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
| 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 (%) | +43 | +42 | +30 | -14 | +35 | +46 | -15 | -31 | +45 | -27 | +26 | |
| Steps (reduced) |
151 (56) |
221 (31) |
267 (77) |
301 (16) |
329 (44) |
352 (67) |
371 (86) |
388 (8) |
404 (24) |
417 (37) |
430 (50) | |
It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 1331/1323, 176/175, 6250/6237 and 4000/3993 in the 11-limit, and 196/195, 640/637, 325/324, 364/363, 847/845, 1001/1000 and 2200/2197 in the 13-limit.
It supports the rank 2 temperaments enneadecal, magus, gorgik, octacot, quinmite, tetracot and trisedodge.
It supports the rank 3 temperaments breed, manwe, octagari, octarod and shrusus.
It provides the optimal patent val for the rank 3 shrusus temperament.
95 factors as 5*19, so it contains both 5edo and 19edo. It is also a dual-fifth tuning.
Intervals
| Steps | Cents | Ups and downs notation (dual flat fifth 55\95) |
Ups and downs notation (dual sharp fifth 56\95) |
Approximate ratios |
|---|---|---|---|---|
| 0 | 0 | D | D | 1/1 |
| 1 | 12.6316 | ^D, v4Ebb | ^D, v4Eb | |
| 2 | 25.2632 | ^^D, v3Ebb | ^^D, v3Eb | 66/65, 78/77 |
| 3 | 37.8947 | ^3D, vvEbb | ^3D, vvEb | 49/48, 50/49 |
| 4 | 50.5263 | ^4D, vEbb | ^4D, vEb | 36/35, 65/63 |
| 5 | 63.1579 | D#, Ebb | ^5D, Eb | 26/25, 80/77 |
| 6 | 75.7895 | ^D#, v4Eb | ^6D, v11E | 22/21 |
| 7 | 88.4211 | ^^D#, v3Eb | ^7D, v10E | 21/20 |
| 8 | 101.053 | ^3D#, vvEb | ^8D, v9E | 35/33, 52/49, 55/52 |
| 9 | 113.684 | ^4D#, vEb | ^9D, v8E | 77/72 |
| 10 | 126.316 | Dx, Eb | ^10D, v7E | 14/13 |
| 11 | 138.947 | ^Dx, v4E | ^11D, v6E | 13/12 |
| 12 | 151.579 | ^^Dx, v3E | D#, v5E | 12/11 |
| 13 | 164.211 | ^3Dx, vvE | ^D#, v4E | 11/10 |
| 14 | 176.842 | ^4Dx, vE | ^^D#, v3E | 72/65 |
| 15 | 189.474 | E | ^3D#, vvE | 39/35, 49/44 |
| 16 | 202.105 | ^E, v4Fb | ^4D#, vE | 55/49 |
| 17 | 214.737 | ^^E, v3Fb | E | |
| 18 | 227.368 | ^3E, vvFb | ^E, v4F | 8/7 |
| 19 | 240 | ^4E, vFb | ^^E, v3F | 55/48, 63/55 |
| 20 | 252.632 | E#, Fb | ^3E, vvF | 15/13 |
| 21 | 265.263 | ^E#, v4F | ^4E, vF | 7/6 |
| 22 | 277.895 | ^^E#, v3F | F | |
| 23 | 290.526 | ^3E#, vvF | ^F, v4Gb | 13/11, 77/65 |
| 24 | 303.158 | ^4E#, vF | ^^F, v3Gb | 25/21 |
| 25 | 315.789 | F | ^3F, vvGb | 6/5 |
| 26 | 328.421 | ^F, v4Gbb | ^4F, vGb | 40/33 |
| 27 | 341.053 | ^^F, v3Gbb | ^5F, Gb | |
| 28 | 353.684 | ^3F, vvGbb | ^6F, v11G | 49/40, 60/49 |
| 29 | 366.316 | ^4F, vGbb | ^7F, v10G | 26/21 |
| 30 | 378.947 | F#, Gbb | ^8F, v9G | |
| 31 | 391.579 | ^F#, v4Gb | ^9F, v8G | 44/35, 49/39 |
| 32 | 404.211 | ^^F#, v3Gb | ^10F, v7G | 63/50 |
| 33 | 416.842 | ^3F#, vvGb | ^11F, v6G | 14/11, 33/26 |
| 34 | 429.474 | ^4F#, vGb | F#, v5G | 50/39, 77/60 |
| 35 | 442.105 | Fx, Gb | ^F#, v4G | |
