# 2711edo

 ← 2710edo 2711edo 2712edo →
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 2711ed2), also called 2711-tone equal temperament (2711tet) or 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 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 (%) +0.0 +16.7 +25.3 +26.1 +48.1 +10.8 -11.2 -13.1 -37.6 +1.4 +17.4
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

Francium