structures. I found musical order in the digits of pi base 12.
I made a music with Euler's #, and I wrote the first section of Tau. Also, I have explored phi/golden ratio but no music yet.