Here are pieces in three different tuning systems:
The tuning system 12edo is the standard tuning system that divides octaves into 12 equal steps. The piece in 34edo also uses 12 notes per octave, but spaced unequally, as I described here in
an earlier post. I had my algorithmic composition software build a piece with 12 traversals of the diaschisma comma in 34edo; the 34edo piece here is the result. The 12edo piece is just a mapping of this tuning back to conventional tuning. So these first two pieces should sound almost identical. The 34edo piece should sound a bit more consonant. This is a demonstration of what is possible with precise control of tuning. I presented a similar contrast already in
an earlier post; this new piece is just the result with
the new interval comparison function.
The piece in 36edo is something very different. It has the same rhythmic topology as the pieces in 12edo and 34edo, but the pitch assignments are entirely different. This piece was inspired by the work of Maat DeMeritt, which used the Well-Tuned Piano system of La Monte Young. The 36edo scale I used differs from the system of La Monte Young in several ways:
- My scale is built from an equal tempered tuning, rather than using just intonation.
- My scale uses 11 notes per octave, instead of 12.
- My scale supports traversal of the slendric comma 1029:1024; just intonation does not allow comma traversal.
Kyle Gann's presentation of La Monte Young's system, linked above, very nicely lays out the scale in a tonnetz diagram based on 3:2 and 7:4. Hmmm, my diagram seems to be upside-down compared to his diagram, but anyway the similarity should be clear. Here is the scale in this 36edo piece:
I think La Monte Young used 12 notes per octave because that is how pianos are set up. I used 11 notes because that gives a scale with two sizes of intervals between notes in the scale: 1 and 6 steps of 34edo.
