15625/15552: Difference between revisions
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{{Wikipedia|Kleisma}} | {{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). | '''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]]). | ||
== See also == | == See also == | ||
Revision as of 19:38, 3 April 2023
| Interval information |
Tribiyo comma
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 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 S-expression of S252 * S26 directly implies that it is expressible as (25/24)2/(27/25).
See also
- Small comma
- Kleismic family, the rank-2 temperament family where it is tempered out
- Kleismic rank three family, the rank-3 temperament family where it is tempered out
- Kleisma (disambiguation page)