15625/15552

Interval information

Ratio	15625/15552
Factorization	2-6 × 3-5 × 56
Monzo	[-6 -5 6⟩
Size in cents	8.107279¢
Name	kleisma
Color name	y6-2, tribiyo negative 2nd, Tribiyo comma
FJS name	[math]\displaystyle{ \text{dd}{-2}^{5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	27.8564
Weil height (log2 max(n, d))	27.8631
Wilson height (sopfr(nd))	57
Comma size	small
S-expression	S252 × S26
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English Wikipedia has an article on:

Kleisma

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 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 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)