131edo

 ← 130edo 131edo 132edo →
Prime factorization 131 (prime)
Step size 9.16031¢
Fifth 77\131 (705.344¢)
Semitones (A1:m2) 15:8 (137.4¢ : 73.28¢)
Dual sharp fifth 77\131 (705.344¢)
Dual flat fifth 76\131 (696.183¢)
Dual major 2nd 22\131 (201.527¢)
Consistency limit 3
Distinct consistency limit 3

131 equal divisions of the octave (abbreviated 131edo or 131ed2), also called 131-tone equal temperament (131tet) or 131 equal temperament (131et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 131 equal parts of about 9.16 ¢ each. Each step represents a frequency ratio of 21/131, or the 131st root of 2.

Theory

131edo is inconsistent to the 5-odd-limit and the error of harmonic 3 is quite large. However, it is the next edo after 81edo on the Golden Tone System (Das Goldene Tonsystem) of Thorvald Kornerup, using the 131b val. The patent val has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out 81/80 it tempers out the immunity comma, 1638400/1594323. In the 7-limit it tempers out 3125/3087 and 245/243, so that it supports bophier.

Odd harmonics

Approximation of odd harmonics in 131edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +3.39 -1.58 +2.17 -2.38 -1.70 +2.22 +1.81 -4.19 -4.38 -3.61 +3.79
Relative (%) +37.0 -17.3 +23.7 -26.0 -18.6 +24.2 +19.7 -45.8 -47.9 -39.4 +41.3
Steps
(reduced)
208
(77)
304
(42)
368
(106)
415
(22)
453
(60)
485
(92)
512
(119)
535
(11)
556
(32)
575
(51)
593
(69)

Subsets and supersets

131edo is the 32nd prime edo, following 127edo and before 137edo.

Scales

Mos scales

 33 16 33 33 16 Pentatonic (comparable with 8edo and 99edo) 23 23 8 23 23 23 8 Pythagorean tuning (comparable with 17edo) 21 21 13 21 21 21 13 Meantone tuning (comparable with 50edo) 19 12 19 19 12 19 19 12 Father Tuning (comparable with 55edo) 18 18 18 18 18 18 18 5 Porcupine Tuning (comparable with 29edo and 80edo) 17 17 17 6 17 17 17 17 6 Superdiatonic tuning (comparable with 23edo) 16 16 16 16 16 16 16 16 3 Bohpier tuning (comparable with 41edo) 13 13 9 13 13 13 9 13 13 13 9 Sensi-11 Tuning 11 11 11 11 11 5 11 11 11 11 11 11 5 De Vries 13-tone Tuning 10 10 10 7 10 10 10 10 7 10 10 10 10 7 Ketradektriatoh Tuning 21 17 21 17 17 21 17 mohaha7 4 17 17 17 4 17 17 4 17 17 mohaha10