73edt
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 | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 26.0542 | 66/65 | |
| 2 | 52.1084 | 34/33 | |
| 3 | 78.1625 | 68/65 | |
| 4 | 104.2167 | 17/16 | |
| 5 | 130.2709 | 55/51 | |
| 6 | 156.3251 | ||
| 7 | 182.3792 | 10/9 | |
| 8 | 208.4334 | 44/39 | pseudo-9/8 |
| 9 | 234.4876 | 63/55 | pseudo-8/7 |
| 10 | 260.5418 | pseudo-7/6 | |
| 11 | 286.5960 | ||
| 12 | 312.6501 | pseudo-6/5 | |
| 13 | 338.7043 | ||
| 14 | 364.7585 | 100/81 | |
| 15 | 390.8127 | pseudo-5/4 | |
| 16 | 416.8668 | 14/11 | |
| 17 | 442.9210 | 31/24 | |
| 18 | 468.9752 | ||
| 19 | 495.0294 | pseudo-4/3 | |
| 20 | 521.0836 | ||
| 21 | 547.1377 | ||
| 22 | 573.1919 | 39/28 | |
| 23 | 599.2461 | 140/99 | |
| 24 | 625.3003 | ||
| 25 | 651.3545 | ||
| 26 | 677.4086 | ||
| 27 | 703.4628 | pseudo-3/2 | |
| 28 | 729.5170 | 32/21 | |
| 29 | 755.5712 | ||
| 30 | 781.6253 | (11/7) | |
| 31 | 807.6795 | ||
| 32 | 833.7337 | 34/21 | |
| 33 | 859.7879 | ||
| 34 | 885.8421 | pseudo-5/3 | |
| 35 | 911.8962 | ||
| 36 | 937.9504 | ||
| 37 | 964.0046 | ||
| 38 | 990.0588 | ||
| 39 | 1016.1129 | pseudo-9/5 | |
| 40 | 1042.1671 | 42/23 | |
| 41 | 1068.2213 | ||
| 42 | 1094.2755 | ||
| 43 | 1120.3297 | ||
| 44 | 1146.3838 | 64/33 | |
| 45 | 1172.4380 | 63/32 | |
| 46 | 1198.4922 | pseudo-octave | |
| 47 | 1224.5464 | ||
| 48 | 1250.6005 | 35/17 | |
| 49 | 1276.6547 | 23/11 | |
| 50 | 1302.7089 | ||
| 51 | 1328.7631 | 28/13 | |
| 52 | 1354.8173 | ||
| 53 | 1380.8714 | ||
| 54 | 1406.9256 | ||
| 55 | 1432.9798 | ||
| 56 | 1459.0340 | ||
| 57 | 1485.0882 | ||
| 58 | 1511.1423 | pseudo-12/5 | |
| 59 | 1537.1965 | ||
| 60 | 1563.2507 | ||
| 61 | 1589.3049 | pseudo-5/2 | |
| 62 | 1615.3590 | ||
| 63 | 1641.4132 | ||
| 64 | 1667.4674 | ||
| 65 | 1693.5216 | ||
| 66 | 1719.5758 | 27/10 | |
| 67 | 1745.6299 | ||
| 68 | 1771.6841 | ||
| 69 | 1797.7383 | 48/17 | |
| 70 | 1823.7925 | ||
| 71 | 1849.8466 | 99/34 | |
| 72 | 1875.9008 | 65/22 | |
| 73 | 1901.9550 | 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