Mersenne comma

Revision as of 14:59, 4 October 2023 by FloraC (talk | contribs) (Mark clarify; section title; recategorize)

A Mersenne comma is a comma 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[clarification needed]. 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
11 2048/2047 2.23.89 [11 -1 -1
12 4096/4095 2.3.5.7.13 [12 -2 -1 -1 -1 Schismina