15625/15552
Ratio | 15625/15552 |
Factorization | 2^{-6} × 3^{-5} × 5^{6} |
Monzo | [-6 -5 6⟩ |
Size in cents | 8.1072789¢ |
Name | kleisma |
Color name | y^{6}-2, tribiyo negative 2nd, Tribiyo comma |
FJS name | [math]\text{dd}{-2}^{5,5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 27.8564 |
Weil height (log_{2} 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 | S25^{2} × S26 |
open this interval in xen-calc |
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, and is also the difference between the classic chromatic semitone (25/24) and the greater diesis (648/625). 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 S25^{2} × 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)