95edo
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Prime factorization
5 × 19
Step size
12.6316¢
Fifth
56\95 (707.368¢)
Semitones (A1:m2)
12:5 (151.6¢ : 63.16¢)
Dual sharp fifth
56\95 (707.368¢)
Dual flat fifth
55\95 (694.737¢) (→11\19)
Dual major 2nd
16\95 (202.105¢)
Consistency limit
7
Distinct consistency limit
7
| ← 94edo | 95edo | 96edo → |
95 equal divisions of the octave (abbreviated 95edo or 95ed2), also called 95-tone equal temperament (95tet) or 95 equal temperament (95et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 95 equal parts of about 12.6 ¢ each. Each step represents a frequency ratio of 21/95, or the 95th root of 2.
Theory
95edo is a dual-fifth tuning. However, the patent val makes for a reasonable sharp-tending system, and tempers out 245/243, 2401/2400, and 4000/3969 in the 7-limit, 176/175, 1331/1323, 4000/3993 and 6250/6237 in the 11-limit, and 196/195, 325/324, 364/363, 640/637, 847/845, 1001/1000 and 2200/2197 in the 13-limit.
It supports rank-2 temperaments such as enneadecal, magus, gorgik, octacot, quinmite, tetracot and trisedodge, and rank-3 temperaments such as manwe and shrusus. It provides the optimal patent val for shrusus.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.41 | +5.27 | +3.81 | -1.80 | +4.47 | +5.79 | -1.95 | -3.90 | +5.64 | -3.41 | +3.30 |
| Relative (%) | +42.9 | +41.7 | +30.1 | -14.3 | +35.4 | +45.8 | -15.5 | -30.9 | +44.7 | -27.0 | +26.2 | |
| Steps (reduced) |
151 (56) |
221 (31) |
267 (77) |
301 (16) |
329 (44) |
352 (67) |
371 (86) |
388 (8) |
404 (24) |
417 (37) |
430 (50) | |
Subsets and supersets
Since 95 factors as 5 × 19, 95edo contains 5edo and 19edo as its subsets.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation (Dual flat fifth 55\95) |
Ups and downs notation (Dual sharp fifth 56\95) |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D | D |
| 1 | 12.6 | ^D, ^E♭♭♭ | ^D, v4E♭ | |
| 2 | 25.3 | ^^D, ^^E♭♭♭ | ^^D, v3E♭ | |
| 3 | 37.9 | vvD♯, vvE♭♭ | ^3D, vvE♭ | |
| 4 | 50.5 | 36/35 | vD♯, vE♭♭ | ^4D, vE♭ |
