2320edo
| ← 2319edo | 2320edo | 2321edo → |
2320 equal divisions of the octave (abbreviated 2320edo or 2320ed2), also called 2320-tone equal temperament (2320tet) or 2320 equal temperament (2320et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2320 equal parts of about 0.517 ¢ each. Each step represents a frequency ratio of 21/2320, or the 2320th root of 2.
2320edo is consistent in the 21-odd-limit and is overall a strong 19-limit system with errors less than 19%, although it does not support any "famous temperaments". Nonetheless, in the 5-limit, it supports the 29th-octave temperament copper. In higher limits, it supports 80th-octave temperaments tetraicosic and mercury, as well as an unnamed 400 & 1920 temperament which also divides the octave in 80 and can also be consistently described to the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.058 | +0.066 | -0.033 | +0.061 | -0.010 | +0.045 | -0.099 | +0.174 | +0.250 | +0.137 |
| relative (%) | +0 | -11 | +13 | -6 | +12 | -2 | +9 | -19 | +34 | +48 | +26 | |
| Steps (reduced) |
2320 (0) |
3677 (1357) |
5387 (747) |
6513 (1873) |
8026 (1066) |
8585 (1625) |
9483 (203) |
9855 (575) |
10495 (1215) |
11271 (1991) |
11494 (2214) | |
Subsets and supersets
Since 2320 factors into 24 × 5 × 29, 2320edo has subset edos 2, 4, 5, 8, 10, 16, 20, 29, 40, 58, 80, 116, 145, 232, 290, 464, 580, and 1160.