2477edo
| ← 2476edo | 2477edo | 2478edo → |
2477 equal divisions of the octave (abbreviated 2477edo or 2477ed2), also called 2477-tone equal temperament (2477tet) or 2477 equal temperament (2477et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2477 equal parts of about 0.484 ¢ each. Each step represents a frequency ratio of 21/2477, or the 2477th root of 2.
Theory
2477edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.13.23.29 subgroup, tempering out 4225/4224, 7425/7424, 256000/255879, 4785/4784, 1917625/1916928 and 56953125/56909567. Using the 2.3.7.13.23.31 subgroup, it tempers out 4992/4991. Using the 2.3.7.11.13.19.23.41 subgroup, it tempers out 10374/10373.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.023 | -0.201 | +0.088 | -0.006 | +0.005 | +0.172 | -0.056 | +0.066 | -0.106 | +0.221 |
| Relative (%) | +0.0 | +4.8 | -41.6 | +18.2 | -1.2 | +1.1 | +35.5 | -11.6 | +13.7 | -21.9 | +45.6 | |
| Steps (reduced) |
2477 (0) |
3926 (1449) |
5751 (797) |
6954 (2000) |
8569 (1138) |
9166 (1735) |
10125 (217) |
10522 (614) |
11205 (1297) |
12033 (2125) |
12272 (2364) | |
Subsets and supersets
2477edo is the 367th prime edo. 4954edo, which doubles it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [3926 -2477⟩ | [⟨2477 3926]] | -0.0073 | 0.0073 | 1.51 |
| 2.3.5 | [-97 7 37⟩, [93 -66 5⟩ | [⟨2477 3926 5751]] | +0.0240 | 0.0448 | 9.25 |