73edt

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Division of the third harmonic into 73 equal parts (73EDT) is related to 46 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 1.5078 cents compressed and the step size is about 26.0542 cents. It is consistent to the 18-integer-limit. In comparison, 46edo is only consistent up to the 14-integer-limit.

Interval

degree cents value hekts corresponding
JI intervals
comments
0 exact 1/1
1 26.0542 17.8082 66/65
2 52.1084 35.6164 34/33
3 78.1625 53.4247 68/65
4 104.2167 71.2329 17/16
5 130.2709 89.0411 55/51
6 156.3251 106.8493 23/21
7 182.3792 124.6575 10/9
8 208.4334 142.46575 44/39 pseudo-9/8
9 234.4876 160.274 63/55 pseudo-8/7
10 260.5418 178.0822 pseudo-7/6
11 286.596 195.8904 13/11
12 312.6501 213.6986 pseudo-6/5
13 338.7043 231.50685 17/14
14 364.7585 249.3151 100/81
15 390.8127 267.1233 pseudo-5/4
16 416.8668 284.9315 14/11
17 442.921 302.7397 31/24
18 468.9752 320.54795 21/16
19 495.0294 338.3562 pseudo-4/3
20 521.0836 356.1644 27/20
21 547.1377 373.9726 11/8
22 573.1919 391.7808 39/28 pseudo-7/5
23 599.2461 409.589 140/99
24 625.3003 427.3973 56/39 pseudo-10/7
25 651.3545 445.2055 16/11
26 677.4086 463.0137 40/27
27 703.4628 480.8219 pseudo-3/2
28 729.517 498.6301 32/21
29 755.5712 516.4384 48/31
30 781.6253 534.2466 (11/7)
31 807.6795 552.0548 pseudo-8/5
32 833.7337 569.863 34/21
33 859.7879 587.6712 28/17
34 885.8421 605.47945 pseudo-5/3
35 911.8962 623.2877 22/13
36 937.9504 641.0959 pseudo-12/7
37 964.0046 658.9041 110/63 pseudo-7/4
38 990.0588 676.7123 39/22 pseudo-16/9
39 1016.1129 694.52055 9/5
40 1042.1671 712.3288 42/23
41 1068.2213 730.137 102/55
42 1094.2755 747.9452 17/8
43 1120.3297 765.7534 65/34
44 1146.3838 783.5616 64/33
45 1172.438 801.3699 63/32
46 1198.4922 819.1781 pseudo-octave
47 1224.5464 836.9863 81/40
48 1250.6005 854.7945 35/17
49 1276.6547 872.6027 23/11
50 1302.7089 890.411 17/8
51 1328.7631 908.2192 28/13
52 1354.8173 926.0274 24/11
53 1380.8714 943.8356 20/9
54 1406.9256 961.6438 9/4
55 1432.9798 979.45205 16/7
56 1459.034 997.2603 pseudo-7/3
57 1485.0882 1015.0685 26/11
58 1511.1423 1032.8767 pseudo-12/5
59 1537.1965 1050.6849 17/7
60 1563.2507 1068.49315 42/17
61 1589.3049 1086.3014 pseudo-5/2
62 1615.359 1104.1096 28/11
63 1641.4132 1121.9178 pseudo-18/7
64 1667.4674 1139.726 21/8
65 1693.5216 1157.53425 8/3
66 1719.5758 1175.3425 27/10
67 1745.6299 1193.1507 11/4
68 1771.6841 1210.9589 39/14
69 1797.7383 1228.7671 48/17
70 1823.7925 1246.5753 112/39
71 1849.8466 1264.3836 99/34
72 1875.9008 1282.1918 65/22
73 1901.9550 1300 exact 3/1 just perfect fifth plus an octave

Related regular temperament

73edt is also related to the microtemperament which tempers out |73 -153 73> in the 5-limit, which is supported by 46, 783, 829, 1612, 2395, 3128, and 4007 EDOs.

5-limit 46&783

Comma: |73 -153 73>

POTE generator: ~|21 -44 21> = 26.0543

Map: [<1 0 -1|, <0 73 153|]

EDOs: 46, 737, 783, 829, 875, 1612, 2395, 2441, 3128, 4007, 5573, 6402

7-limit 46&783

Commas: 4375/4374, |-92 20 3 19>

POTE generator: ~335544320/330812181 = 26.0533

Map: [<1 0 -1 5|, <0 73 153 -101|]

EDOs: 46, 691, 737, 783, 829, 1520, 1612

11-limit 46&783

Commas: 4375/4374, 806736/805255, 2097152/2096325

POTE generator: ~3072/3025 = 26.0542

Map: [<1 0 -1 5 6|, <0 73 153 -101 -117|]

EDOs: 46, 737, 783, 829, 875