130edo
130edo divides the octave into 130 parts of size 9.231 cents each.
Theory
130edo is a zeta peak edo, a zeta peak integer edo, and a zeta integral edo but not a gap edo. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischis. It also can be used to tune the rank-three temperament jove, tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and 595/594 for the 17-limit. It gives the optimal patent val for 11-limit hemiwürschmidt and sesquart and 13-limit harry temperaments.
Prime harmonics
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Intervals
| Degree | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0.000 | 1/1 |
| 1 | 9.231 | 126/125, 225/224 |
| 2 | 18.462 | 81/80 |
| 3 | 27.692 | 64/63 |
| 4 | 36.923 | 49/48, 50/49 |
| 5 | 46.154 | 36/35 |
| 6 | 55.385 | 33/32 |
| 7 | 64.615 | 28/27, 27/26 |
| 8 | 73.846 | 25/24 |
| 9 | 83.077 | 21/20, 22/21 |
| 10 | 92.308 | 135/128 |
| 11 | 101.538 | 35/33 |
| 12 | 110.769 | 16/15 |
| 13 | 120.000 | 15/14 |
| 14 | 129.231 | 14/13 |
| 15 | 138.462 | 13/12 |
| 16 | 147.692 | 12/11 |
| 17 | 156.923 | 35/32 |
| 18 | 166.154 | 11/10 |
| 19 | 175.385 | 72/65 |
| 20 | 184.615 | 10/9 |
| 21 | 193.846 | 28/25 |
| 22 | 203.077 | 9/8 |
| 23 | 212.308 | 44/39 |
| 24 | 221.538 | 25/22 |
| 25 | 230.769 | 8/7 |
| 26 | 240.000 | 55/48 |
| 27 | 249.231 | 15/13 |
| 28 | 258.462 | 64/55 |
| 29 | 267.692 | 7/6 |
| 30 | 276.923 | 75/64 |
| 31 | 286.154 | 13/11 |
| 32 | 295.385 | 32/27 |
| 33 | 304.615 | 25/21 |
| 34 | 313.846 | 6/5 |
| 35 | 323.077 | 65/54 |
| 36 | 332.308 | 40/33 |
| 37 | 341.538 | 39/32 |
| 38 | 350.769 | 11/9, 27/22 |
| 39 | 360.000 | 16/13 |
| 40 | 369.231 | 26/21 |
| 41 | 378.462 | 56/45 |
| 42 | 387.692 | 5/4 |
| 43 | 396.923 | 63/50 |
| 44 | 406.154 | 81/64 |
| 45 | 415.385 | 14/11 |
| 46 | 424.615 | 32/25 |
| 47 | 433.846 | 9/7 |
| 48 | 443.077 | 128/99 |
| 49 | 452.308 | 13/10 |
| 50 | 461.538 | 72/55 |
| 51 | 470.769 | 21/16 |
| 52 | 480.000 | 33/25 |
| 53 | 489.231 | 250/189 |
| 54 | 498.462 | 4/3 |
| 55 | 507.692 | 75/56 |
| 56 | 516.923 | 27/20 |
| 57 | 526.154 | 65/48 |
| 58 | 535.385 | 15/11 |
| 59 | 544.615 | 48/35 |
| 60 | 553.846 | 11/8 |
| 61 | 563.077 | 18/13 |
| 62 | 572.308 | 25/18 |
| 63 | 581.538 | 7/5 |
| 64 | 590.769 | 45/32 |
| 65 | 600.000 | 99/70, 140/99 |
| … | … | … |
Regular temperament properties
Commas
7-limit commas: 2401/2400, 3136/3125, 19683/19600
11-limit commas: 441/440, 540/539, 3136/3125, 4000/3993
13-limit commas: 3136/3125, 243/242, 441/440, 351/350, 364/363
17-limit commas: 221/220, 364/363, 442/441, 595/594, 1275/1274, 4913/4875
Rank-2 temperaments
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 19\130 | 175.38 | 72/65 | Sesquiquartififths / sesquart |
| 1 | 21\130 | 193.85 | 28/25 | Didacus / hemiwürschmidt |
| 1 | 27\130 | 249.23 | 15/13 | Hemischis |
| 2 | 9\130 | 83.08 | 21/20 | Harry |
Scales
| Step | Cents | Distance to the nearest JI interval (selected ratios) |
|---|---|---|
| 13 (13/130) | 120.000 | 15/14 (+0.557 ¢) |
| 7 (20/130) | 184.615 | 10/9 (+2.211 ¢) |
| 9 (29/130) | 267.692 | 7/6 (+0,821 ¢) |
| 9 (38/130) | 350.769 | 11/9 (+3.361 ¢) |
| 9 (47/130) | 433.846 | 9/7 (-1.238 ¢) |
| 7 (54/130) | 498.462 | 4/3 (+0.417 ¢) |
| 13 (67/130) | 618.462 | 10/7 (+0.974 ¢) |
| 9 (76/130) | 701.538 | 3/2 (-0.417 ¢) |
| 7 (83/130) | 766.154 | 14/9 (+1.238 ¢) |
| 13 (96/130) | 886.154 | 5/3 (+1.795 ¢) |
| 5 (101/130) | 932.308 | 12/7 (-0.821 ¢) |
| 13 (114/130) | 1052.308 | 11/6 (+2.945 ¢) |
| 7 (121/130) | 1116.923 | 21/11 (-2.540 ¢) |
| 9 (130/130) | 1200.000 | Octave (2/1, ±0 ¢) |
Music
- The Paradise of Cantor play by Gene Ward Smith
- "Narrative Wars" by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of 130-EDO, from the 2016 compilation album "Next Xen")