92edo

← 91edo

92edo

93edo →

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 2^1/92, or the 92nd root of 2.

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	+38	-28	+37	-27	-44	-43	-5	+19	-9	-17
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	Ups and downs notation	Approximate ratios
0	0	D	1/1
1	13.0435	↑D, ↓5E♭
2	26.087	↑↑D, ↓4E♭	56/55, 64/63, 65/64, 66/65, 78/77, 81/80
3	39.1304	↑3D, ↓3E♭
4	52.1739	↑4D, ↓↓E♭	33/32, 36/35, 65/63
5	65.2174	↑5D, ↓E♭
6	78.2609	↑6D, E♭	22/21
7	91.3043	↑7D, ↓9E
8	104.348	↑8D, ↓8E	35/33, 52/49
9	117.391	↑9D, ↓7E
10	130.435	D♯, ↓6E	14/13, 27/25
11	143.478	↑D♯, ↓5E
12	156.522	↑↑D♯, ↓4E	35/32
13	169.565	↑3D♯, ↓3E
14	182.609	↑4D♯, ↓↓E	10/9, 39/35, 49/44
15	195.652	↑5D♯, ↓E
16	208.696	E	9/8, 44/39
17	221.739	↑E, ↓5F
18	234.783	↑↑E, ↓4F	8/7, 55/48, 63/55
19	247.826	↑3E, ↓3F
20	260.87	↑4E, ↓↓F	64/55, 65/56
21	273.913	↑5E, ↓F
22	286.957	F	13/11, 33/28
23	300	↑F, ↓5G♭
24	313.043	↑↑F, ↓4G♭	6/5
25	326.087	↑3F, ↓3G♭
26	339.13	↑4F, ↓↓G♭	39/32
27	352.174	↑5F, ↓G♭
28	365.217	↑6F, G♭	26/21
29	378.261	↑7F, ↓9G
30	391.304	↑8F, ↓8G	5/4, 44/35, 49/39
31	404.348	↑9F, ↓7G
32	417.391	F♯, ↓6G	14/11, 33/26, 80/63
33	430.435	↑F♯, ↓5G
34	443.478	↑↑F♯, ↓4G
35	456.522	↑3F♯, ↓3G
36	469.565	↑4F♯, ↓↓G	21/16, 55/42, 72/55
37	482.609	↑5F♯, ↓G
38	495.652	G	4/3
39	508.696	↑G, ↓5A♭
40	521.739	↑↑G, ↓4A♭	27/20, 65/48
41	534.783	↑3G, ↓3A♭
42	547.826	↑4G, ↓↓A♭	11/8, 48/35
43	560.87	↑5G, ↓A♭
44	573.913	↑6G, A♭	25/18, 39/28
45	586.957	↑7G, ↓9A
46	600	↑8G, ↓8A	55/39, 78/55
47	613.043	↑9G, ↓7A
48	626.087	G♯, ↓6A	36/25, 56/39, 63/44
49	639.13	↑G♯, ↓5A
50	652.174	↑↑G♯, ↓4A	16/11, 35/24
51	665.217	↑3G♯, ↓3A
52	678.261	↑4G♯, ↓↓A	40/27, 65/44, 77/52
53	691.304	↑5G♯, ↓A
54	704.348	A	3/2
55	717.391	↑A, ↓5B♭
56	730.435	↑↑A, ↓4B♭	32/21, 55/36
57	743.478	↑3A, ↓3B♭
58	756.522	↑4A, ↓↓B♭	65/42
59	769.565	↑5A, ↓B♭
60	782.609	↑6A, B♭	11/7, 52/33, 63/40
61	795.652	↑7A, ↓9B
62	808.696	↑8A, ↓8B	8/5, 35/22, 78/49
63	821.739	↑9A, ↓7B
64	834.783	A♯, ↓6B	21/13, 81/50
65	847.826	↑A♯, ↓5B
66	860.87	↑↑A♯, ↓4B	64/39
67	873.913	↑3A♯, ↓3B
68	886.957	↑4A♯, ↓↓B	5/3
69	900	↑5A♯, ↓B
70	913.043	B	22/13, 56/33
71	926.087	↑B, ↓5C
72	939.13	↑↑B, ↓4C	55/32
73	952.174	↑3B, ↓3C
74	965.217	↑4B, ↓↓C	7/4
75	978.261	↑5B, ↓C
76	991.304	C	16/9, 39/22
77	1004.35	↑C, ↓5D♭
78	1017.39	↑↑C, ↓4D♭	9/5, 70/39
79	1030.43	↑3C, ↓3D♭
80	1043.48	↑4C, ↓↓D♭	64/35
81	1056.52	↑5C, ↓D♭
82	1069.57	↑6C, D♭	13/7, 50/27
83	1082.61	↑7C, ↓9D
84	1095.65	↑8C, ↓8D	49/26, 66/35
85	1108.7	↑9C, ↓7D
86	1121.74	C♯, ↓6D	21/11
87	1134.78	↑C♯, ↓5D
88	1147.83	↑↑C♯, ↓4D	35/18, 64/33
89	1160.87	↑3C♯, ↓3D
90	1173.91	↑4C♯, ↓↓D	55/28, 63/32, 65/33, 77/39
91	1186.96	↑5C♯, ↓D
92	1200	D	2/1