User:Francium/2347edo
| ← 2346edo | 2347edo | 2348edo → |
2347 equal divisions of the octave (abbreviated 2347edo or 2347ed2), also called 2347-tone equal temperament (2347tet) or 2347 equal temperament (2347et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2347 equal parts of about 0.511 ¢ each. Each step represents a frequency ratio of 21/2347, or the 2347th root of 2.
Theory
2347edo is consistent to the 9-odd-limit, tempering out 200120949/200000000, 94143178827/94119200000 and 587068342272/586181640625 in the 7-limit. It is strong in the 2.3.7.13.19.23 subgroup, tempering out 369664/369603, 1609699/1609632, 2359296/2358811, 25871872/25865973 and 1181745152/1181393343.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.048 | +0.222 | +0.071 | +0.095 | -0.146 | +0.035 | -0.241 | -0.141 | +0.058 | +0.118 | +0.102 |
| Relative (%) | +9.3 | +43.5 | +13.8 | +18.6 | -28.6 | +6.8 | -47.2 | -27.5 | +11.4 | +23.1 | +20.0 | |
| Steps (reduced) |
3720 (1373) |
5450 (756) |
6589 (1895) |
7440 (399) |
8119 (1078) |
8685 (1644) |
9169 (2128) |
9593 (205) |
9970 (582) |
10309 (921) |
10617 (1229) | |
Subsets and supersets
2347edo is the 348th prime edo. 4694edo, which doubles it, gives a good correction to its harmonic 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [3720 - 2347⟩ | [⟨2347 3720]] | −0.0150 | 0.0150 | 2.93 |
| 2.3.5 | [100 -25 -26⟩, [30 47 -45⟩ | [⟨2347 3720 5450]] | −0.0419 | 0.0340 | 6.65 |
| 2.3.5.7 | 200120949/200000000, 94143178827/94119200000, 587068342272/586181640625 | [⟨2347 3720 5450 6589]] | −0.0377 | 0.0354 | 6.92 |