One of the projects that I’ve been working on for a while is exploring musical patterns (melodies and rhythms) that occur in irrational, non-repeating numbers. For Pi Day about 10 years ago, I wrote a little piano piece that assigned each digit of π a corresponding note and duration.
Excel: a composer’s tool
So the first five notes in the melody are F-D-G-D-A.
Harmony and basslines were calculated by continuing the sequence of π digits, and transposing down a fourth and an octave, respectively.
While not really Second Viennese School twelve-tone, it certainly had an atonal feel to it. But it was a lot of work, and the result was not particularly musical.
I still like the idea, though.
One of the ways we can force it to be more musical is to use something other than a major scale that (in C) includes the notes A B C D E F & G. There are lots of alternative scales, but a decatonic (10 note) scale isn’t going to be more musical than a 7 note one.¹
One solution would be to use two consecutive pentatonic scales, but I don’t really want to span two octaves. That seems like cheating.
Have you figured out the solution yet?
What about using π in base 5?
That way, each digit can be one note of a musically pleasing scale.
But since we’re already onto new bases, why not keep going? If we want the rhythm to be a combination of 32nd, 16th, 8th & quarter notes, we can use base 4 for that.
Or we can throw rhythm totally out the window and divide each measure into 64 parts with base 64.
Or we can decouple note-on messages from note-duration messages, allowing π to create its own harmonies as notes overlap, each with separate bases.
Or we can modify pretty much any other synth parameter, like velocity, or pitch bend, or filter frequency, or…
And then there’s e, or e^π, or π^e, or √2, or…
10 years later I have fun new tools that make experiments like this much easier. One such tool takes a CSV file (formatted a particular way) and spits out a midi file that can be dropped right into a sequencer. Add in a little bit of programming, and we can iterate through several variations until we find one we like.
Like this one:
That’s π base 5 driving a pentatonic scale of 16th notes. It also drives the same scale lowered an octave with note durations of derived skipped, 16th, 8th, quarter or half notes. Each set of notes are arpeggiated so that they bounce between the two tones, and finally a drum loop is thrown on top.
¹Note that I cheated on the original when I used a major scale, which has 7 notes. I emphasized the tonic C by including it twice, and I added two rests so that it wouldn’t sound more like a scrambled mess than it already does.