40edf
| ← 39edf | 40edf | 41edf → |
40EDF is the equal division of the just perfect fifth into 40 parts of 17.5489 cents each, corresponding to 68.3805 edo. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by 68edo, 274edo, 342edo, 410edo, 616edo, and 752edo among others.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 17.5489 | 100/99, 99/98, 81/80 | |
| 2 | 35.09775 | 50/49, 49/48 | |
| 3 | 52.6466 | 33/32 | |
| 4 | 70.1955 | 25/24 | |
| 5 | 87.7444 | 20/19 | |
| 6 | 105.29325 | 17/16 | |
| 7 | 122.8421 | 15/14 | |
| 8 | 140.391 | 13/12 | |
| 9 | 157.9399 | 23/21 | |
| 10 | 175.48875 | 10/9 | |
| 11 | 193.0376 | 19/17 | |
| 12 | 210.5865 | 17/15 | |
| 13 | 228.1354 | 8/7 | |
| 14 | 245.68425 | 15/13 | |
| 15 | 263.2331 | 7/6 | |
| 16 | 280.782 | 20/17 | |
| 17 | 298.3309 | 19/16 | |
| 18 | 315.87975 | 6/5 | |
| 19 | 333.4286 | 63/52 | |
| 20 | 350.9775 | 60/49, 49/40 | |
| 21 | 368.5264 | 26/21 | |
| 22 | 386.07525 | 5/4 | |
| 23 | 403.6241 | 24/19 | |
| 24 | 421.173 | 51/40 | |
| 25 | 438.7219 | 9/7 | |
| 26 | 456.27075 | 13/10 | |
| 27 | 473.8196 | 21/16 | |
| 28 | 491.3685 | 4/3 | |
| 29 | 508.9174 | 66/49 | |
| 30 | 526.46625 | 200/147, 49/36, 27/20 | |
| 31 | 544.0151 | 11/8 | |
| 32 | 561.564 | 25/18 | |
| 33 | 579.1129 | 7/5 | |
| 34 | 596.66175 | 24/17 | |
| 35 | 614.2106 | 10/7 | |
| 36 | 631.7595 | 36/25 | |
| 37 | 649.3084 | 16/11 | |
| 38 | 666.85725 | 147/100, 72/49 | |
| 39 | 684.4061 | 297/200, 49/33, 40/27 | |
| 40 | 701.955 | exact 3/2 | just perfect fifth |
| 41 | 719.5039 | 50/33, 297/196, 243/160, 32/21 | |
| 42 | 737.05275 | 75/49, 49/32 | |
| 43 | 754.6016 | 99/64 | |
| 44 | 772.1505 | 25/16 | |
| 45 | 789.6994 | 30/19 | |
| 46 | 807.24825 | 51/32 | |
| 47 | 824.7971 | 45/28 | |
| 48 | 842.346 | 13/8 | |
| 49 | 859.8949 | 32/14 | |
| 50 | 877.44375 | 5/3 | |
| 51 | 894.9926 | 57/34 | |
| 52 | 912.5415 | 17/10 | |
| 53 | 930.0904 | 12/7 | |
| 54 | 947.63925 | 45/26 | |
| 55 | 965.1981 | 7/4 | |
| 56 | 982.737 | 30/17 | |
| 57 | 1000.2859 | 57/32 | |
| 58 | 1017.83275 | 9/5 | |
| 59 | 1035.3836 | 189/104 | |
| 60 | 1052.9325 | 90/49, 147/80 | |
| 61 | 1070.4814 | 13/7 | |
| 62 | 1088.03025 | 15/8 | |
| 63 | 1105.4791 | 36/19 | |
| 64 | 1123.128 | 153/80 | |
| 65 | 1140.6769 | 27/14 | |
| 66 | 1158.22575 | 39/20 | |
| 67 | 1175.7746 | 63/32 | |
| 68 | 1193.3235 | 2/1 | |
| 69 | 1210.8724 | 99/49 | |
| 70 | 1228.42125 | 300/147, 49/24, 81/40 | |
| 71 | 1246.9701 | 33/16 | |
| 72 | 1263.519 | 25/12 | |
| 73 | 1281.0679 | 21/10 | |
| 74 | 1298.61675 | 36/17 | |
| 75 | 1316.1756 | 15/7 | |
| 76 | 1333.7145 | 54/25 | |
| 77 | 1351.2634 | 24/11 | |
| 78 | 1368.81375 | 441/200, 108/49 | |
| 79 | 1386.3611 | 891/400, 49/22, 20/9 | |
| 80 | 1403.91 | exact 9/8 | |
Related regular temperaments
Adding one half of the octave as a generator, 40EDF leads the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit.
11-limit 68&342
Commas: 2401/2400, 9801/9800, 9453125/9437184
POTE generator: ~99/98 = 17.545
Mapping: [<2 2 4 5 8|, <0 40 22 21 -37|]
EDOs: 68, 274, 342, 410, 616, 752
2.3.5.7.11.17 subgroup 68&342
Commas: 1089/1088, 1225/1224, 2401/2400, 24576/24565
POTE generator: ~99/98 = 17.546
Mapping: [<2 2 4 5 8 8|, <0 40 22 21 -37 6|]
EDOs: 68, 274, 342, 410, 616, 752
2.3.5.7.11.17.19 subgroup 68&342
Commas: 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2401/2400
POTE generator: ~96/95 = 17.547
Mapping: [<2 2 4 5 8 8 8|, <0 40 22 21 -37 6 17|]
EDOs: 68, 274, 342, 410, 616, 752h
2.3.5.7.11.17.19.23 subgroup 68&342
Commas: 875/874, 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2024/2023
POTE generator: ~96/95 = 17.546
Mapping: [<2 2 4 5 8 8 8 7|, <0 40 22 21 -37 6 17 70|]
EDOs: 68, 274, 342, 410, 616i, 752h