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		^D, v5E♭
2	26.1		^^D, v4E♭
3	39.1	42/41, 43/42	^3D, v3E♭
4	52.2	33/32, 34/33, 35/34	^4D, vvE♭
5	65.2		^5D, vE♭
6	78.3	22/21, 23/22	v4D♯, E♭
7	91.3	19/18, 20/19, 39/37	v3D♯, ^E♭
8	104.3	17/16, 35/33	vvD♯, ^^E♭
9	117.4	31/29	vD♯, ^3E♭
10	130.4	14/13, 41/38	D♯, ^4E♭
11	143.5	38/35	^D♯, v5E
12	156.5	23/21, 35/32	^^D♯, v4E
13	169.6	32/29, 43/39	^3D♯, v3E
14	182.6	10/9	^4D♯, vvE
15	195.7	37/33	^5D♯, vE
16	208.7	35/31	E
17	221.7	33/29, 42/37	^E, v5F
18	234.8		^^E, v4F
19	247.8		^3E, v3F
20	260.9	36/31, 43/37	^4E, vvF
21	273.9	34/29, 41/35	^5E, vF
22	287	13/11, 33/28	F
23	300	19/16	^F, v5G♭
24	313	6/5	^^F, v4G♭
25	326.1	29/24, 35/29, 41/34	^3F, v3G♭
26	339.1	28/23	^4F, vvG♭
27	352.2	38/31	^5F, vG♭
28	365.2	21/17	v4F♯, G♭
29	378.3	41/33	v3F♯, ^G♭
30	391.3		vvF♯, ^^G♭
31	404.3	24/19, 43/34	vF♯, ^3G♭
32	417.4	14/11	F♯, ^4G♭
33	430.4	41/32	^F♯, v5G
34	443.5	31/24, 40/31	^^F♯, v4G
35	456.5	43/33	^3F♯, v3G
36	469.6	21/16, 38/29	^4F♯, vvG
37	482.6	37/28, 41/31	^5F♯, vG
38	495.7	4/3	G
39	508.7		^G, v5A♭
40	521.7	23/17, 27/20	^^G, v4A♭
41	534.8		^3G, v3A♭
42	547.8		^4G, vvA♭
43	560.9	29/21	^5G, vA♭
44	573.9	32/23, 39/28	v4G♯, A♭
45	587		v3G♯, ^A♭
46	600	41/29	vvG♯, ^^A♭
47	613	37/26	vG♯, ^3A♭
48	626.1	23/16, 33/23	G♯, ^4A♭
49	639.1	42/29	^G♯, v5A
50	652.2	35/24	^^G♯, v4A
51	665.2		^3G♯, v3A
52	678.3	34/23, 40/27	^4G♯, vvA
53	691.3		^5G♯, vA
54	704.3	3/2	A
55	717.4		^A, v5B♭
56	730.4	29/19, 32/21	^^A, v4B♭
57	743.5	43/28	^3A, v3B♭
58	756.5	31/20	^4A, vvB♭
59	769.6		^5A, vB♭
60	782.6	11/7	v4A♯, B♭
61	795.7	19/12	v3A♯, ^B♭
62	808.7		vvA♯, ^^B♭
63	821.7	37/23	vA♯, ^3B♭
64	834.8	34/21	A♯, ^4B♭
65	847.8	31/19	^A♯, v5B
66	860.9	23/14	^^A♯, v4B
67	873.9		^3A♯, v3B
68	887	5/3	^4A♯, vvB
69	900	32/19, 37/22	^5A♯, vB
70	913	22/13, 39/23	B
71	926.1	29/17, 41/24	^B, v5C
72	939.1	31/18	^^B, v4C
73	952.2		^3B, v3C
74	965.2		^4B, vvC
75	978.3	37/21	^5B, vC
76	991.3	39/22	C
77	1004.3		^C, v5D♭
78	1017.4	9/5	^^C, v4D♭
79	1030.4	29/16	^3C, v3D♭
80	1043.5	42/23	^4C, vvD♭
81	1056.5	35/19	^5C, vD♭
82	1069.6	13/7	v4C♯, D♭
83	1082.6	43/23	v3C♯, ^D♭
84	1095.7	32/17	vvC♯, ^^D♭
85	1108.7	19/10, 36/19	vC♯, ^3D♭
86	1121.7	21/11	C♯, ^4D♭
87	1134.8		^C♯, v5D
88	1147.8	33/17	^^C♯, v4D
89	1160.9	41/21, 43/22	^3C♯, v3D
90	1173.9		^4C♯, vvD
91	1187		^5C♯, vD
92	1200	2/1	D