271edo
| ← 270edo | 271edo | 272edo → |
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
| 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 (%) | +48 | -24 | +21 | -5 | +49 | +18 | +23 | +30 | -19 | -32 | +11 | |
| 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.