14618edo
| ← 14617edo | 14618edo | 14619edo → |
14618 equal divisions of the octave (abbreviated 14618edo or 14618ed2), also called 14618-tone equal temperament (14618tet) or 14618 equal temperament (14618et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 14618 equal parts of about 0.0821 ¢ each. Each step represents a frequency ratio of 21/14618, or the 14618th root of 2.
14618edo is an extremely strong 13-limit system, with a lower relative error than any previous equal temperaments, beating 6079 and not until 73591 do we find a better equal temperament in the same subgroup. A comma basis is {123201/123200, 1990656/1990625, 3294225/3294172, 4084223/4084101, 781258401/781250000}. It is much less impressive beyond that limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup, holding the record of lowest relative error until 16808.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0015 | +0.0045 | +0.0070 | +0.0023 | -0.0023 | +0.0384 | -0.0168 | -0.0352 |
| Relative (%) | +0.0 | +1.8 | +5.5 | +8.6 | +2.9 | -2.8 | +46.8 | -20.4 | -42.9 | |
| Steps (reduced) |
14618 (0) |
23169 (8551) |
33942 (4706) |
41038 (11802) |
50570 (6716) |
54093 (10239) |
59751 (1279) |
62096 (3624) |
66125 (7653) | |
| Harmonic | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0028 | -0.0363 | +0.0173 | +0.0250 | -0.0113 | +0.0017 | +0.0212 | -0.0391 | +0.0395 |
| Relative (%) | +3.4 | -44.2 | +21.1 | +30.5 | -13.8 | +2.0 | +25.9 | -47.6 | +48.2 | |
| Steps (reduced) |
71014 (12542) |
72420 (13948) |
76152 (3062) |
78317 (5227) |
79321 (6231) |
81197 (8107) |
83731 (10641) |
85992 (12902) |
86696 (13606) | |
Subsets and supersets
29236edo, which doubles 14618edo, provides a good correction to the harmonics 17 and 23.