Mersenne comma

A Mersenne comma is a comma of the form [math]\displaystyle{ \frac{2^n}{2^n-1} }[/math].

Since Mersenne prime commas are of the form 2 / M, they are of no interest to EDO theory at all, as they are merely equate a specific prime harmonic with the octave. Therefore, this time Mersenne composite numbers enter the stage - sequence A135972 in OEIS.

List of Mersenne commas

Table of first Mersenne composite commas

Index	Comma	Subgroup	S. Monzo	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⟩	Kilobyte comma
11	2048/2047	2.23.89	[11 -1 -1⟩
12	4096/4095	2.3.5.7.13	[12 -2 -1 -1 -1⟩	Schismina
	16384/16383	2.3.43.127	[14 -1 -1 -1⟩
	32768/32767	2.7.31.151	[15 -1 -1 -1⟩
	65536/65535	2.3.5.17.257	[16 -1 -1 -1 -1⟩
	262144/262143	2.3.7.19.73	[18 -3 -1 -1 -1⟩
	1048576/1048575	2.3.5.11.31.41	[20 -1 -2 -1 -1 -1⟩
	2097152/2097151	2.7.127.337	[21 -2 -1 -1⟩
	4194304/4194303	2.3.23.89.683	[22 -1 -1 -1 -1⟩
	8388608/8388607	2.47.178481	[23 -1 -1⟩