User:Eliora/1ed81/80
| ← 0ed81/80 | 1ed81/80 | 2ed81/80 → |
1 equal division of 81/80 (1ed81/80), also known as ambitonal sequence of 81/80 (AS81/80) or 81/80 equal-step tuning, is an equal multiplication of the syntonic comma. It corresponds to 55.79763 edo. It is almost exactly 80edn.
Theory
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 | +3.75 | -8.69 | +3.66 | -2.50 | -5.88 | -6.70 | -5.14 | -1.37 | +4.45 | -9.30 | +0.25 | -10.01 | +2.83 | -4.34 | -10.10 | +6.99 | +3.83 | +1.87 | +1.05 | +1.32 |
| Relative (%) | +20.2 | -43.7 | +40.5 | +44.2 | -23.5 | +35.6 | -39.3 | +12.6 | -35.6 | -2.8 | -3.2 | -47.6 | -44.1 | +0.5 | -19.1 | -7.1 | +32.8 | -2.4 | -15.3 | -8.1 | +17.4 | -40.4 | +17.0 | -11.6 | -27.3 | -31.1 | -23.9 | -6.4 | +20.7 | -43.2 | +1.2 | -46.5 | +13.2 | -20.2 | -47.0 | +32.5 | +17.8 | +8.7 | +4.9 | +6.1 | |
| Step | 56 | 88 | 112 | 130 | 144 | 157 | 167 | 177 | 185 | 193 | 200 | 206 | 212 | 218 | 223 | 228 | 233 | 237 | 241 | 245 | 249 | 252 | 256 | 259 | 262 | 265 | 268 | 271 | 274 | 276 | 279 | 281 | 284 | 286 | 288 | 291 | 293 | 295 | 297 | 299 | |
1ed81/80 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.