A doodle I for a musical tuning system Erv Wilson called meta-pelog. Take the sequence a_n = a_{n-1} + a_{n-3} and the limit of the ratio of terms, then use this as a frequency ratio to build a circle. This forms 5, 7 and 9-note MOS scales, and is approximated very closely in 29EDO (a subset of 58!)
November 11, 2024 at 1:54 AM
A doodle I for a musical tuning system Erv Wilson called meta-pelog. Take the sequence a_n = a_{n-1} + a_{n-3} and the limit of the ratio of terms, then use this as a frequency ratio to build a circle. This forms 5, 7 and 9-note MOS scales, and is approximated very closely in 29EDO (a subset of 58!)
Want to be active here, so here's a couple simple harmonic lattices. The way the first 17 harmonics show up in the circle of fifths in 46EDO and 58EDO. Both of these are really pretty to me! They're both para-Pythagorean, so four 3/2s give a 14/11. Everything's a lil sharp in 58, which I love.
November 10, 2024 at 6:36 AM
Want to be active here, so here's a couple simple harmonic lattices. The way the first 17 harmonics show up in the circle of fifths in 46EDO and 58EDO. Both of these are really pretty to me! They're both para-Pythagorean, so four 3/2s give a 14/11. Everything's a lil sharp in 58, which I love.