73edt
| ← 72edt | 73edt | 74edt → |
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.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.5 | +0.0 | -3.0 | +1.5 | -1.5 | -7.8 | -4.5 | +0.0 | -0.0 | -8.7 | -3.0 |
| Relative (%) | -5.8 | +0.0 | -11.6 | +5.7 | -5.8 | -30.1 | -17.4 | +0.0 | -0.1 | -33.4 | -11.6 | |
| Steps (reduced) |
46 (46) |
73 (0) |
92 (19) |
107 (34) |
119 (46) |
129 (56) |
138 (65) |
146 (0) |
153 (7) |
159 (13) |
165 (19) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | -9.3 | +1.5 | -6.0 | -6.8 | -1.5 | +9.1 | -1.5 | -7.8 | -10.2 | -9.0 |
| Relative (%) | -43.4 | -35.9 | +5.7 | -23.1 | -26.0 | -5.8 | +34.9 | -5.9 | -30.1 | -39.2 | -34.6 | |
| Steps (reduced) |
170 (24) |
175 (29) |
180 (34) |
184 (38) |
188 (42) |
192 (46) |
196 (50) |
199 (53) |
202 (56) |
205 (59) |
208 (62) | |
Intervals
| 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 temperaments
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
Mapping: [<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
Mapping: [<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
Mapping: [<1 0 -1 5 6|, <0 73 153 -101 -117|]