131edo

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← 130edo131edo132edo →
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 131-tone equal temperament (131tet), 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 of 131edo represents a frequency ratio of 21/131, or the 131st root of 2.

Theory

131edo 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 temperament.

131edo is the 32nd prime EDO.

Approximation of prime harmonics in 131edo
Harmonic 3 5 7 11 13 17 19 23 29 31 37
Error absolute (¢) +3.39 -1.58 +2.17 -1.70 +2.22 -4.19 -4.38 +3.79 -3.62 +0.00 -4.02
relative (%) +37 -17 +24 -19 +24 -46 -48 +41 -40 +0 -44
Steps
(reduced)
208
(77)
304
(42)
368
(106)
453
(60)
485
(92)
535
(11)
556
(32)
593
(69)
636
(112)
649
(125)
682
(27)

Some MOS Scales in 131-EDO:

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