Extrospection by jdfreivald

This piece is in Wurschmidt temperament in 31 EDO.

Wurschmidt has a near-just 5/4 as generator, with eight making a 3/2. In 31 EDO, carried out to a 16-note MOS, it has excellent seven-limit harmonies, and even some 11-limit as well. It also has little-itty-bitty steps, though, and not a lot of perfect fifths except on chords that are pretty close together (e.g., major chords 40 cents apart).

Because of the excellent 5- and 7-limit harmonies, I went for heavy strings and a slowish tempo, so you can really hear and feel the sound. This isn't the boldest thing I've ever done, and I may modify it with different chords in the future, but I like the sounds anyway.

Part of my goal is always to do something that I couldn't do in 12 EDO. I don't feel like I fully exploited that, but I did somewhat. Here, although the main chords (C#m and A) are essentially the same as (though in better tune than) in 12 EDO, you couldn't get the same sound -- the seven limit (a bit of 7/6 and 10/7) and a few excellent augmented chords (truly two 5/4s stacked, meaning you hear the 25th harmonic clearly) just wouldn't be the same. I used eight (octave-equivalent) tones of the 16-tone MOS.

Written in Lilypond, using Saggital notation that was pre-processed to scordatura before compiling. Rendered with Timidity++.

It repeats somewhat, but that's just because I don't really want it to end. I like those big broad chords. :)