Magic

Here's a new piece of algorithmic music: 19edo 2026.

This piece is in 19edo, the tuning system that divides octaves into 19 equal steps. 19edo is a meantone tuning, so conventional note names work well. The tonnetz diagram above shows how 19edo pitch classes are related by the fundamental intervals of perfect fifths, perfect fourths, major thirds, minor thirds, major sixths, and minor sixths. Start at a C note and move four perfect fifths, to G, D, A, and E. From E move a minor sixth to C, the pitch class at the start of this sequence. This combination of intervals is a syntonic comma (81:80). The fact that the combination returns to the starting pitch class is due to 19edo tempering out the syntonic comma, which is why it is a meantone tuning.

Another comma tempered out by 19edo is the magic comma (3125:3072). Start from the C pitch class and move five major thirds, to E, G#, Cb. Eb. and G. From there, move a perfect fourth to return to the starting pitch class of C.

The conventional diatonic scale is built by stacking perfect fifths. The piece posted above is built from an unconventional scale, built from stacking major thirds. The scale diagram above is like a piece of the tonnetz diagram, but then folded into a loop to show how the magic comma is tempered out.