37edf
37EDF is the equal division of the just perfect fifth into 37 parts of 18.9718 cents each, corresponding to 63.2519 edo (similar to every fourth step of 253edo).
| ← 36edf | 37edf | 38edf → |
It is related to the regular temperament which tempers out 385/384, 12005/11979, and 820125/819896 in the 11-limit, which is supported by 63edo, 190edo, and 253edo among others.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.78 | -4.78 | +9.41 | +2.53 | +9.41 | +8.15 | +4.63 | +9.41 | -2.24 | +3.50 | +4.63 |
| Relative (%) | -25.2 | -25.2 | +49.6 | +13.4 | +49.6 | +42.9 | +24.4 | +49.6 | -11.8 | +18.4 | +24.4 | |
| Steps (reduced) |
63 (26) |
100 (26) |
127 (16) |
147 (36) |
164 (16) |
178 (30) |
190 (5) |
201 (16) |
210 (25) |
219 (34) |
227 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.14 | +3.37 | -2.24 | -0.15 | +8.73 | +4.63 | +5.89 | -7.02 | +3.37 | -1.28 | -2.35 |
| Relative (%) | -6.0 | +17.7 | -11.8 | -0.8 | +46.0 | +24.4 | +31.0 | -37.0 | +17.7 | -6.8 | -12.4 | |
| Steps (reduced) |
234 (12) |
241 (19) |
247 (25) |
253 (31) |
259 (0) |
264 (5) |
269 (10) |
273 (14) |
278 (19) |
282 (23) |
286 (27) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 18.9718 | ||
| 2 | 37.9435 | 45/44 | |
| 3 | 56.9153 | ||
| 4 | 75.887 | 25/24 | |
| 5 | 94.8588 | ||
| 6 | 113.8305 | 16/15 | |
| 7 | 132.8023 | ||
| 8 | 151.7741 | 12/11 | |
| 9 | 170.7458 | ||
| 10 | 189.7176 | 10/9 | |
| 11 | 208.6893 | 9/8 | |
| 12 | 227.6611 | 8/7 | |
| 13 | 246.6328 | 15/13 | |
| 14 | 265.6046 | 7/6 | |
| 15 | 284.5764 | 33/28 | |
| 16 | 303.5481 | 25/21 | |
| 17 | 322.5199 | 6/5 | |
| 18 | 341.4916 | 11/9 | |
| 19 | 360.4634 | 27/22 | |
| 20 | 379.4351 | 5/4 | |
| 21 | 398.4069 | 34/27 | |
| 22 | 417.3786 | 14/11 | |
| 23 | 436.3504 | 9/7 | |
| 24 | 455.3222 | 13/10 | |
| 25 | 474.2939 | ||
| 26 | 493.2657 | 4/3 | |
| 27 | 512.2374 | ||
| 28 | 531.2092 | 15/11 | |
| 29 | 550.1809 | 11/8 | pseudo-25/18 |
| 30 | 569.1527 | real 25/18 | |
| 31 | 588.1245 | 45/32, 7/5 | |
| 32 | 607.0962 | 64/45, 10/7 | |
| 33 | 626.068 | real 36/25 | |
| 34 | 645.0397 | 16/11 | pseudo-36/25 |
| 35 | 664.0115 | 22/15 | |
| 36 | 682.9832 | 40/27 | |
| 37 | 701.955 | exact 3/2 | just perfect fifth |
| 38 | 720.9268 | ||
| 39 | 739.8985 | 135/88 | |
| 40 | 758.8703 | ||
| 41 | 777.842 | 25/16 | |
| 42 | 796.8138 | ||
| 43 | 815.7855 | 8/5 | |
| 44 | 834.7573 | ||
| 45 | 853.7291 | 18/11 | |
| 46 | 872.7008 | ||
| 47 | 891.6726 | 5/3 | |
| 48 | 910.6443 | 27/16 | |
| 49 | 929.6161 | 12/7 | |
| 50 | 948.5978 | 45/26 | |
| 51 | 967.5596 | 7/4 | |
| 52 | 986.5314 | 99/56 | |
| 53 | 1005.5031 | 25/14 | |
| 54 | 1024.4749 | 9/5 | |
| 55 | 1043.4466 | ||
| 56 | 1062.4184 | ||
| 57 | 1081.3901 | 15/8 | |
| 58 | 1100.3619 | 17/9 | |
| 59 | 1119.3336 | 21/11 | |
| 60 | 1138.3054 | 27/14 | |
| 61 | 1157.2772 | 39/20 | |
| 62 | 1176.2489 | ||
| 63 | 1195.2007 | 2/1 | |
| 64 | 1214.1924 | ||
| 65 | 1233.1642 | 45/22 | |
| 66 | 1252.1359 | 33/16 | pseudo-25/12 |
| 67 | 1271.1077 | real 25/12 | |
| 68 | 1290.0795 | 135/64, 21/10 | |
| 69 | 1309.0512 | 32/15, 15/7 | |
| 70 | 1328.023 | real 54/25 | |
| 71 | 1347.9947 | 24/11 | pseudo-54/25 |
| 72 | 1365.9668 | 11/5 | |
| 73 | 1385.9382 | 20/9 | |
| 74 | 1403.91 | exact 9/4 | |
Related regular temperaments
7-limit 63&190
Commas: 2460375/2458624, 514714375/509607936
POTE generator: ~1728/1715 = 18.957
Mapping: [<1 1 3 2|, <0 37 -43 51|]
EDOs: 63, 190, 253
11-limit 63&190
Commas: 385/384, 12005/11979, 820125/819896
POTE generator: ~99/98 = 18.957
Mapping: [<1 1 3 2 3|, <0 37 -43 51 29|]
EDOs: 63, 190, 253
13-limit 63&190
Commas: 385/384, 1575/1573, 2200/2197, 4459/4455
POTE generator: ~99/98 = 18.959
Mapping: [<1 1 3 2 3 4|, <0 37 -43 51 29 -19|]
EDOs: 63, 190, 253