92edo

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← 91edo92edo93edo →
Prime factorization 22 × 23
Step size 13.0435¢ 
Fifth 54\92 (704.348¢) (→27\46)
Semitones (A1:m2) 10:6 (130.4¢ : 78.26¢)
Consistency limit 5
Distinct consistency limit 5

92 equal divisions of the octave (abbreviated 92edo or 92ed2), also called 92-tone equal temperament (92tet) or 92 equal temperament (92et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 92 equal parts of about 13 ¢ each. Each step represents a frequency ratio of 21/92, or the 92nd root of 2.

Theory

The equal temperament is contorted through the 17-limit, with the same tuning and commas as 46edo, and hence attracts little interest. That said, the approximation to the 19th harmonic is much improved. Like 46, the patent fifth (54\92) is about 2.4 cents sharp. The alternate fifth 53\92 is a very flat fifth, flatter even than 26edo, and the 92bcccd val supports flattone. 92edo is the highest in a series of four consecutive edos to temper out the quartisma (117440512/117406179).

Odd harmonics

Approximation of odd harmonics in 92edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.39 +4.99 -3.61 +4.79 -3.49 -5.75 -5.66 -0.61 +2.49 -1.22 -2.19
Relative (%) +18.3 +38.3 -27.7 +36.7 -26.8 -44.0 -43.4 -4.7 +19.1 -9.3 -16.8
Steps
(reduced)
146
(54)
214
(30)
258
(74)
292
(16)
318
(42)
340
(64)
359
(83)
376
(8)
391
(23)
404
(36)
416
(48)

Subsets and supersets

Since 92 factors into 22 × 23, 92edo has subset edos 2, 4, 23, and 46.

Intervals

Steps Cents Approximate Ratios Ups and Downs Notation
0 0 1/1 D
1 13.043 ^D, v5E♭
2 26.087 56/55, 64/63, 65/64, 66/65, 78/77, 81/80 ^^D, v4E♭
3 39.13 ^3D, v3E♭
4 52.174 33/32, 36/35, 65/63 ^4D, vvE♭
5 65.217 ^5D, vE♭
6 78.261 22/21 ^6D, E♭
7 91.304 ^7D, v9E
8 104.348 35/33, 52/49 ^8D, v8E
9 117.391 ^9D, v7E
10 130.435 14/13, 27/25 D♯, v6E
11 143.478 ^D♯, v5E
12 156.522 35/32 ^^D♯, v4E
13 169.565 ^3D♯, v3E
14 182.609 10/9, 39/35, 49/44 ^4D♯, vvE
15 195.652 ^5D♯, vE
16 208.696 9/8, 44/39 E
17 221.739 ^E, v5F
18 234.783 8/7, 55/48, 63/55 ^^E, v4F
19 247.826 ^3E, v3F
20 260.87 64/55, 65/56 ^4E, vvF
21 273.913 ^5E, vF
22 286.957 13/11, 33/28 F
23 300 ^F, v5G♭
24 313.043 6/5 ^^F, v4G♭
25 326.087 ^3F, v3G♭
26 339.13 39/32 ^4F, vvG♭
27 352.174 ^5F, vG♭
28 365.217 26/21 ^6F, G♭
29 378.261 ^7F, v9G
30 391.304 5/4, 44/35, 49/39 ^8F, v8G
31 404.348 ^9F, v7G
32 417.391 14/11, 33/26, 80/63 F♯, v6G
33 430.435 ^F♯, v5G
34 443.478 ^^F♯, v4G
35 456.522 ^3F♯, v3G
36 469.565 21/16, 55/42, 72/55 ^4F♯, vvG
37 482.609 ^5F♯, vG
38 495.652 4/3 G
39 508.696 ^G, v5A♭
40 521.739 27/20, 65/48 ^^G, v4A♭
41 534.783 ^3G, v3A♭
42 547.826 11/8, 48/35 ^4G, vvA♭
43 560.87 ^5G, vA♭
44 573.913 25/18, 39/28 ^6G, A♭
45 586.957 ^7G, v9A
46 600 55/39, 78/55 ^8G, v8A
47 613.043 ^9G, v7A
48 626.087 36/25, 56/39, 63/44 G♯, v6A
49 639.13 ^G♯, v5A
50 652.174 16/11, 35/24 ^^G♯, v4A
51 665.217 ^3G♯, v3A
52 678.261 40/27, 65/44, 77/52 ^4G♯, vvA
53 691.304 ^5G♯, vA
54 704.348 3/2 A
55 717.391 ^A, v5B♭
56 730.435 32/21, 55/36 ^^A, v4B♭
57 743.478 ^3A, v3B♭
58 756.522 65/42 ^4A, vvB♭
59 769.565 ^5A, vB♭
60 782.609 11/7, 52/33, 63/40 ^6A, B♭
61 795.652 ^7A, v9B
62 808.696 8/5, 35/22, 78/49 ^8A, v8B
63 821.739 ^9A, v7B
64 834.783 21/13, 81/50 A♯, v6B
65 847.826 ^A♯, v5B
66 860.87 64/39 ^^A♯, v4B
67 873.913 ^3A♯, v3B
68 886.957 5/3 ^4A♯, vvB
69 900 ^5A♯, vB
70 913.043 22/13, 56/33 B
71 926.087 ^B, v5C
72 939.13 55/32 ^^B, v4C
73 952.174 ^3B, v3C
74 965.217 7/4 ^4B, vvC
75 978.261 ^5B, vC
76 991.304 16/9, 39/22 C
77 1004.348 ^C, v5D♭
78 1017.391 9/5, 70/39 ^^C, v4D♭
79 1030.435 ^3C, v3D♭
80 1043.478 64/35 ^4C, vvD♭
81 1056.522 ^5C, vD♭
82 1069.565 13/7, 50/27 ^6C, D♭
83 1082.609 ^7C, v9D
84 1095.652 49/26, 66/35 ^8C, v8D
85 1108.696 ^9C, v7D
86 1121.739 21/11 C♯, v6D
87 1134.783 ^C♯, v5D
88 1147.826 35/18, 64/33 ^^C♯, v4D
89 1160.87 ^3C♯, v3D
90 1173.913 55/28, 63/32, 65/33, 77/39 ^4C♯, vvD
91 1186.957 ^5C♯, vD
92 1200 2/1 D