| 36 | 454.737 | ^Fx, v4G | ^^F#, v3G | 13/10 |
| 37 | 467.368 | ^^Fx, v3G | ^3F#, vvG | 55/42, 72/55 |
| 38 | 480 | ^3Fx, vvG | ^4F#, vG | 33/25 |
| 39 | 492.632 | ^4Fx, vG | G | 65/49 |
| 40 | 505.263 | G | ^G, v4Ab | |
| 41 | 517.895 | ^G, v4Abb | ^^G, v3Ab | 35/26, 66/49 |
| 42 | 530.526 | ^^G, v3Abb | ^3G, vvAb | 49/36 |
| 43 | 543.158 | ^3G, vvAbb | ^4G, vAb | 48/35 |
| 44 | 555.789 | ^4G, vAbb | ^5G, Ab | 11/8 |
| 45 | 568.421 | G#, Abb | ^6G, v11A | 18/13, 25/18 |
| 46 | 581.053 | ^G#, v4Ab | ^7G, v10A | 7/5 |
| 47 | 593.684 | ^^G#, v3Ab | ^8G, v9A | 55/39 |
| 48 | 606.316 | ^3G#, vvAb | ^9G, v8A | 78/55 |
| 49 | 618.947 | ^4G#, vAb | ^10G, v7A | 10/7 |
| 50 | 631.579 | Gx, Ab | ^11G, v6A | 13/9, 36/25 |
| 51 | 644.211 | ^Gx, v4A | G#, v5A | 16/11 |
| 52 | 656.842 | ^^Gx, v3A | ^G#, v4A | 35/24 |
| 53 | 669.474 | ^3Gx, vvA | ^^G#, v3A | 72/49 |
| 54 | 682.105 | ^4Gx, vA | ^3G#, vvA | 49/33, 52/35, 77/52 |
| 55 | 694.737 | A | ^4G#, vA | |
| 56 | 707.368 | ^A, v4Bbb | A | |
| 57 | 720 | ^^A, v3Bbb | ^A, v4Bb | 50/33 |
| 58 | 732.632 | ^3A, vvBbb | ^^A, v3Bb | 55/36 |
| 59 | 745.263 | ^4A, vBbb | ^3A, vvBb | 20/13, 77/50 |
| 60 | 757.895 | A#, Bbb | ^4A, vBb | 65/42 |
| 61 | 770.526 | ^A#, v4Bb | ^5A, Bb | 39/25 |
| 62 | 783.158 | ^^A#, v3Bb | ^6A, v11B | 11/7, 52/33 |
| 63 | 795.789 | ^3A#, vvBb | ^7A, v10B | |
| 64 | 808.421 | ^4A#, vBb | ^8A, v9B | 35/22, 78/49 |
| 65 | 821.053 | Ax, Bb | ^9A, v8B | 77/48 |
| 66 | 833.684 | ^Ax, v4B | ^10A, v7B | 21/13 |
| 67 | 846.316 | ^^Ax, v3B | ^11A, v6B | 49/30, 80/49 |
| 68 | 858.947 | ^3Ax, vvB | A#, v5B | |
| 69 | 871.579 | ^4Ax, vB | ^A#, v4B | 33/20 |
| 70 | 884.211 | B | ^^A#, v3B | 5/3 |
| 71 | 896.842 | ^B, v4Cb | ^3A#, vvB | 42/25 |
| 72 | 909.474 | ^^B, v3Cb | ^4A#, vB | 22/13 |
| 73 | 922.105 | ^3B, vvCb | B | |
| 74 | 934.737 | ^4B, vCb | ^B, v4C | 12/7 |
| 75 | 947.368 | B#, Cb | ^^B, v3C | 26/15 |
| 76 | 960 | ^B#, v4C | ^3B, vvC | |
| 77 | 972.632 | ^^B#, v3C | ^4B, vC | 7/4 |
| 78 | 985.263 | ^3B#, vvC | C | |
| 79 | 997.895 | ^4B#, vC | ^C, v4Db | |
| 80 | 1010.53 | C | ^^C, v3Db | 70/39 |
| 81 | 1023.16 | ^C, v4Dbb | ^3C, vvDb | 65/36 |
| 82 | 1035.79 | ^^C, v3Dbb | ^4C, vDb | 20/11 |
| 83 | 1048.42 | ^3C, vvDbb | ^5C, Db | 11/6 |
| 84 | 1061.05 | ^4C, vDbb | ^6C, v11D | 24/13 |
| 85 | 1073.68 | C#, Dbb | ^7C, v10D | 13/7 |
| 86 | 1086.32 | ^C#, v4Db | ^8C, v9D | |
| 87 | 1098.95 | ^^C#, v3Db | ^9C, v8D | 49/26, 66/35 |
| 88 | 1111.58 | ^3C#, vvDb | ^10C, v7D | 40/21 |
| 89 | 1124.21 | ^4C#, vDb | ^11C, v6D | 21/11 |
| 90 | 1136.84 | Cx, Db | C#, v5D | 25/13, 77/40 |
| 91 | 1149.47 | ^Cx, v4D | ^C#, v4D | 35/18 |
| 92 | 1162.11 | ^^Cx, v3D | ^^C#, v3D | 49/25 |
| 93 | 1174.74 | ^3Cx, vvD | ^3C#, vvD | 65/33, 77/39 |
| 94 | 1187.37 | ^4Cx, vD | ^4C#, vD | |
| 95 | 1200 | D | D | 2/1 |