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 13.043 ¢ 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, v5Eb
2	26.087	^^D, v4Eb	56/55, 64/63, 65/64, 66/65, 78/77, 81/80
3	39.1304	^3D, v3Eb
4	52.1739	^4D, vvEb	33/32, 36/35, 65/63
5	65.2174	^5D, vEb
6	78.2609	^6D, Eb	22/21
7	91.3043	^7D, v9E
8	104.348	^8D, v8E	35/33, 52/49
9	117.391	^9D, v7E
10	130.435	D#, v6E	14/13, 27/25
11	143.478	^D#, v5E
12	156.522	^^D#, v4E	35/32
13	169.565	^3D#, v3E
14	182.609	^4D#, vvE	10/9, 39/35, 49/44
15	195.652	^5D#, vE
16	208.696	E	9/8, 44/39
17	221.739	^E, v5F
18	234.783	^^E, v4F	8/7, 55/48, 63/55
19	247.826	^3E, v3F
20	260.87	^4E, vvF	64/55, 65/56
21	273.913	^5E, vF
22	286.957	F	13/11, 33/28
23	300	^F, v5Gb
24	313.043	^^F, v4Gb	6/5
25	326.087	^3F, v3Gb
26	339.13	^4F, vvGb	39/32
27	352.174	^5F, vGb
28	365.217	^6F, Gb	26/21
29	378.261	^7F, v9G
30	391.304	^8F, v8G	5/4, 44/35, 49/39
31	404.348	^9F, v7G
32	417.391	F#, v6G	14/11, 33/26, 80/63
33	430.435	^F#, v5G
34	443.478	^^F#, v4G
35	456.522	^3F#, v3G
36	469.565	^4F#, vvG	21/16, 55/42, 72/55
37	482.609	^5F#, vG
38	495.652	G	4/3
39	508.696	^G, v5Ab
40	521.739	^^G, v4Ab	27/20, 65/48
41	534.783	^3G, v3Ab
42	547.826	^4G, vvAb	11/8, 48/35
43	560.87	^5G, vAb
44	573.913	^6G, Ab	25/18, 39/28
45	586.957	^7G, v9A
46	600	^8G, v8A	55/39, 78/55
47	613.043	^9G, v7A
48	626.087	G#, v6A	36/25, 56/39, 63/44
49	639.13	^G#, v5A
50	652.174	^^G#, v4A	16/11, 35/24
51	665.217	^3G#, v3A
52	678.261	^4G#, vvA	40/27, 65/44, 77/52
53	691.304	^5G#, vA
54	704.348	A	3/2
55	717.391	^A, v5Bb
56	730.435	^^A, v4Bb	32/21, 55/36
57	743.478	^3A, v3Bb
58	756.522	^4A, vvBb	65/42
59	769.565	^5A, vBb
60	782.609	^6A, Bb	11/7, 52/33, 63/40
61	795.652	^7A, v9B
62	808.696	^8A, v8B	8/5, 35/22, 78/49
63	821.739	^9A, v7B
64	834.783	A#, v6B	21/13, 81/50
65	847.826	^A#, v5B
66	860.87	^^A#, v4B	64/39
67	873.913	^3A#, v3B
68	886.957	^4A#, vvB	5/3
69	900	^5A#, vB
70	913.043	B	22/13, 56/33
71	926.087	^B, v5C
72	939.13	^^B, v4C	55/32
73	952.174	^3B, v3C
74	965.217	^4B, vvC	7/4
75	978.261	^5B, vC
76	991.304	C	16/9, 39/22
77	1004.35	^C, v5Db
78	1017.39	^^C, v4Db	9/5, 70/39
79	1030.43	^3C, v3Db
80	1043.48	^4C, vvDb	64/35
81	1056.52	^5C, vDb
82	1069.57	^6C, Db	13/7, 50/27
83	1082.61	^7C, v9D
84	1095.65	^8C, v8D	49/26, 66/35
85	1108.7	^9C, v7D
86	1121.74	C#, v6D	21/11
87	1134.78	^C#, v5D
88	1147.83	^^C#, v4D	35/18, 64/33
89	1160.87	^3C#, v3D
90	1173.91	^4C#, vvD	55/28, 63/32, 65/33, 77/39
91	1186.96	^5C#, vD
92	1200	D	2/1