95edo
← 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 | 12.632 | ^D, v4E♭♭ | ^D, v4E♭ | |
2 | 25.263 | 66/65, 78/77 | ^^D, v3E♭♭ | ^^D, v3E♭ |
3 | 37.895 | 49/48, 50/49 | ^3D, vvE♭♭ | ^3D, vvE♭ |
4 | 50.526 | 36/35, 65/63 | ^4D, vE♭♭ | ^4D, vE♭ |
5 | 63.158 | 26/25, 80/77 | D♯, E♭♭ | ^5D, E♭ |
6 | 75.789 | 22/21 | ^D♯, v4E♭ | ^6D, v11E |
7 | 88.421 | 21/20 | ^^D♯, v3E♭ | ^7D, v10E |
8 | 101.053 | 35/33, 52/49, 55/52 | ^3D♯, vvE♭ | ^8D, v9E |
9 | 113.684 | 77/72 | ^4D♯, vE♭ | ^9D, v8E |
10 | 126.316 | 14/13 | D𝄪, E♭ | ^10D, v7E |
11 | 138.947 | 13/12 | ^D𝄪, v4E | ^11D, v6E |
12 | 151.579 | 12/11 | ^^D𝄪, v3E | D♯, v5E |
13 | 164.211 | 11/10 | ^3D𝄪, vvE | ^D♯, v4E |
14 | 176.842 | 72/65 | ^4D𝄪, vE | ^^D♯, v3E |
15 | 189.474 | 39/35, 49/44 | E | ^3D♯, vvE |
16 | 202.105 | 55/49 | ^E, v4F♭ | ^4D♯, vE |
17 | 214.737 | ^^E, v3F♭ | E | |
18 | 227.368 | 8/7 | ^3E, vvF♭ | ^E, v4F |
19 | 240 | 55/48, 63/55 | ^4E, vF♭ | ^^E, v3F |
20 | 252.632 | 15/13 | E♯, F♭ | ^3E, vvF |
21 | 265.263 | 7/6 | ^E♯, v4F | ^4E, vF |
22 | 277.895 | ^^E♯, v3F | F | |
23 | 290.526 | 13/11, 77/65 | ^3E♯, vvF | ^F, v4G♭ |
24 | 303.158 | 25/21 | ^4E♯, vF | ^^F, v3G♭ |
25 | 315.789 | 6/5 | F | ^3F, vvG♭ |
26 | 328.421 | 40/33 | ^F, v4G♭♭ | ^4F, vG♭ |
27 | 341.053 | ^^F, v3G♭♭ | ^5F, G♭ | |
28 | 353.684 | 49/40, 60/49 | ^3F, vvG♭♭ | ^6F, v11G |
29 | 366.316 | 26/21 | ^4F, vG♭♭ | ^7F, v10G |
30 | 378.947 | F♯, G♭♭ | ^8F, v9G | |
31 | 391.579 | 44/35, 49/39 | ^F♯, v4G♭ | ^9F, v8G |
32 | 404.211 | 63/50 | ^^F♯, v3G♭ | ^10F, v7G |
33 | 416.842 | 14/11, 33/26 | ^3F♯, vvG♭ | ^11F, v6G |
34 | 429.474 | 50/39, 77/60 | ^4F♯, vG♭ | F♯, v5G |
35 | 442.105 | F𝄪, G♭ | ^F♯, v4G | |
36 | 454.737 | 13/10 | ^F𝄪, v4G | ^^F♯, v3G |
37 | 467.368 | 55/42, 72/55 | ^^F𝄪, v3G | ^3F♯, vvG |
38 | 480 | 33/25 | ^3F𝄪, vvG | ^4F♯, vG |
39 | 492.632 | 65/49 | ^4F𝄪, vG | G |
40 | 505.263 | G | ^G, v4A♭ | |
41 | 517.895 | 35/26, 66/49 | ^G, v4A♭♭ | ^^G, v3A♭ |
42 | 530.526 | 49/36 | ^^G, v3A♭♭ | ^3G, vvA♭ |
43 | 543.158 | 48/35 | ^3G, vvA♭♭ | ^4G, vA♭ |
44 | 555.789 | 11/8 | ^4G, vA♭♭ | ^5G, A♭ |
45 | 568.421 | 18/13, 25/18 | G♯, A♭♭ | ^6G, v11A |
46 | 581.053 | 7/5 | ^G♯, v4A♭ | ^7G, v10A |
47 | 593.684 | 55/39 | ^^G♯, v3A♭ | ^8G, v9A |