| 5 | 63.2 | 29/28 | D♯, E♭♭ | ^5D, E♭ |
| 6 | 75.8 | 23/22, 24/23 | ^D♯, ^E♭♭ | ^6D, ^E♭ |
| 7 | 88.4 | 20/19 | ^^D♯, ^^E♭♭ | v5D♯, ^^E♭ |
| 8 | 101.1 | 35/33 | vvD𝄪, vvE♭ | v4D♯, ^3E♭ |
| 9 | 113.7 | 31/29 | vD𝄪, vE♭ | v3D♯, ^4E♭ |
| 10 | 126.3 | 14/13 | D𝄪, E♭ | vvD♯, ^5E♭ |
| 11 | 138.9 | 13/12 | ^D𝄪, ^E♭ | vD♯, v6E |
| 12 | 151.6 | 12/11 | ^^D𝄪, ^^E♭ | D♯, v5E |
| 13 | 164.2 | 11/10 | vvD♯𝄪, vvE | ^D♯, v4E |
| 14 | 176.8 | 31/28, 41/37 | vD♯𝄪, vE | ^^D♯, v3E |
| 15 | 189.5 | 29/26, 39/35 | E | ^3D♯, vvE |
| 16 | 202.1 | ^E, ^F♭♭ | ^4D♯, vE | |
| 17 | 214.7 | 26/23 | ^^E, ^^F♭♭ | E |
| 18 | 227.4 | vvE♯, vvF♭ | ^E, v4F | |
| 19 | 240 | 23/20 | vE♯, vF♭ | ^^E, v3F |
| 20 | 252.6 | 22/19, 37/32 | E♯, F♭ | ^3E, vvF |
| 21 | 265.3 | 7/6 | ^E♯, ^F♭ | ^4E, vF |
| 22 | 277.9 | ^^E♯, ^^F♭ | F | |
| 23 | 290.5 | 13/11 | vvE𝄪, vvF | ^F, v4G♭ |
| 24 | 303.2 | 25/21, 31/26 | vE𝄪, vF | ^^F, v3G♭ |
| 25 | 315.8 | 6/5 | F | ^3F, vvG♭ |
| 26 | 328.4 | 23/19, 29/24 | ^F, ^G♭♭♭ | ^4F, vG♭ |
| 27 | 341.1 | 28/23 | ^^F, ^^G♭♭♭ | ^5F, G♭ |
| 28 | 353.7 | 38/31 | vvF♯, vvG♭♭ | ^6F, ^G♭ |
| 29 | 366.3 | vF♯, vG♭♭ | v5F♯, ^^G♭ | |
| 30 | 378.9 | F♯, G♭♭ | v4F♯, ^3G♭ | |
| 31 | 391.6 | ^F♯, ^G♭♭ | v3F♯, ^4G♭ | |
| 32 | 404.2 | 24/19, 43/34 | ^^F♯, ^^G♭♭ | vvF♯, ^5G♭ |
| 33 | 416.8 | 14/11 | vvF𝄪, vvG♭ | vF♯, v6G |
| 34 | 429.5 | 41/32 | vF𝄪, vG♭ | F♯, v5G |
| 35 | 442.1 | 31/24, 40/31 | F𝄪, G♭ | ^F♯, v4G |
| 36 | 454.7 | 13/10 | ^F𝄪, ^G♭ | ^^F♯, v3G |
| 37 | 467.4 | 38/29 | ^^F𝄪, ^^G♭ | ^3F♯, vvG |
| 38 | 480 | 29/22, 33/25, 37/28 | vvF♯𝄪, vvG | ^4F♯, vG |
| 39 | 492.6 | vF♯𝄪, vG | G | |
| 40 | 505.3 | G | ^G, v4A♭ | |
| 41 | 517.9 | 31/23 | ^G, ^A♭♭♭ | ^^G, v3A♭ |
| 42 | 530.5 | 19/14 | ^^G, ^^A♭♭♭ | ^3G, vvA♭ |
| 43 | 543.2 | 26/19 | vvG♯, vvA♭♭ | ^4G, vA♭ |
| 44 | 555.8 | 40/29 | vG♯, vA♭♭ | ^5G, A♭ |
| 45 | 568.4 | 25/18 | G♯, A♭♭ | ^6G, ^A♭ |
| 46 | 581.1 | 7/5 | ^G♯, ^A♭♭ | v5G♯, ^^A♭ |
| 47 | 593.7 | 31/22 | ^^G♯, ^^A♭♭ | v4G♯, ^3A♭ |
| 48 | 606.3 | vvG𝄪, vvA♭ | v3G♯, ^4A♭ | |
