85edo
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.93 | -5.14 | +5.29 | -6.26 | -0.73 | +6.53 | -1.21 | -6.13 | -1.04 | -4.90 | +7.02 |
| Relative (%) | +27.8 | -36.4 | +37.5 | -44.4 | -5.2 | +46.3 | -8.6 | -43.4 | -7.4 | -34.7 | +49.7 | |
| Steps (reduced) |
135 (50) |
197 (27) |
239 (69) |
269 (14) |
294 (39) |
315 (60) |
332 (77) |
347 (7) |
361 (21) |
373 (33) |
385 (45) | |
85 = 5 * 17, and it shares the same 3.9 cent sharp fifth as 17, 34, and 68. The patent val tempers out 3125/3072 in the 5-limit and 875/864, 245/243 and 225/224 in the 7-limit, so that it supports magic. It tempers out 100/99 and 245/243 in the 11-limit, supporting 11-limit magic, and 1188/1183, 847/845 and 1575/1573 in the 13-limit. It provides the optimal patent val for the 13-limit temperament tempering out 100/99, 540/539, 847/845 and 1575/1573.
Interval table
| Steps | Cents | Approximate ratios | Ups and downs notation |
|---|---|---|---|
| 0 | 0 | 1/1 | D |
| 1 | 14.1 | ^D, v4E♭ | |
| 2 | 28.2 | ^^D, v3E♭ | |
| 3 | 42.4 | 41/40 | ^3D, vvE♭ |
| 4 | 56.5 | 30/29, 31/30, 32/31 | ^4D, vE♭ |
| 5 | 70.6 | ^5D, E♭ | |
| 6 | 84.7 | v4D♯, ^E♭ | |
| 7 | 98.8 | 37/35 | v3D♯, ^^E♭ |
| 8 | 112.9 | 16/15, 31/29 | vvD♯, ^3E♭ |
| 9 | 127.1 | 14/13 | vD♯, ^4E♭ |
| 10 | 141.2 | 13/12, 38/35 | D♯, v5E |
| 11 | 155.3 | 23/21, 35/32 | ^D♯, v4E |
| 12 | 169.4 | 32/29 | ^^D♯, v3E |
| 13 | 183.5 | ^3D♯, vvE | |
| 14 | 197.6 | 37/33 | ^4D♯, vE |
| 15 | 211.8 | 26/23, 35/31 | E |
| 16 | 225.9 | 33/29 | ^E, v4F |
| 17 | 240 | ^^E, v3F | |
| 18 | 254.1 | 22/19, 37/32 | ^3E, vvF |
| 19 | 268.2 | 7/6 | ^4E, vF |
| 20 | 282.4 | 20/17, 33/28 | F |
| 21 | 296.5 | 19/16 | ^F, v4G♭ |
| 22 | 310.6 | ^^F, v3G♭ | |
| 23 | 324.7 | 29/24, 35/29, 41/34 | ^3F, vvG♭ |
| 24 | 338.8 | 28/23 | ^4F, vG♭ |
| 25 | 352.9 | 38/31 | ^5F, G♭ |
| 26 | 367.1 | 26/21 | v4F♯, ^G♭ |
| 27 | 381.2 | v3F♯, ^^G♭ | |
| 28 | 395.3 | vvF♯, ^3G♭ | |
| 29 | 409.4 | 19/15 | vF♯, ^4G♭ |
| 30 | 423.5 | 23/18, 37/29 | F♯, v5G |
| 31 | 437.6 | 9/7 | ^F♯, v4G |
| 32 | 451.8 | ^^F♯, v3G | |
| 33 | 465.9 | 38/29 | ^3F♯, vvG |
| 34 | 480 | 29/22, 37/28 | ^4F♯, vG |
| 35 | 494.1 | G | |
| 36 | 508.2 | ^G, v4A♭ | |
| 37 | 522.4 | ^^G, v3A♭ | |
| 38 | 536.5 | 15/11 | ^3G, vvA♭ |
| 39 | 550.6 | 11/8 | ^4G, vA♭ |
| 40 | 564.7 | 18/13 | ^5G, A♭ |
| 41 | 578.8 | v4G♯, ^A♭ | |
| 42 | 592.9 | 31/22 | v3G♯, ^^A♭ |
| 43 | 607.1 | vvG♯, ^3A♭ | |
| 44 | 621.2 | vG♯, ^4A♭ | |
| 45 | 635.3 | 13/9 | G♯, v5A |
| 46 | 649.4 | 16/11 | ^G♯, v4A |
| 47 | 663.5 | 22/15 | ^^G♯, v3A |
| 48 | 677.6 | ^3G♯, vvA | |
| 49 | 691.8 | ^4G♯, vA | |
| 50 | 705.9 | A | |
| 51 | 720 | ^A, v4B♭ | |
| 52 | 734.1 | 29/19 | ^^A, v3B♭ |
| 53 | 748.2 | 37/24 | ^3A, vvB♭ |
| 54 | 762.4 | 14/9 | ^4A, vB♭ |
| 55 | 776.5 | 36/23 | ^5A, B♭ |
| 56 | 790.6 | 30/19 | v4A♯, ^B♭ |
| 57 | 804.7 | 35/22 | v3A♯, ^^B♭ |
| 58 | 818.8 | vvA♯, ^3B♭ | |
| 59 | 832.9 | 21/13 | vA♯, ^4B♭ |
| 60 | 847.1 | 31/19 | A♯, v5B |
| 61 | 861.2 | 23/14 | ^A♯, v4B |
| 62 | 875.3 | ^^A♯, v3B | |
| 63 | 889.4 | ^3A♯, vvB | |
| 64 | 903.5 | 32/19 | ^4A♯, vB |
| 65 | 917.6 | 17/10 | B |
| 66 | 931.8 | 12/7 | ^B, v4C |
| 67 | 945.9 | 19/11 | ^^B, v3C |
| 68 | 960 | ^3B, vvC | |
| 69 | 974.1 | ^4B, vC | |
| 70 | 988.2 | 23/13 | C |
| 71 | 1002.4 | ^C, v4D♭ | |
| 72 | 1016.5 | ^^C, v3D♭ | |
| 73 | 1030.6 | 29/16 | ^3C, vvD♭ |
| 74 | 1044.7 | ^4C, vD♭ | |
| 75 | 1058.8 | 24/13, 35/19 | ^5C, D♭ |
| 76 | 1072.9 | 13/7 | v4C♯, ^D♭ |
| 77 | 1087.1 | 15/8 | v3C♯, ^^D♭ |
| 78 | 1101.2 | vvC♯, ^3D♭ | |
| 79 | 1115.3 | vC♯, ^4D♭ | |
| 80 | 1129.4 | C♯, v5D | |
| 81 | 1143.5 | 29/15, 31/16 | ^C♯, v4D |
| 82 | 1157.6 | ^^C♯, v3D | |
| 83 | 1171.8 | ^3C♯, vvD | |
| 84 | 1185.9 | ^4C♯, vD | |
| 85 | 1200 | 2/1 | D |