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
| 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.