| 49 | 618.9 | 10/7 | vG𝄪, vA♭ | vvG♯, ^5A♭ |
| 50 | 631.6 | 36/25 | G𝄪, A♭ | vG♯, v6A |
| 51 | 644.2 | 29/20 | ^G𝄪, ^A♭ | G♯, v5A |
| 52 | 656.8 | 19/13 | ^^G𝄪, ^^A♭ | ^G♯, v4A |
| 53 | 669.5 | 28/19 | vvG♯𝄪, vvA | ^^G♯, v3A |
| 54 | 682.1 | vG♯𝄪, vA | ^3G♯, vvA | |
| 55 | 694.7 | A | ^4G♯, vA | |
| 56 | 707.4 | ^A, ^B♭♭♭ | A | |
| 57 | 720 | ^^A, ^^B♭♭♭ | ^A, v4B♭ | |
| 58 | 732.6 | 29/19 | vvA♯, vvB♭♭ | ^^A, v3B♭ |
| 59 | 745.3 | 20/13 | vA♯, vB♭♭ | ^3A, vvB♭ |
| 60 | 757.9 | 31/20 | A♯, B♭♭ | ^4A, vB♭ |
| 61 | 770.5 | 39/25 | ^A♯, ^B♭♭ | ^5A, B♭ |
| 62 | 783.2 | 11/7 | ^^A♯, ^^B♭♭ | ^6A, ^B♭ |
| 63 | 795.8 | 19/12 | vvA𝄪, vvB♭ | v5A♯, ^^B♭ |
| 64 | 808.4 | vA𝄪, vB♭ | v4A♯, ^3B♭ | |
| 65 | 821.1 | 37/23 | A𝄪, B♭ | v3A♯, ^4B♭ |
| 66 | 833.7 | ^A𝄪, ^B♭ | vvA♯, ^5B♭ | |
| 67 | 846.3 | 31/19 | ^^A𝄪, ^^B♭ | vA♯, v6B |
| 68 | 858.9 | 23/14 | vvA♯𝄪, vvB | A♯, v5B |
| 69 | 871.6 | 38/23 | vA♯𝄪, vB | ^A♯, v4B |
| 70 | 884.2 | 5/3 | B | ^^A♯, v3B |
| 71 | 896.8 | 42/25 | ^B, ^C♭♭ | ^3A♯, vvB |
| 72 | 909.5 | 22/13 | ^^B, ^^C♭♭ | ^4A♯, vB |
| 73 | 922.1 | vvB♯, vvC♭ | B | |
| 74 | 934.7 | 12/7 | vB♯, vC♭ | ^B, v4C |
| 75 | 947.4 | 19/11 | B♯, C♭ | ^^B, v3C |
| 76 | 960 | 40/23 | ^B♯, ^C♭ | ^3B, vvC |
| 77 | 972.6 | ^^B♯, ^^C♭ | ^4B, vC | |
| 78 | 985.3 | 23/13 | vvB𝄪, vvC | C |
| 79 | 997.9 | vB𝄪, vC | ^C, v4D♭ | |
| 80 | 1010.5 | C | ^^C, v3D♭ | |
| 81 | 1023.2 | ^C, ^D♭♭♭ | ^3C, vvD♭ | |
| 82 | 1035.8 | 20/11 | ^^C, ^^D♭♭♭ | ^4C, vD♭ |
| 83 | 1048.4 | 11/6 | vvC♯, vvD♭♭ | ^5C, D♭ |
| 84 | 1061.1 | 24/13 | vC♯, vD♭♭ | ^6C, ^D♭ |
| 85 | 1073.7 | 13/7 | C♯, D♭♭ | v5C♯, ^^D♭ |
| 86 | 1086.3 | ^C♯, ^D♭♭ | v4C♯, ^3D♭ | |
| 87 | 1098.9 | ^^C♯, ^^D♭♭ | v3C♯, ^4D♭ | |
| 88 | 1111.6 | 19/10 | vvC𝄪, vvD♭ | vvC♯, ^5D♭ |
| 89 | 1124.2 | 23/12 | vC𝄪, vD♭ | vC♯, v6D |
| 90 | 1136.8 | C𝄪, D♭ | C♯, v5D | |
| 91 | 1149.5 | 35/18 | ^C𝄪, ^D♭ | ^C♯, v4D |
| 92 | 1162.1 | ^^C𝄪, ^^D♭ | ^^C♯, v3D | |
| 93 | 1174.7 | vvC♯𝄪, vvD | ^3C♯, vvD | |
| 94 | 1187.4 | vC♯𝄪, vD | ^4C♯, vD | |
| 95 | 1200 | 2/1 | D | D |
Music
- Puget Sound Asleep (2024)