User:Eliora/1ed81/80: Difference between revisions
Created page with "'''81/80s equal temperament''' (AS81/80) is an equal multiplication of the syntonic comma. It corresponds to 55.79763 EDO. == Theory == 81/80s equal temperament can be re..." |
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'''81/ | {{todo|merge articles|inline=1|text=Merge into [[81/80]] and/or [[56edo]]? (in a "[[stretched and compressed tuning]]s" section)}} | ||
{{Infobox ET|1ed81/80}} | |||
'''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 == | == Theory == | ||
81 | {{Harmonics in equal|1|81|80|columns=11}} | ||
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. | 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. | |||
Latest revision as of 14:11, 1 August 2025
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Todo: merge articles
Merge into 81/80 and/or 56edo? (in a "stretched and compressed tunings" section) |
| ← 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 (%) | +20.2 | -43.7 | +40.5 | +44.2 | -23.5 | +35.6 | -39.3 | +12.6 | -35.6 | -2.8 | -3.2 | |
| Step | 56 | 88 | 112 | 130 | 144 | 157 | 167 | 177 | 185 | 193 | 200 | |
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.