Mersenne comma: Difference between revisions
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Mersenne | A '''Mersenne comma''' is a [[comma]] of the form <math>\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 [https://oeis.org/A135972 A135972] in OEIS. | Since Mersenne prime commas effectively set their own prime limit, they are of no interest to EDO theory{{clarify}}. Therefore, this time Mersenne composite numbers enter the stage - sequence [https://oeis.org/A135972 A135972] in OEIS. | ||
== | == List of Mersenne commas == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Table of first Mersenne composite commas | |+Table of first Mersenne composite commas | ||
!Index | ! Index | ||
!Comma | ! Comma | ||
! | ! Subgroup | ||
Subgroup | ! S. Monzo | ||
!Monzo | ! Comments | ||
!Comments | |||
|- | |- | ||
|4 | | 4 | ||
|[[16/15]] | | [[16/15]] | ||
|2.3.5 | | 2.3.5 | ||
| | | {{monzo| 4 -1 -1 }} | ||
|Classic diatonic semitone | | Classic diatonic semitone | ||
|- | |- | ||
|6 | | 6 | ||
|[[64/63]] | | [[64/63]] | ||
|2.3.7 | | 2.3.7 | ||
| | | {{monzo| 6 -2 -1 }} | ||
|Septimal comma | | Septimal comma | ||
|- | |- | ||
|8 | | 8 | ||
|[[256/255]] | | [[256/255]] | ||
|2.3.5.17 | | 2.3.5.17 | ||
| | | {{monzo| 8 -1 -1 -1 }} | ||
|Septendecimal kleisma | | Septendecimal kleisma | ||
|- | |- | ||
|9 | | 9 | ||
|[[512/511]] | | [[512/511]] | ||
|2.7.73 | | 2.7.73 | ||
| | | {{monzo| 9 -1 -1 }} | ||
| | | | ||
|- | |- | ||
|10 | | 10 | ||
|[[1024/1023]] | | [[1024/1023]] | ||
|2.3.11.31 | | 2.3.11.31 | ||
| | | {{monzo| 10 -1 -1 -1 }} | ||
| | | | ||
|- | |- | ||
|11 | | 11 | ||
|[[2048/2047]] | | [[2048/2047]] | ||
|2.23.89 | | 2.23.89 | ||
| | | {{monzo| 11 -1 -1 }} | ||
| | | | ||
|- | |- | ||
|12 | | 12 | ||
|[[4096/4095]] | | [[4096/4095]] | ||
|2.3.5.7.13 | | 2.3.5.7.13 | ||
| | | {{monzo| 12 -2 -1 -1 -1 }} | ||
|Schismina | | Schismina | ||
|} | |} | ||
[[Category: | [[Category:Ratio]] | ||
Revision as of 14:59, 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 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
| 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 |