4375/4374
Ratio | 4375/4374 |
Factorization | 2^{-1} × 3^{-7} × 5^{4} × 7 |
Monzo | [-1 -7 4 1⟩ |
Size in cents | 0.39575587¢ |
Name | ragisma |
Color name | zy^{4}1, zoquadyo 1sn, Zoquadyo comma |
FJS name | [math]\text{A1}^{5,5,5,5,7}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 24.1898 |
Weil height (log_{2} max(n, d)) | 24.1901 |
Wilson height (sopfr (nd)) | 50 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20056 bits |
Comma size | unnoticeable |
S-expression | S25 / S27 |
open this interval in xen-calc |
4375/4374, the ragisma, being the difference between a stack of two large limmas and 7/6, is an unnoticeable 7-limit comma. It is the smallest 7-limit superparticular ratio. 4375/4374 is also equal to (25/18)^{2}/(27/14) and the difference between a kleisma (S25^{2} × S26) and a marvel comma (S15 = S25 × S26 × S27), hence its expression as S25 / S27 which directly implies it can be expressed as (28/24 = 7/6)/(27/25)^{2}.
Temperaments
Tempering out this comma leads to the ragismic temperament, enabling ragismic chords in the 27-odd-limit. See Ragismic family for the rank-3 family where it is tempered out. See Ragismic microtemperaments for a collection of rank-2 temperaments where it is tempered out.
Etymology
This comma was allegedly named by Erv Wilson no later than 2001^{[1]}. Interestingly, by 2004 people had already lost track of its origin and meaning^{[2]}. Maybe it was named after Indian ragas? (Pure speculation.)