4375/4374

Interval information

Ratio	4375/4374
Factorization	2-1 × 3-7 × 54 × 7
Monzo	[-1 -7 4 1⟩
Size in cents	0.3957559¢
Name	ragisma
Color name	zy41, zoquadyo 1sn, Zoquadyo comma
FJS name	[math]\text{A1}^{5,5,5,5,7}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	24.1898
Weil height (log2 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

English Wikipedia has an article on:

Ragisma

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 (S25² × 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. Interestingly, by 2004 people had already lost track of its origin and meaning. Maybe it was named after Indian ragas? (Pure speculation.)

See also

• List of superparticular intervals