User:Eliora/1ed81/80: Difference between revisions
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'''81/80s equal | '''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 == | == Theory == | ||
81 | |||
{{harmonics in equal|1|81|80|columns=20}} | |||
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. | 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. | |||
Revision as of 21:11, 26 January 2022
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 (%) | +20.2 | -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 | |
| 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.