2320edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 2319edo2320edo2321edo →
Prime factorization 24 × 5 × 29
Step size 0.517241¢
Fifth 1357\2320 (701.897¢)
Semitones (A1:m2) 219:175 (113.3¢ : 90.52¢)
Consistency limit 21
Distinct consistency limit 21

2320 equal divisions of the octave (abbreviated 2320edo), or 2320-tone equal temperament (2320tet), 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 of 2320edo 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

Approximation of prime harmonics in 2320edo
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.