Würschmidt diesis spiral progression
The Würschmidt diesis spiral progression is a type of chord progression that hinges on the Würschmidt comma being tempered out, enabling three instances of 128/125 to add up to 16/15. As such, this progression is available in EDOs that support Würschmidt temperament, such as 31edo, 34edo and 65edo.
Arguably the best known form of this type of spiral progression is found in 31edo, though there are other, non-meantone interpretations. Regardless, each chord change effectively moves upward or downward by a Ptolemaic major third, that is, 5/4, thus creating a sort of chromatic-mediant-type motion.
Würschmidt diesis spiral for three voices
| If you're on: | For downward spiral, move thus: | For upward spiral: |
| 5th | up 2 dieses | up 3 dieses |
| 3rd | stay | down 2 dieses |
| root | down 3 dieses | stay |
- Decide on downward (C-E-G#-B#) or upward (C-Ab-Fb-Dbb) root movement. We found downward easier almost every time.
- Sing a just major triad (4:5:6), any inversion, open or closed spacing. Tune and match vowel to lowest voice.
- Move in accordance with the chart. Since two people are moving each time, make eye contact to synchronize the change.
After three moves, you will have the same triad one diesis up or down, and indeed one can keep going.
recording on [u]: magic spiral basic (andrew jacob ryan) 5_11_07.mp3