2711edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 2710edo2711edo2712edo →
Prime factorization 2711 (prime)
Step size 0.442641¢
Fifth 1586\2711 (702.029¢)
Semitones (A1:m2) 258:203 (114.2¢ : 89.86¢)
Consistency limit 15
Distinct consistency limit 15

2711 equal divisions of the octave (abbreviated 2711edo), or 2711-tone equal temperament (2711tet), 2711 equal temperament (2711et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2711 equal parts of about 0.443 ¢ each. Each step of 2711edo represents a frequency ratio of 21/2711, or the 2711th root of 2.

Theory

2711edo is distinctly consistent to the 15-odd-limit, or the no-11 19-odd-limit. The equal temperament tempers out 78125000/78121827 in the 7-limit; 35156250/35153041, 14348907/14348180, 21437500/21434787, 151263/151250, 2359296/2358125, 5767168/5764801 and 199297406/199290375 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 2711edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.074 +0.112 +0.115 +0.213 +0.048 -0.049 -0.058 -0.167 +0.006 +0.077
relative (%) +0 +17 +25 +26 +48 +11 -11 -13 -38 +1 +17
Steps
(reduced)
2711
(0)
4297
(1586)
6295
(873)
7611
(2189)
9379
(1246)
10032
(1899)
11081
(237)
11516
(672)
12263
(1419)
13170
(2326)
13431
(2587)

Subsets and supersets

2711edo is the 395th prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [4297 -2711 [2711 4297]] -0.0233 0.0233 5.26
2.3.5 [77 -31 -12, [18 -89 53 [2711 4297 6295]] -0.0316 0.0223 5.04
2.3.5.7 [3 -13 10 -2, [37 -9 -11 1, [0 -11 -7 12 [2711 4297 6295 7611]] -0.0340 0.0198 4.47
2.3.5.7.11 151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787 [2711 4297 6295 7611 9379]] -0.0395 0.0209 4.72
2.3.5.7.11.13 4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675 [2711 4297 6295 7611 9379 10032]] -0.0351 0.0215 4.86

Scales

Music

Francium