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.

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