92edt

← 91edt

92edt

93edt →

Prime factorization	22 × 23
Step size	20.6734 ¢
Octave	58\92edt (1199.06 ¢) (→ 29\46edt)
Consistency limit	18
Distinct consistency limit	12

92 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 92edt or 92ed3), is a nonoctave tuning system that divides the interval of 3/1 into 92 equal parts of about 20.7 ¢ each. Each step represents a frequency ratio of 3^1/92, or the 92nd root of 3.

Theory

92edt is related to 58edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.941 cents compressed. Like 58edo, 92edt is consistent to the 18-integer-limit. The prime harmonics 5, 7, 11, and 13, which are tuned sharp in 58edo, remain sharp here, but significantly less so. The 17, which is flat to begin with, becomes worse.

Harmonics

Approximation of harmonics in 92edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.94	+0.00	-1.88	+4.60	-0.94	+0.94	-2.82	+0.00	+3.66	+4.04	-1.88
	Relative (%)	-4.6	+0.0	-9.1	+22.2	-4.6	+4.6	-13.7	+0.0	+17.7	+19.5	-9.1
Steps (reduced)		58 (58)	92 (0)	116 (24)	135 (43)	150 (58)	163 (71)	174 (82)	184 (0)	193 (9)	201 (17)	208 (24)

Approximation of harmonics in 92edt (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+4.26	+0.00	+4.60	-3.77	-5.35	-0.94	+8.82	+2.72	+0.94	+3.10	+8.84	-2.82
	Relative (%)	+20.6	+0.0	+22.2	-18.2	-25.9	-4.6	+42.7	+13.1	+4.6	+15.0	+42.7	-13.7
Steps (reduced)		215 (31)	221 (37)	227 (43)	232 (48)	237 (53)	242 (58)	247 (63)	251 (67)	255 (71)	259 (75)	263 (79)	266 (82)

Subsets and supersets

Since 92 factors into primes as 2² × 23, 92edt contains subset edts 2, 4, 23, and 46.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	20.7	14.1
2	41.3	28.3	40/39, 41/40, 42/41, 43/42
3	62	42.4	28/27, 29/28
4	82.7	56.5	21/20, 22/21, 43/41
5	103.4	70.7	17/16, 35/33
6	124	84.8	29/27, 43/40
7	144.7	98.9	25/23, 37/34, 38/35
8	165.4	113	11/10
9	186.1	127.2	39/35
10	206.7	141.3
11	227.4	155.4	41/36
12	248.1	169.6	15/13
13	268.8	183.7	7/6
14	289.4	197.8	13/11
15	310.1	212	43/36
16	330.8	226.1	23/19, 40/33
17	351.4	240.2	38/31
18	372.1	254.3	26/21, 31/25, 36/29
19	392.8	268.5
20	413.5	282.6	33/26
21	434.1	296.7	9/7
22	454.8	310.9	13/10
23	475.5	325	25/19
24	496.2	339.1	4/3
25	516.8	353.3	27/20, 31/23, 35/26
26	537.5	367.4	15/11
27	558.2	381.5	29/21, 40/29
28	578.9	395.7
29	599.5	409.8	24/17, 41/29
30	620.2	423.9	10/7
31	640.9	438	29/20, 42/29
32	661.5	452.2	22/15, 41/28
33	682.2	466.3	40/27, 43/29
34	702.9	480.4	3/2
35	723.6	494.6	38/25, 41/27
36	744.2	508.7	20/13, 43/28
37	764.9	522.8	14/9
38	785.6	537
39	806.3	551.1	35/22, 43/27
40	826.9	565.2	29/18
41	847.6	579.3	31/19
42	868.3	593.5	33/20, 38/23, 43/26
43	889	607.6
44	909.6	621.7	22/13
45	930.3	635.9
46	951	650	26/15
47	971.7	664.1
48	992.3	678.3	39/22
49	1013	692.4
50	1033.7	706.5	20/11
51	1054.3	720.7
52	1075	734.8	41/22
53	1095.7	748.9	32/17
54	1116.4	763	40/21
55	1137	777.2	27/14
56	1157.7	791.3	39/20, 41/21, 43/22
57	1178.4	805.4
58	1199.1	819.6	2/1
59	1219.7	833.7
60	1240.4	847.8	41/20, 43/21
61	1261.1	862	29/14
62	1281.8	876.1	21/10
63	1302.4	890.2	17/8
64	1323.1	904.3	43/20
65	1343.8	918.5	37/17
66	1364.4	932.6	11/5
67	1385.1	946.7	20/9
68	1405.8	960.9	9/4
69	1426.5	975	41/18
70	1447.1	989.1	30/13
71	1467.8	1003.3	7/3
72	1488.5	1017.4	26/11
73	1509.2	1031.5	43/18
74	1529.8	1045.7	29/12
75	1550.5	1059.8
76	1571.2	1073.9
77	1591.9	1088
78	1612.5	1102.2	33/13
79	1633.2	1116.3	18/7
80	1653.9	1130.4	13/5
81	1674.5	1144.6
82	1695.2	1158.7
83	1715.9	1172.8	35/13
84	1736.6	1187	30/11
85	1757.2	1201.1
86	1777.9	1215.2
87	1798.6	1229.3
88	1819.3	1243.5	20/7
89	1839.9	1257.6
90	1860.6	1271.7	41/14
91	1881.3	1285.9
92	1902	1300	3/1

See also

• 34edf – relative edf
• 58edo – relative edo
• 150ed6 – relative ed6
• 163ed7 – relative ed7