95edo

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← 94edo95edo96edo →
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

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

Approximation of odd harmonics in 95edo
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

JUMBLE
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