User:Eliora/1ed81/80: Difference between revisions

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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~~.

{{todo|merge articles|inline=1|text=Merge into [[81/80]] and/or [[56edo]]? (in a "[[stretched and compressed tuning]]s" section)}}

'''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 ==

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]].

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.

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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.
+{{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 ==
+{{Harmonics in equal|1|81|80|columns=11}}
-{{harmonics in equal|1|81|80|columns=20}}
-/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]].
+ed81/80 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.