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 norm (log2 nd)	27.8564
Weil norm (log2 max(n, d))	27.8631
Wilson norm (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 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, or a stack of three diptolemaic chromatic semitones (25/24) with the Pythagorean whole tone (9/8). 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 kleismic temperament. See Kleismic family for the rank-2 temperament family where it is tempered out and 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)

External links

• Tonalsoft Encyclopedia | Kleisma