4501edo
Jump to navigation
Jump to search
Prime factorization
7 × 643
Step size
0.266607¢
Fifth
2633\4501 (701.977¢)
Semitones (A1:m2)
427:338 (113.8¢ : 90.11¢)
Consistency limit
39
Distinct consistency limit
39
| ← 4500edo | 4501edo | 4502edo → |
4501 equal divisions of the octave (abbreviated 4501edo or 4501ed2), also called 4501-tone equal temperament (4501tet) or 4501 equal temperament (4501et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4501 equal parts of about 0.267 ¢ each. Each step represents a frequency ratio of 21/4501, or the 4501st root of 2.
4501edo is a very strong high-limit system, distinctly consistent through the 39-odd-limit, and has the lowest 31- and 37-limit relative error of any equal temperament until 16808. The 4501m val likewise performs well in the 41- and 43-limit, with the lowest relative error of any equal temperament until 7361.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.022 | +0.000 | +0.025 | +0.026 | +0.086 | +0.088 | +0.021 | +0.119 | +0.061 | +0.043 | +0.067 | -0.091 | +0.102 | -0.055 |
| relative (%) | +0 | +8 | +0 | +10 | +10 | +32 | +33 | +8 | +45 | +23 | +16 | +25 | -34 | +38 | -20 | |
| Steps (reduced) |
4501 (0) |
7134 (2633) |
10451 (1449) |
12636 (3634) |
15571 (2068) |
16656 (3153) |
18398 (394) |
19120 (1116) |
20361 (2357) |
21866 (3862) |
22299 (4295) |
23448 (943) |
24114 (1609) |
24424 (1919) |
25001 (2496) | |