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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~1.20056 bits
Comma size	unnoticeable
S-expression	S25 / S27
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English Wikipedia has an article on:

Ragisma

4375/4374, the ragisma, is an unnoticeable 7-limit comma which is the difference between a stack of two large limmas and 7/6, the difference between a stack of four classical whole tones (10/9) and 32/21, and the difference between a stack of four classical minor thirds (6/5) octave-reduced and 28/27. It is the smallest 7-limit superparticular ratio. It is also equal to 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. It is speculated that it could have been named after Indian ragas.

See also

• List of superparticular intervals