81/80 equal-step tuning

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81/80s 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 13 14 15 16 17 18 19 20 21
Error absolute (¢) +4.35 -9.40 +8.70 +9.50 -5.05 +7.66 -8.45 +2.70 -7.65 -0.60 -0.70 -10.23 -9.49 +0.10 -4.10 -1.52 +7.06 -0.52 -3.30 -1.74
relative (%) +20 -44 +40 +44 -23 +36 -39 +13 -36 -3 -3 -48 -44 +0 -19 -7 +33 -2 -15 -8
Step 56 88 112 130 144 157 167 177 185 193 200 206 212 218 223 228 233 237 241 245

81/80s equal temperament 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 ED2 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.