92edt

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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
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