Mersenne comma: Difference between revisions
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A '''Mersenne comma''' is a [[comma]] of the form <math>\frac{2^n}{2^n-1}</math>. | A '''Mersenne comma''' is a [[comma]] of the form <math>\frac{2^n}{2^n-1}</math>. | ||
Since Mersenne prime commas | 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 [https://oeis.org/A135972 A135972] in OEIS. | ||
== List of Mersenne commas == | == List of Mersenne commas == | ||
Revision as of 19:16, 4 October 2023
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
| 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 |