131edo
Theory
131edo is the next EDO, after 81edo, on the "Golden Tone System" (Das Goldene Tonsystem) of Thorvald Kornerup, using the 131b val. The patent val has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out 81/80 it tempers out the immunity comma, 1638400/1594323. In the 7-limit it tempers out 3125/3087 and 245/243, so that it supports bophier temperament.
131edo is the 32nd prime EDO.
| Harmonic | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.39 | -1.58 | +2.17 | -1.70 | +2.22 | -4.19 | -4.38 | +3.79 | -3.62 | +0.00 | -4.02 |
| Relative (%) | +37.0 | -17.3 | +23.7 | -18.6 | +24.2 | -45.8 | -47.9 | +41.3 | -39.6 | +0.0 | -43.8 | |
| Steps (reduced) |
208 (77) |
304 (42) |
368 (106) |
453 (60) |
485 (92) |
535 (11) |
556 (32) |
593 (69) |
636 (112) |
649 (125) |
682 (27) | |
Some MOS Scales in 131-EDO:
| 33 16 33 33 16 | Pentatonic (comparable with 8edo and 99edo) |
| 23 23 8 23 23 23 8 | Pythagorean tuning (comparable with 17edo) |
| 21 21 13 21 21 21 13 | Meantone tuning (comparable with 50edo) |
| 19 12 19 19 12 19 19 12 | Father Tuning (comparable with 55edo) |
| 18 18 18 18 18 18 18 5 | Porcupine Tuning (comparable with 29edo and 80edo) |
| 17 17 17 6 17 17 17 17 6 | Superdiatonic tuning (comparable with 23edo) |
| 16 16 16 16 16 16 16 16 3 | Bohpier tuning (comparable with 41edo) |
| 13 13 9 13 13 13 9 13 13 13 9 | Sensi-11 Tuning |
| 11 11 11 11 11 5 11 11 11 11 11 11 5 | De Vries 13-tone Tuning |
| 10 10 10 7 10 10 10 10 7 10 10 10 10 7 | Ketradektriatoh Tuning |
| 21 17 21 17 17 21 17 | mohaha7 |
| 4 17 17 17 4 17 17 4 17 17 | mohaha10 |