48 | 606.316 | 78/55 | ^3G♯, vvA♭ | ^9G, v8A |
49 | 618.947 | 10/7 | ^4G♯, vA♭ | ^10G, v7A |
50 | 631.579 | 13/9, 36/25 | G𝄪, A♭ | ^11G, v6A |
51 | 644.211 | 16/11 | ^G𝄪, v4A | G♯, v5A |
52 | 656.842 | 35/24 | ^^G𝄪, v3A | ^G♯, v4A |
53 | 669.474 | 72/49 | ^3G𝄪, vvA | ^^G♯, v3A |
54 | 682.105 | 49/33, 52/35, 77/52 | ^4G𝄪, vA | ^3G♯, vvA |
55 | 694.737 | A | ^4G♯, vA | |
56 | 707.368 | ^A, v4B♭♭ | A | |
57 | 720 | 50/33 | ^^A, v3B♭♭ | ^A, v4B♭ |
58 | 732.632 | 55/36 | ^3A, vvB♭♭ | ^^A, v3B♭ |
59 | 745.263 | 20/13, 77/50 | ^4A, vB♭♭ | ^3A, vvB♭ |
60 | 757.895 | 65/42 | A♯, B♭♭ | ^4A, vB♭ |
61 | 770.526 | 39/25 | ^A♯, v4B♭ | ^5A, B♭ |
62 | 783.158 | 11/7, 52/33 | ^^A♯, v3B♭ | ^6A, v11B |
63 | 795.789 | ^3A♯, vvB♭ | ^7A, v10B | |
64 | 808.421 | 35/22, 78/49 | ^4A♯, vB♭ | ^8A, v9B |
65 | 821.053 | 77/48 | A𝄪, B♭ | ^9A, v8B |
66 | 833.684 | 21/13 | ^A𝄪, v4B | ^10A, v7B |
67 | 846.316 | 49/30, 80/49 | ^^A𝄪, v3B | ^11A, v6B |
68 | 858.947 | ^3A𝄪, vvB | A♯, v5B | |
69 | 871.579 | 33/20 | ^4A𝄪, vB | ^A♯, v4B |
70 | 884.211 | 5/3 | B | ^^A♯, v3B |
71 | 896.842 | 42/25 | ^B, v4C♭ | ^3A♯, vvB |
72 | 909.474 | 22/13 | ^^B, v3C♭ | ^4A♯, vB |
73 | 922.105 | ^3B, vvC♭ | B | |
74 | 934.737 | 12/7 | ^4B, vC♭ | ^B, v4C |
75 | 947.368 | 26/15 | B♯, C♭ | ^^B, v3C |
76 | 960 | ^B♯, v4C | ^3B, vvC | |
77 | 972.632 | 7/4 | ^^B♯, v3C | ^4B, vC |
78 | 985.263 | ^3B♯, vvC | C | |
79 | 997.895 | ^4B♯, vC | ^C, v4D♭ | |
80 | 1010.526 | 70/39 | C | ^^C, v3D♭ |
81 | 1023.158 | 65/36 | ^C, v4D♭♭ | ^3C, vvD♭ |
82 | 1035.789 | 20/11 | ^^C, v3D♭♭ | ^4C, vD♭ |
83 | 1048.421 | 11/6 | ^3C, vvD♭♭ | ^5C, D♭ |
84 | 1061.053 | 24/13 | ^4C, vD♭♭ | ^6C, v11D |
85 | 1073.684 | 13/7 | C♯, D♭♭ | ^7C, v10D |
86 | 1086.316 | ^C♯, v4D♭ | ^8C, v9D | |
87 | 1098.947 | 49/26, 66/35 | ^^C♯, v3D♭ | ^9C, v8D |
88 | 1111.579 | 40/21 | ^3C♯, vvD♭ | ^10C, v7D |
89 | 1124.211 | 21/11 | ^4C♯, vD♭ | ^11C, v6D |
90 | 1136.842 | 25/13, 77/40 | C𝄪, D♭ | C♯, v5D |
91 | 1149.474 | 35/18 | ^C𝄪, v4D | ^C♯, v4D |
92 | 1162.105 | 49/25 | ^^C𝄪, v3D | ^^C♯, v3D |
93 | 1174.737 | 65/33, 77/39 | ^3C𝄪, vvD | ^3C♯, vvD |
94 | 1187.368 | ^4C𝄪, vD | ^4C♯, vD | |
95 | 1200 | 2/1 | D | D |
Music
- Puget Sound Asleep (2024)