14124edo
14124 equal divisions of the octave (abbreviated 14124edo or 14124ed2), also called 14124-tone equal temperament (14124tet) or 14124 equal temperament (14124et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 14124 equal parts of about 0.085 ¢ each. Each step represents a frequency ratio of 21/14124, or the 14124th root of 2.
| ← 14123edo | 14124edo | 14125edo → |
14124edo is consistent in the 17-odd-limit and tempers out Kirnberger's atom. It is a zeta peak integer edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0009 | +0.0074 | -0.0069 | -0.0010 | -0.0009 | -0.0276 | +0.0231 | +0.0179 | -0.0105 | -0.0058 |
| Relative (%) | +0.0 | -1.0 | +8.8 | -8.1 | -1.2 | -1.1 | -32.5 | +27.2 | +21.1 | -12.4 | -6.9 | |
| Steps (reduced) |
14124 (0) |
22386 (8262) |
32795 (4547) |
39651 (11403) |
48861 (6489) |
52265 (9893) |
57731 (1235) |
59998 (3502) |
63891 (7395) |
68614 (12118) |
69973 (13477) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0271 | -0.0055 | +0.0371 | -0.0011 | -0.0126 | -0.0383 | +0.0226 | -0.0377 | -0.0024 | -0.0070 | +0.0340 |
| Relative (%) | -31.9 | -6.5 | +43.7 | -1.3 | -14.9 | -45.0 | +26.6 | -44.4 | -2.8 | -8.2 | +40.1 | |
| Steps (reduced) |
73578 (2958) |
75670 (5050) |
76641 (6021) |
78453 (7833) |
80901 (10281) |
83086 (12466) |
83766 (13146) |
85677 (933) |
86859 (2115) |
87425 (2681) |
89035 (4291) | |
Subsets and supersets
Since 14124 factors into primes as 22 × 3 × 11 × 107, it has subset edos 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 107, 132, 214, 321, 428, 642, 1177, 1284, 2354, 3531, 4708, and 7062.