# 271edo

 ← 270edo 271edo 272edo →
Prime factorization 271 (prime)
Step size 4.42804¢
Fifth 159\271 (704.059¢)
Semitones (A1:m2) 29:18 (128.4¢ : 79.7¢)
Dual sharp fifth 159\271 (704.059¢)
Dual flat fifth 158\271 (699.631¢)
Dual major 2nd 46\271 (203.69¢)
Consistency limit 3
Distinct consistency limit 3

271 equal divisions of the octave (abbreviated 271edo or 271ed2), also called 271-tone equal temperament (271tet) or 271 equal temperament (271et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 271 equal parts of about 4.43 ¢ each. Each step represents a frequency ratio of 21/271, or the 271st root of 2.

## Theory

271edo is the highest edo where the perfect fifth has greater absolute error than 12edo. It is inconsistent in the 5-odd-limit. Using the patent val nonetheless, the equal temperament tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is the optimal patent val for the pepperoni temperament, tempering out 352/351 and 364/363 on the 2.3.11/7.13/7 subgroup of the 13-limit.

### Odd harmonics

Approximation of odd harmonics in 271edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.10 -1.07 +0.92 -0.22 +2.19 +0.80 +1.03 +1.32 -0.83 -1.41 +0.51
Relative (%) +47.5 -24.3 +20.7 -5.0 +49.4 +18.1 +23.3 +29.8 -18.8 -31.8 +11.5
Steps
(reduced)
430
(159)
629
(87)
761
(219)
859
(46)
938
(125)
1003
(190)
1059
(246)
1108
(24)
1151
(67)
1190
(106)
1226
(142)

### Subsets and supersets

271edo is the 58th prime edo.