81/80 equal-step tuning

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← 0ed81/801ed81/802ed81/80 →
Prime factorization n/a
Special properties
Step size 21.5063¢
Fifth 33\1ed81/80 (709.708¢)
(convergent)
Octave 56\1ed81/80 (1204.35¢)
(convergent)
Semitones (A1:m2) 7:3 (150.5¢ : 64.52¢)
Sharp fifth 33\1ed81/80 (709.708¢)
(convergent)
Flat fifth 32\1ed81/80 (688.201¢)
(convergent)
Major 2nd 9\1ed81/80 (193.557¢)
(convergent)
Consistency limit 2
Distinct consistency limit 1

81/80 equal-step tuning (AS81/80, ambitonal sequence 81/80) is an equal multiplication of the syntonic comma. It corresponds to 55.79763 edo.

Theory

Approximation of harmonics in 1ed81/80
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error absolute (¢) +4.35 -9.40 +8.70 +9.50 -5.05 +7.66 -8.45 +2.70 -7.65 -0.60 -0.70
relative (%) +20 -44 +40 +44 -23 +36 -39 +13 -36 -3 -3
Step 56 88 112 130 144 157 167 177 185 193 200

81/80 equal-step tuning can be regarded as a subset of 5-limit just intonation. Some intervals it approximates well are 5/4, 7/4, 12/11, 14/13, and 15/11. In addition, it represents well certain compound intervals such as 8/3, 11/1, 12/1 while omitting their octave reductions. With a stretch, 53edo can be regarded as its edo equivalent. However, the closest direct approximation is 56edo.

AS81/80 has a good representation of the 11.17.19 prime number subgroup. This time, the octave equivalence is not applied.