15625/15552: Difference between revisions

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'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six [[6/5]]'s with [[3/1]]. It is tempered out in [[Hanson|Hanson temperament]] and the kleismic family. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is ~~blown up~~ to ~~a whole semitone − six~~ 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps). Its [[Square_superparticular#Glossary|S-expression]] of S252 * S26 directly implies that it is expressible as ([[25/24]])2/([[27/25]]).

'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], and is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]). It is tempered out in [[Hanson|Hanson temperament]] and the kleismic family. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[Square_superparticular#Glossary|S-expression]] of S252 * S26 directly implies that it is expressible as ([[25/24]])2/([[27/25]]).

== See also ==

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 {{Wikipedia|Kleisma}}
-'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six [[6/5]]'s with [[3/1]]. It is tempered out in [[Hanson|Hanson temperament]] and the kleismic family. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is blown up to a whole semitone − six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps). Its [[Square_superparticular#Glossary|S-expression]] of S25<sup>2</sup> * S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).
+'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], and is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]). It is tempered out in [[Hanson|Hanson temperament]] and the kleismic family. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[Square_superparticular#Glossary|S-expression]] of S25<sup>2</sup> * S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).
 == See also ==