106edo
Theory
Since 106 = 2 × 53, 106edo is closely related to 53edo, and is contorted through the 7-limit, tempering out the same commas (32805/32768, 15625/15552, 1600000/1594323, 2109375/2097152 in the 5-limit, 3125/3087, 225/224, 4000/3969, 1728/1715, 2430/2401, 4375/4374 in the 7-limit) as the patent val for 53edo. In the 11-limit it also tempers out 243/242, 3025/3024 and 9801/9800, so that it supports spectacle temperament and borwell temperament.
The division is notable for the fact that it is related to the turkish cent, or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the relative cent division for 106edo. Conversely, it makes the Pythagorean relative cent (or pion, symbol π¢, πr¢), which most closely approximates equally dividing an exact 3/2.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.07 | -1.41 | +4.76 | +3.40 | -2.79 | -3.07 | -3.17 | -5.63 | +0.61 | -1.64 | -2.29 | +1.13 | -2.08 | +2.42 | -1.81 |
| Relative (%) | +0.0 | -0.6 | -12.4 | +42.0 | +30.0 | -24.7 | -27.1 | -28.0 | -49.8 | +5.4 | -14.5 | -20.2 | +9.9 | -18.4 | +21.4 | -16.0 | |
| Steps (reduced) |
106 (0) |
168 (62) |
246 (34) |
298 (86) |
367 (49) |
392 (74) |
433 (9) |
450 (26) |
479 (55) |
515 (91) |
525 (101) |
552 (22) |
568 (38) |
575 (45) |
589 (59) |
607 (77) | |
Scales
Since 106edo has a step of 11.321 cents, it also allows one to use its MOS scales as circulating temperaments[clarification needed].
| Tones | Pattern | L:s |
|---|---|---|
| 5 | 1L 4s | 22:21 |
| 6 | 4L 2s | 18:17 |
| 7 | 1L 6s | 16:15 |
| 8 | 2L 6s | 14:13 |
| 9 | 7L 2s | 12:11 |
| 10 | 6L 4s | 11:10 |
| 11 | 7L 4s | 10:9 |
| 12 | 10L 2s | 9:8 |
| 13 | 2L 11s | |
| 14 | 8L 6s | 8:7 |
| 15 | 1L 14s | |
| 16 | 10L 6s | 7:6 |
| 17 | 4L 13s | |
| 18 | 16L 2s | 6:5 |
| 19 | 11L 8s | |
| 20 | 6L 14s | |
| 21 | 1L 20s | |
| 22 | 18L 4s | 5:4 |
| 23 | 14L 9s | |
| 24 | 10L 14s | |
| 25 | 6L 19s | |
| 26 | 2L 24s | |
| 27 | 25L 2s | 4:3 |
| 28 | 22L 6s | |
| 29 | 19L 10s | |
| 30 | 16L 14s | |
| 31 | 13L 18s | |
| 32 | 10L 22s | |
| 33 | 7L 26s | |
| 34 | 4L 30s | |
| 35 | 1L 34s | |
| 36 | 34L 2s | 3:2 |
| 37 | 32L 5s | |
| 38 | 30L 8s | |
| 39 | 28L 11s | |
| 40 | 26L 14s | |
| 41 | 24L 17s | |
| 42 | 22L 20s | |
| 43 | 20L 23s | |
| 44 | 18L 26s | |
| 45 | 16L 29s | |
| 46 | 14L 32s | |
| 47 | 12L 35s | |
| 48 | 10L 38s | |
| 49 | 8L 41s | |
| 50 | 6L 44s | |
| 51 | 4L 47s | |
| 52 | 2L 50s | |
| 53 | 53edo | equal |
| 54 | 52L 2s | 2:1 |
| 55 | 51L 4s | |
| 56 | 50L 6s | |
| 57 | 49L 8s | |
| 58 | 48L 10s | |
| 59 | 47L 12s | |
| 60 | 46L 14s | |
| 61 | 45L 16s | |
| 62 | 44L 18s | |
| 63 | 43L 20s | |
| 64 | 42L 22s | |
| 65 | 41L 24s | |
| 66 | 40L 26s | |
| 67 | 39L 28s | |
| 68 | 38L 30s | |
| 69 | 37L 32s | |
| 70 | 36L 34s | |
| 71 | 35L 36s | |
| 72 | 34L 38s | |
| 73 | 33L 40s | |
| 74 | 32L 42s | |
| 75 | 31L 44s | |
| 76 | 30L 46s | |
| 77 | 29L 48s | |
| 78 | 28L 50s | |
| 79 | 27L 52s | |
| 80 | 26L 54s | |
| 81 | 25L 56s | |
| 82 | 24L 58s | |
| 83 | 23L 60s | |
| 84 | 22L 62s |
See also
Artists using 106 et: