15625/15552: Difference between revisions
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{{Wikipedia|Kleisma}} | {{Wikipedia|Kleisma}} | ||
'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], | '''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], or a stack of five 6/5s with [[5/2]]. It is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]), which is also known as the diminished comma. 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]]). | ||
== Temperaments == | == Temperaments == | ||
Revision as of 01:42, 5 August 2025
| Interval information |
Tribiyo comma
15625/15552, which is sometimes called the kleisma, is the small 5-limit comma that separates a stack of six classic minor thirds of 6/5 with 3/1, or a stack of five 6/5s with 5/2. It is also the difference between the classic chromatic semitone (25/24) and the greater diesis (648/625), which is also known as the diminished comma. 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 S-expression of S252 × S26 directly implies that it is expressible as (25/24)2/(27/25).
Temperaments
This comma is tempered out in the hanson temperament. See Kleismic family for the rank-2 temperament family where it is tempered out. See Kleismic rank-3 family for the rank-3 temperament family where it is tempered out.
Etymology
This comma was named by Shohé Tanaka in 1890.
See also
- Kleisma (disambiguation page)