136/135: Difference between revisions

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'''136/135''', the '''diatisma''', '''diatic comma''' or '''fiventeen comma''', is a [[17-limit]] [[small comma]]. It is equal to ([[32/27]])/([[20/17]]) and also ([[51/40]])/([[81/64]]). It is also the difference between [[16/15]] and [[18/17]] which is easily deduced from its S-expression of S16 * S17, and is therefore the difference between ([[17/16]])([[16/15]]) = [[17/15]] and ([[18/17]])([[17/16]]) = [[9/8]] as the two 17/16's cancel.

'''136/135''', the '''diatisma''', '''diatic comma''' or '''fiventeen comma''', is a [[17-limit]] [[small comma]]. It is equal to ([[32/27]])/([[20/17]]) and also ([[51/40]])/([[81/64]]). It is also the difference between [[16/15]] and [[18/17]] which is easily deduced from its S-expression of [[256/255|S16]] * [[289/288|S17]], and is therefore the difference between ([[17/16]])([[16/15]]) = [[17/15]] and ([[18/17]])([[17/16]]) = [[9/8]] as the two 17/16's cancel.

== Temperaments ==

=== Fiventeen ===

[[17edo]] makes a good tuning (especially for its size) for the 2.3.17/5-subgroup {136/135} rank 2 temperament which implies a [[supersoft]] [[pentic]] pentad of 30:34:40:45:51:60 (because as aforementioned [[17/15]] is equated with [[9/8]]) although [[80edo]] might be preferred for a more accurate [[51/40]] and it and [[46edo]] might be preferred for more accurate fifths. The same is true of the related rank 3 temperament diatic, described below.

[[17edo]] makes a good tuning (especially for its size) for the 2.3.17/5-subgroup {136/135} rank 2 temperament which implies a [[supersoft]] [[pentic]] pentad of 30:34:40:45:51:60 (because as aforementioned [[17/15]] is equated with [[9/8]]) although [[80edo]] might be preferred for a more accurate [[51/40]] and to optimize plausibility slightly more, and it and [[46edo]] might be preferred for more accurate fifths. The same is true of the related rank 3 temperament diatic, described below.

[[Subgroup]]: 2.3.17/5

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 | Comma = yes
 }}
-'''136/135''', the '''diatisma''', '''diatic comma''' or '''fiventeen comma''', is a [[17-limit]] [[small comma]]. It is equal to ([[32/27]])/([[20/17]]) and also ([[51/40]])/([[81/64]]). It is also the difference between [[16/15]] and [[18/17]] which is easily deduced from its S-expression of S16 * S17, and is therefore the difference between ([[17/16]])([[16/15]]) = [[17/15]] and ([[18/17]])([[17/16]]) = [[9/8]] as the two 17/16's cancel.
+'''136/135''', the '''diatisma''', '''diatic comma''' or '''fiventeen comma''', is a [[17-limit]] [[small comma]]. It is equal to ([[32/27]])/([[20/17]]) and also ([[51/40]])/([[81/64]]). It is also the difference between [[16/15]] and [[18/17]] which is easily deduced from its S-expression of [[256/255|S16]] * [[289/288|S17]], and is therefore the difference between ([[17/16]])([[16/15]]) = [[17/15]] and ([[18/17]])([[17/16]]) = [[9/8]] as the two 17/16's cancel.
 == Temperaments ==
 === Fiventeen ===
-[[17edo]] makes a good tuning (especially for its size) for the 2.3.17/5-subgroup {136/135} rank 2 temperament which implies a [[supersoft]] [[pentic]] pentad of 30:34:40:45:51:60 (because as aforementioned [[17/15]] is equated with [[9/8]]) although [[80edo]] might be preferred for a more accurate [[51/40]] and it and [[46edo]] might be preferred for more accurate fifths. The same is true of the related rank 3 temperament diatic, described below.
+[[17edo]] makes a good tuning (especially for its size) for the 2.3.17/5-subgroup {136/135} rank 2 temperament which implies a [[supersoft]] [[pentic]] pentad of 30:34:40:45:51:60 (because as aforementioned [[17/15]] is equated with [[9/8]]) although [[80edo]] might be preferred for a more accurate [[51/40]] and to optimize plausibility slightly more, and it and [[46edo]] might be preferred for more accurate fifths. The same is true of the related rank 3 temperament diatic, described below.
 [[Subgroup]]: 2.3.17/5