Mersenne comma

Mersenne commas are a series of commas of the form [math]\displaystyle{ \frac{2^n}{2^n-1} }[/math].

Since Mersenne prime commas effectively set their own prime limit, they are of no interest to EDO theory. Therefore, this time Mersenne composite numbers enter the stage - sequence A135972 in OEIS.

Theory

Table of first Mersenne composite commas

Index	Comma	Prime Subgroup	Monzo (zeroes skipped)	Comments
4	16/15	2.3.5	[4 -1 -1⟩	Classic diatonic semitone.
6	64/63	2.3.7	[6 -2 -1⟩	Septimal comma.
8	256/255	2.3.5.17	[8 -1 -1 -1⟩	Septendecimal kleisma.
9	512/511	2.7.73	[9 -1 -1⟩
10	1024/1023	2.3.11.31	[10 -1 -1 -1⟩
11	2048/2047	2.23.89	[11 -1 -1⟩
12	4096/4095	2.3.5.7.13	[12 -2 -1 -1 -1⟩	Schismina.