15625/15552

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 15625/15552
Factorization 2-6 × 3-5 × 56
Monzo [-6 -5 6
Size in cents 8.1072789¢
Name kleisma
Color name y6-2, tribiyo negative 2nd,
Tribiyo comma
FJS name [math]\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
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.79205 bits
Comma size small
S-expression S252 × S26
open this interval in xen-calc
English Wikipedia has an article on:

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