23edf
Jump to navigation
Jump to search
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).
History
A proponent of 23edf is Petr Pařízek. The first to write about 23edf on this wiki was Todd Harrop in 2015.
Theory
23edf is close to 39edo and/or 62edt, however, the respective octave and twelfth would need to be nearly 10 cents flat.
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¢ |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.7 | -9.7 | +11.1 | -9.0 | +11.1 | -11.6 | +1.3 | +11.1 | +11.8 | -0.6 | +1.3 |
| Relative (%) | -31.9 | -31.9 | +36.2 | -29.5 | +36.2 | -38.2 | +4.4 | +36.2 | +38.6 | -2.1 | +4.4 | |
| Steps (reduced) |
39 (16) |
62 (16) |
79 (10) |
91 (22) |
102 (10) |
110 (18) |
118 (3) |
125 (10) |
131 (16) |
136 (21) |
141 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.2 | +9.1 | +11.8 | -8.4 | +8.7 | +1.3 | -0.7 | +2.0 | +9.1 | -10.4 | +4.2 |
| Relative (%) | -49.7 | +30.0 | +38.6 | -27.5 | +28.6 | +4.4 | -2.3 | +6.7 | +30.0 | -33.9 | +13.9 | |
| Steps (reduced) |
145 (7) |
150 (12) |
154 (16) |
157 (19) |
161 (0) |
164 (3) |
167 (6) |
170 (9) |
173 (12) |
175 (14) |
178 (17) | |
Intervals
| Step number | Size (cents) |
|---|---|
| 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 |
 |
Todo: complete table Add at least one more column, showing what the notes are named, what JI they approximate, or anything else interesting about them individually. |