325/324
Ratio | 325/324 |
Factorization | 2^{-2} × 3^{-4} × 5^{2} × 13 |
Monzo | [-2 -4 2 0 0 1⟩ |
Size in cents | 5.335086¢ |
Name | marveltwin comma |
Color name | 3oyy1, thoyoyo 1sn, Thoyoyo comma |
FJS name | [math]\text{P1}^{5,5,13}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 16.6841 |
Weil height (log_{2} max(n, d)) | 16.6886 |
Wilson height (sopfr (nd)) | 39 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.46029 bits |
Comma size | small |
S-expressions | S25 × S26, S10 / S12 |
open this interval in xen-calc |
The marveltwin comma, 325/324, is a 13-limit (also 2.3.5.13 subgroup) comma measuring about 5.3 ¢. Its significance is in that it marks the difference between 16/13 and a stack of two 10/9's, or between 13/9 and a stack of two 6/5's. It can also be expressed as (25/24)/(27/26) and (100/99)/(144/143), among other expressions.
Being a triangle superparticular, it factors neatly into (625/624)(676/675). Other factorizations are (385/384)(2080/2079), (364/363)(3025/3024), (352/351)(4225/4224), and (351/350)(4375/4374). In the 17-limit it additionally factors into (595/594)(715/714).
Temperaments
Tempering out this comma leads to the rank-5 marveltwin temperament, which identifies 16/13 by two 10/9's stacked and enables marveltwin chords. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 subgroup is the rank-2 cata temperament.