61edo
Theory
61edo provides the optimal patent val for the freivald (24&37) temperament in the 7-, 11- and 13-limit.
61edo is the 18th prime edo, after of 59edo and before of 67edo.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.24 | +7.13 | -4.89 | -7.19 | -0.50 | +5.37 | -6.30 | -6.59 | -2.43 | +1.35 | +1.23 |
| Relative (%) | +31.7 | +36.2 | -24.9 | -36.5 | -2.5 | +27.3 | -32.0 | -33.5 | -12.4 | +6.9 | +6.3 | |
| Steps (reduced) |
97 (36) |
142 (20) |
171 (49) |
193 (10) |
211 (28) |
226 (43) |
238 (55) |
249 (5) |
259 (15) |
268 (24) |
276 (32) | |
Table of intervals
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 19.7 | ^D, vvE♭ | |
| 2 | 39.3 | ^^D, vE♭ | |
| 3 | 59 | 29/28, 32/31 | ^3D, E♭ |
| 4 | 78.7 | 22/21, 23/22 | ^4D, ^E♭ |
| 5 | 98.4 | 35/33 | v3D♯, ^^E♭ |
| 6 | 118 | 31/29 | vvD♯, ^3E♭ |
| 7 | 137.7 | 13/12 | vD♯, v4E |
| 8 | 157.4 | 23/21, 34/31, 35/32 | D♯, v3E |
| 9 | 177 | 21/19, 31/28 | ^D♯, vvE |
| 10 | 196.7 | 19/17 | ^^D♯, vE |
| 11 | 216.4 | 26/23 | E |
| 12 | 236.1 | ^E, vvF | |
| 13 | 255.7 | 22/19 | ^^E, vF |
| 14 | 275.4 | 34/29 | F |
| 15 | 295.1 | 19/16 | ^F, vvG♭ |
| 16 | 314.8 | 6/5 | ^^F, vG♭ |
| 17 | 334.4 | 17/14, 23/19 | ^3F, G♭ |
| 18 | 354.1 | ^4F, ^G♭ | |
| 19 | 373.8 | 26/21 | v3F♯, ^^G♭ |
| 20 | 393.4 | vvF♯, ^3G♭ | |
| 21 | 413.1 | 14/11, 33/26 | vF♯, v4G |
| 22 | 432.8 | F♯, v3G | |
| 23 | 452.5 | 13/10 | ^F♯, vvG |
| 24 | 472.1 | 21/16 | ^^F♯, vG |
| 25 | 491.8 | G | |
| 26 | 511.5 | 35/26 | ^G, vvA♭ |
| 27 | 531.1 | 19/14 | ^^G, vA♭ |
| 28 | 550.8 | 11/8 | ^3G, A♭ |
| 29 | 570.5 | 25/18, 32/23 | ^4G, ^A♭ |
| 30 | 590.2 | 31/22 | v3G♯, ^^A♭ |
| 31 | 609.8 | vvG♯, ^3A♭ | |
| 32 | 629.5 | 23/16 | vG♯, v4A |
| 33 | 649.2 | 16/11, 35/24 | G♯, v3A |
| 34 | 668.9 | 28/19 | ^G♯, vvA |
| 35 | 688.5 | ^^G♯, vA | |
| 36 | 708.2 | A | |
| 37 | 727.9 | 29/19, 32/21, 35/23 | ^A, vvB♭ |
| 38 | 747.5 | 20/13 | ^^A, vB♭ |
| 39 | 767.2 | ^3A, B♭ | |
| 40 | 786.9 | 11/7 | ^4A, ^B♭ |
| 41 | 806.6 | 35/22 | v3A♯, ^^B♭ |
| 42 | 826.2 | 21/13 | vvA♯, ^3B♭ |
| 43 | 845.9 | 31/19 | vA♯, v4B |
| 44 | 865.6 | 28/17, 33/20 | A♯, v3B |
| 45 | 885.2 | 5/3 | ^A♯, vvB |
| 46 | 904.9 | 32/19 | ^^A♯, vB |
| 47 | 924.6 | 29/17 | B |
| 48 | 944.3 | 19/11 | ^B, vvC |
| 49 | 963.9 | ^^B, vC | |
| 50 | 983.6 | 23/13 | C |
| 51 | 1003.3 | 34/19 | ^C, vvD♭ |
| 52 | 1023 | ^^C, vD♭ | |
| 53 | 1042.6 | 31/17 | ^3C, D♭ |
| 54 | 1062.3 | 24/13 | ^4C, ^D♭ |
| 55 | 1082 | v3C♯, ^^D♭ | |
| 56 | 1101.6 | vvC♯, ^3D♭ | |
| 57 | 1121.3 | 21/11 | vC♯, v4D |
| 58 | 1141 | 31/16 | C♯, v3D |
| 59 | 1160.7 | ^C♯, vvD | |
| 60 | 1180.3 | ^^C♯, vD | |
| 61 | 1200 | 2/1 | D |