Mersenne comma
Jump to navigation
Jump to search
A Mersenne comma is a comma of the form [math]\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
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 |