Exotic Intervals

Here's an algorithmic composition in 270edo, the tuning system that divides octaves into 270 equal steps. This precision allows exotic intervals to be introduced with great clarity. This piece uses intervals such as 7:4 and 11:8, and more complex combinations such as 11:7 or 11:10 or 9:7.

Any tuning system with discrete steps will temper out commas, i.e. will map multiple just-tuned intervals to the same pitch. 270edo maps both 96:55 and 110:63 to 217 steps. This new composition is based on a pattern where pitch class 0 moves to pitch class 217 by a sequence of intervals corresponding to one of these just ratios, and then returns by a sequence corresponding to the other.

This composition is built mostly from just 15 pitch classes, out of the full set of 270. This diagram shows the pitch classes used, and the fundamental intervals that relate them to each other. More complex ratios such as 6:5 or 7:6 etc. are not shown.

This pieces progresses clockwise around this diagram 16 times, each cycle taking about 177 seconds.

This score superimposes all 16 cycles to show the general pattern.