23edf
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Prime factorization
23 (prime)
Step size
30.5198¢
Octave
39\23edf (1190.27¢)
Twelfth
62\23edf (1892.23¢)
Consistency limit
2
Distinct consistency limit
2
| ← 22edf | 23edf | 24edf → |
23EDF is the equal division of the just perfect fifth into 23 parts of 30.5198 cents each, corresponding to 39.3188 edo (similar to every third step of 118edo).
Properties
23EDF is close to 39EDO and/or 62ED3, however, the respective octave and twelfth would need to be nearly 10 cents flat.
A proponent of this scale is Petr Pařízek.
Some intervals in table below, selected on the basis of single-use of primes (for most cases):
| Step | Size
(cents) |
Approx.
(JI) ratio |
Error from
ratio (cents) |
| 19 | 579.9 | 7/5 | –2.6¢ |
| 23 | 702 | 3/2 | |
| 24 | 732.5 | 29/19 | +0.4¢ |
| 29 | 885.1 | 5/3 | +0.7¢ |
| 31 | 946.1 | 19/11 | –0.1¢ |
| 35 | 1068 | 13/7 | –3.5¢ |
| 46 | 1404 | 9/4 | |
| 48 | 1465 | 7/3 | –1.9¢ |
| 52 | 1587 | 5/2 | +0.7¢ |
| 55 | 1679 | 29/11 | +0.3¢ |
| 58 | 1770 | 25/9 | +1.4¢ |
| 71 | 2167 | 7/2 | –1.9¢ |
| 1 | 30.5198 |
| 2 | 61.0296 |
| 3 | 91.55935 |
| 4 | 122.0791 |
| 5 | 152.5989 |
| 6 | 183.1187 |
| 7 | 213.6385 |
| 8 | 244.1583 |
| 9 | 274.678 |
| 10 | 305.1978 |
| 11 | 335.7176 |
| 12 | 366.2374 |
| 13 | 396.7572 |
| 14 | 427.277 |
| 15 | 457.7967 |
| 16 | 488.3165 |
| 17 | 518.8363 |
| 18 | 549.3561 |
| 19 | 579.8759 |
| 20 | 610.39565 |
| 21 | 640.9154 |
| 22 | 671.4352 |
| 23 | 701.955 |
| 24 | 732.4748 |
| 25 | 762.9946 |
| 26 | 793.51435 |
| 27 | 824.0341 |
| 28 | 854.5539 |
| 29 | 885.0737 |
| 30 | 915.5935 |
| 31 | 946.1133 |
| 32 | 976.633 |
| 33 | 1007.1529 |
| 34 | 1037.6726 |
| 35 | 1068.1924 |
| 36 | 1098.7122 |
| 37 | 1129.232 |
| 38 | 1159.7517 |
| 39 | 1190.2715 |
| 40 | 1220.7913 |
| 41 | 1251.3111 |
| 42 | 1281.8309 |
| 43 | 1312.35065 |
| 44 | 1342.8704 |
| 45 | 1373.3902 |
| 46 | 1403.91 |
–Todd Harrop (June 2015)