28472edo
28472 equal divisions of the octave (abbreviated 28472edo or 28472ed2), also called 28472-tone equal temperament (28472tet) or 28472 equal temperament (28472et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 28472 equal parts of about 0.0421 ¢ each. Each step represents a frequency ratio of 21/28472, or the 28472nd root of 2.
| ← 28471edo | 28472edo | 28473edo → |
28472edo is a strong 23-limit system, consistent to the 27-odd-limit as well as the no-29 no-37 41-odd-limit. It is the first edo after 16808 with a lower 23-limit absolute error, which has to do with the fact that it is the edo sum of 11664 and 16808, two of the most accurate edos in the 23-limit for their sizes.
As an equal temperament, it tempers out 123201/123200 in the 13-limit; 194481/194480 and 336141/336140 in the 17-limit; 89376/89375, 104976/104975 and 165376/165375 in the 19-limit; and 52326/52325 among others in the 23-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0022 | +0.0027 | -0.0004 | +0.0027 | +0.0034 | -0.0102 | +0.0003 | +0.0061 | -0.0183 | +0.0052 |
| Relative (%) | +0.0 | -5.2 | +6.3 | -0.9 | +6.3 | +8.0 | -24.2 | +0.8 | +14.4 | -43.5 | +12.3 | |
| Steps (reduced) |
28472 (0) |
45127 (16655) |
66110 (9166) |
79931 (22987) |
98497 (13081) |
105359 (19943) |
116378 (2490) |
120947 (7059) |
128795 (14907) |
138316 (24428) |
141056 (27168) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0187 | -0.0093 | +0.0164 | -0.0107 | -0.0148 | +0.0163 | +0.0020 | +0.0130 | +0.0169 | +0.0133 | -0.0103 |
| Relative (%) | +44.4 | -22.1 | +39.0 | -25.4 | -35.1 | +38.7 | +4.7 | +30.9 | +40.0 | +31.5 | -24.5 | |
| Steps (reduced) |
148324 (5964) |
152540 (10180) |
154497 (12137) |
158150 (15790) |
163085 (20725) |
167491 (25131) |
168860 (26500) |
172714 (1882) |
175096 (4264) |
176237 (5405) |
179481 (8649) | |
Subsets and supersets
Since 28472 factors into primes as 23 × 3559, 28472edo has subset edos 2, 4, 8, 3559, 7118, and 14236.