4375/4374

4375/4374, the ragisma, is an unnoticeable 7-limit comma with a size of about 0.396 cents. It is the smallest 7-limit superparticular ratio, being the amount by which a stack of two large limmas falls short of 7/6, (7/6)/(27/25)², as is conveniently codified by its S-expression of S25/S27. It is also 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. In term of other commas, it is equal to the difference between a kleisma and a marvel comma.

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 norm (log2 nd)	24.1898
Weil norm (log2 max(n, d))	24.1901
Wilson norm (sopfr(nd))	50
Comma size	unnoticeable
S-expression	S25/S27
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English Wikipedia has an article on:

Ragisma

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