108edo: Difference between revisions

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== Theory ==

108et [[tempering out|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.

108et [[tempering out|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.

108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.

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=== Prime harmonics ===

=== Subsets and supersets ===

Since 108 factors into {{factorization|108}}, 108edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54 }}.

== Intervals ==

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 == Theory ==
-et [[tempering out|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.
+et [[tempering out|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.
 edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.
@@ Line 9: / Line 9: @@
 === Prime harmonics ===
 {{Harmonics in equal|108}}
+=== Subsets and supersets ===
+Since 108 factors into {{factorization|108}}, 108edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54 }}.
 == Intervals ==