92edt

The 92 equal divisions of the tritave, often abbreviated 92-EDT, is the scale derived by dividing the Tritave into 92 equally-sized steps. Each step represents a frequency ratio of 20.67342392245 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the 11, 13 and 17-limits. It is not the smallest edt which is consistent through the 17-limit, but is the first edt to map the entire 11-limit tonality diamond to distinct scale steps, and hence the first edt which can define a version of the famous 43-note Genesis scale of Harry Partch. It supports hemififths, myna, diaschismic, harry, mystery, buzzard and thuja temperaments, and supplies the optimal patent val for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments thrush, bluebird, aplonis and jofur

While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 92 = 2*46, and 92 shares the same excellent fifth with 46edt.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 92edo (ordered by absolute error).

Interval, complement	Error (abs., in cents)
14/9, 27/14	0.001
13/11, 33/13	0.218
15/13, 13/5	0.34
11/10, 30/11	0.383
15/11, 11/5	0.558
13/10, 30/13	0.601
3/2, 2/1	0.941
9/7, 7/3	0.942
4/3, 9/4	1.883
7/6, 18/7	1.884
10/7, 21/10	2.715
9/8, 8/3	2.824
12/7, 7/4	2.825
11/7, 21/11	3.098
21/13, 13/7	3.316
7/5, 15/7	3.656
10/9, 27/10	3.657
27/16, 16/9	3.766
8/7, 21/8	3.766
14/11, 33/14	4.039
11/9, 27/11	4.04
14/13, 39/14	4.258
13/9, 27/13	4.258
15/14, 14/5	4.598
5/3, 9/5	4.599
21/16, 16/7	4.708
18/11, 11/6	4.982
18/13, 13/6	5.2
6/5, 5/2	5.54
12/11, 11/4	5.923
13/12, 36/13	6.141
5/4, 12/5	6.481
11/8, 24/11	6.865
13/8, 24/13	7.083
8/5, 15/8	7.423
16/11, 33/16	7.806
16/13, 39/16	8.024
16/15, 45/16	8.364

Scales

hemif7

hemif10

hemif17

Intervals

degree of 92edt	cents value	ratios	17-3reduced-limit
0	0	1/1	1/1
1	20.67342392245	56/55, 64/63, 81/80, 128/125
2	41.3468478449	36/35, 49/48, 50/49, 55/54
3	62.02027176735	25/24, 26/25, 27/26, 28/27, 33/32
4	82.693695689799	21/20, 22/21
5	103.36711961225	16/15, 17/16, 18/17	16/15, 18/17, 17/16
6	124.0405435347	14/13, 15/14, 27/25	15/14, 14/13
7	144.71396745715	12/11, 13/12	12/11, 13/12
8	165.3873913796	11/10	11/10
9	186.06081530205	10/9	10/9
10	206.7342392245	9/8, 17/15	9/8, 17/15
11	227.40766314695	8/7	8/7
12	248.0810870694	15/13	15/13
13	268.75451099185	7/6	7/6
14	289.4279349143	13/11, 20/17	13/11
15	310.10135883675	6/5	6/5
16	330.7747827592	17/14	17/14
17	351.44820668165	11/9, 16/13	11/9, 16/13
18	372.1216306041	21/17	21/17
19	392.79505452655	5/4	5/4
20	413.468478449	14/11	14/11
21	434.14190237145	9/7	9/7
22	454.8153262939	13/10, 17/13, 22/17	13/10, 17/13
23	475.48875021635	21/16	21/16
24	496.1621741388	4/3	4/3
25	516.83559806125	27/20
26	537.5090219837	15/11	15/11
27	558.18244590615	11/8, 18/13	11/8, 18/13
28	578.8558698286	7/5	7/5
29	599.52929375105	17/12, 24/17	17/12, 24/17
30	620.2027176735	10/7	10/7
31	640.87614159595	13/9, 16/11	13/9, 16/11
32	661.5495655184	22/15
33	682.22298944085	40/27
34	702.8964133633	3/2	3/2
35	723.56983728575	32/21
36	744.2432612082	20/13, 26/17, 17/11	17/11
37	764.91668513064	14/9	14/9
38	785.59010905309	11/7	11/7
39	806.26353297554	8/5	8/5, 27/17
40	826.93695689799	34/21	21/13
41	847.61038082044	13/8, 18/11	18/11, 13/8
42	868.28380474289	28/17
43	888.95722866534	5/3	5/3
44	909.63065258779	22/13, 17/10	27/16, 17/10
45	930.30407651024	12/7	12/7
46	950.97750043269	26/15
47	971.65092435514	7/4	7/4
48	992.32434827759	16/9, 30/17	16/9, 30/17
49	1012.9977722	9/5	9/5
50	1033.6711961225	20/11
51	1054.3446200449	11/6, 24/13	11/6, 24/13
52	1075.0180439674	13/7, 28/15	13/7
53	1095.6914678898	15/8, 32/17, 17/9	15/8, 17/9
54	1116.3648918123	40/21, 21/11	21/11
55	1137.0383157347		27/14
56	1157.7117396572		33/17
57	1178.3851635796
58	1199.0585875021	2/1	2/1
59	1219.7320114245
60	1240.405435347
61	1261.0788592694		27/13, 33/16
62	1281.7522831919	21/10	21/10
63	1302.4257071143		36/17, 17/8
64	1323.0991310368	15/7	15/7
65	1343.7725549592	24/11	24/11, 13/6
66	1364.4459788817	11/5	11/5
67	1385.1194028041
68	1405.7928267266	9/4	9/4
69	1426.466250649		16/7
70	1447.1396745715		30/13, 39/17
71	1467.8130984939	7/3	7/3
72	1488.4865224164		33/14
73	1509.1599463388	12/5	12/5
74	1529.8333702613		17/7
75	1550.5067941837	27/11	27/11, 39/16
76	1571.1802181062		42/17
77	1591.8536420286	5/2	5/2
78	1612.5270659511		33/13
79	1633.2004898735	18/7	18/7
80	1653.873913796		13/5
81	1674.5473377184	21/8	21/8
82	1695.2207616409	8/3	8/3, 45/17
83	1715.8941855633	27/10	27/10
84	1736.5676094858	30/11	30/11
85	1757.2410334082	11/4	11/4, 36/13
86	1777.9144573307		14/5, 39/14
87	1798.5878812531		45/16, 17/6, 48/17
88	1819.2613051756
89	1839.934729098
90	1860.6081530205
91	1881.2815769429
92	1901.9550008654	3/1	3/1

Rank two temperaments

Period	Generator	Name
1\1	1\58
	3\58
	5\58
	7\58
	9\58
	11\58	Gorgik
	13\58
	15\58	Myna
	17\58	Hemififths
	19\58
	21\58
	23\58	Buzzard
	25\58
	27\58	Thuja
1\2	1\58
	2\58
	3\58
	4\58	Harry
	5\58	Srutal/Diaschismic
	6\58
	7\58
	8\58	Echidna, Supers
	9\58	Secant
	10\58
	11\58
	12\58	Sruti
	13\58
	14\58
1\29	1\58	Mystery