Mersenne comma - Revision history

FloraC: Fixes & add n = 24

2026-03-21T12:47:02Z

Fixes & add n = 24

← Older revision		Revision as of 12:47, 21 March 2026
Line 6:		Line 6:

	== List of Mersenne commas ==		== List of Mersenne commas ==
	{\| class="wikitable"		{\| class="wikitable center-1"
	\|+Table of first Mersenne composite commas		\|+Table of first Mersenne composite commas
	! Index		! Index
Line 17:		Line 17:
	\| [[16/15]]		\| [[16/15]]
	\| 2.3.5		\| 2.3.5
	\|{{Monzo\| 4 -1 -1 }}		\| {{Monzo\| 4 -1 -1 }}
	\| Classic diatonic semitone		\| Classic diatonic semitone
	\|-		\|-
Line 24:		Line 24:
	\| 2.3.7		\| 2.3.7
	\| {{Monzo\| 6 -2 -1 }}		\| {{Monzo\| 6 -2 -1 }}
	\| Septimal comma (Archytas comma)		\| Septimal comma (Archytas' comma)
	\|-		\|-
	\| 8		\| 8
Line 74:		Line 74:
	\|		\|
	\|-		\|-
	\| 19		\| 18
	\| [[262144/262143]]		\| [[262144/262143]]
	\| 2.3.7.19.73		\| 2.3.7.19.73
Line 103:		Line 103:
	\| {{Monzo\| 23 -1 -1 }}		\| {{Monzo\| 23 -1 -1 }}
	\|		\|
			\|-
			\| 24
			\| [[16777216/16777215]]
			\| 2.3.5.7.13.17.241
			\| {{Monzo\| 24 -2 -1 -1 -1 -1 -1 }}
	\|}		\|}

FloraC: Name change followup. Cleanup. Mark todo

2026-03-03T10:21:01Z

Name change followup. Cleanup. Mark todo

← Older revision		Revision as of 10:21, 3 March 2026
Line 1:		Line 1:
	A '''Mersenne comma''' is a [[comma]] of the form <math>\frac{2^n}{2^n-1}</math>. As such, they are also by definition [[octave-reduced]] [[subharmonic]]s.		A '''Mersenne comma''' is a [[comma]] of the form <math>\frac{2^n}{2^n-1}</math>. As such, they are also by definition [[octave-reduced]] [[subharmonic]]s.

	Mersenne prime commas equate a specific prime harmonic with the octave, so they are generally not of interest to ~~EDO~~ theory, with the possible exception of certain equal divisions of a compressed octave.		Mersenne prime commas equate a specific prime harmonic with the octave, so they are generally not of interest to [[edo]] theory, with the possible exception of certain equal divisions of a compressed octave.

	Mersenne composite commas, on the other hand, can have other uses, and the table below includes such notable examples of these as the [[64/63\|~~Septimal~~ comma]]. Mersenne composite numbers can be found in ~~The On-Line Encyclopedia of Integer Sequences (~~OEIS~~) at [[oeis:A135972~~\|~~sequence~~ A135972]].		Mersenne composite commas, on the other hand, can have other uses, and the table below includes such notable examples of these as the [[64/63\|septimal comma]]. Mersenne composite numbers can be found in {{OEIS\|A135972}}.

	==List of Mersenne commas==		== 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~~		! S. monzo
	!Comments		! Comments
	\|-		\|-
	\| 4		\| 4
	\|[[16/15]]		\| [[16/15]]
	\|2.3.5		\| 2.3.5
	\|{{~~monzo~~\| 4 -1 -1 }}		\|{{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 }}		\| {{Monzo\| 6 -2 -1 }}
	\| Septimal comma (Archytas comma)		\| Septimal comma (Archytas comma)
	\|-		\|-
	\|8		\| 8
	\|[[256/255]]		\| [[256/255]]
	\|2.3.5.17		\| 2.3.5.17
	\|{{~~monzo~~\| 8 -1 -1 -1 }}		\| {{Monzo\| 8 -1 -1 -1 }}
	\| ~~Septendecimal kleisma~~		\| Charisma
	\|-		\|-
	\|9		\| 9
	\|[[512/511]]		\| [[512/511]]
	\|2.7.73		\| 2.7.73
	\|{{~~monzo~~\| 9 -1 -1 }}		\| {{Monzo\| 9 -1 -1 }}
	\|		\|
	\|-		\|-
	\|10		\| 10
	\|[[1024/1023]]		\| [[1024/1023]]
	\| 2.3.11.31		\| 2.3.11.31
	\|{{~~monzo~~\| 10 -1 -1 -1 }}		\| {{Monzo\| 10 -1 -1 -1 }}
	\|Kibisma		\| Kibisma
	\|-		\|-
	\|11		\| 11
	\|[[2048/2047]]		\| [[2048/2047]]
	\|2.23.89		\| 2.23.89
	\|{{~~monzo~~\| 11 -1 -1 }}		\| {{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 }}		\| {{Monzo\| 12 -2 -1 -1 -1 }}
	\|~~Schismina~~		\| Minisma
	\|-		\|-
	\|14		\| 14
	\|[[16384/16383]]		\| [[16384/16383]]
	\|2.3.43.127		\| 2.3.43.127
	\|{{~~monzo~~\| 14 -1 -1 -1 }}		\| {{Monzo\| 14 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|15		\| 15
	\|[[32768/32767]]		\| [[32768/32767]]
	\| 2.7.31.151		\| 2.7.31.151
	\|{{~~monzo~~\| 15 -1 -1 -1 }}		\| {{Monzo\| 15 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|16		\| 16
	\|[[65536/65535]]		\| [[65536/65535]]
	\|2.3.5.17.257		\| 2.3.5.17.257
	\|{{~~monzo~~\| 16 -1 -1 -1 -1 }}		\| {{Monzo\| 16 -1 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|19		\| 19
	\|[[262144/262143]]		\| [[262144/262143]]
	\|2.3.7.19.73		\| 2.3.7.19.73
	\|{{monzo\| 18 -3 -1 -1 -1 }}		\| {{monzo\| 18 -3 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|20		\| 20
	\|[[1048576/1048575]]		\| [[1048576/1048575]]
	\|2.3.5.11.31.41		\| 2.3.5.11.31.41
	\|{{~~monzo~~\| 20 -1 -2 -1 -1 -1 }}		\| {{Monzo\| 20 -1 -2 -1 -1 -1 }}
	\|Mebisma		\| Mebisma
	\|-		\|-
	\|21		\| 21
	\|[[2097152/2097151]]		\| [[2097152/2097151]]
	\|2.7.127.337		\| 2.7.127.337
	\|{{~~monzo~~\| 21 -2 -1 -1 }}		\| {{Monzo\| 21 -2 -1 -1 }}
	\|		\|
	\|-		\|-
	\|22		\| 22
	\|[[4194304/4194303]]		\| [[4194304/4194303]]
	\|2.3.23.89.683		\| 2.3.23.89.683
	\|{{~~monzo~~\| 22 -1 -1 -1 -1 }}		\| {{Monzo\| 22 -1 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|23		\| 23
	\|[[8388608/8388607]]		\| [[8388608/8388607]]
	\|2.47.178481		\| 2.47.178481
	\|{{~~monzo~~\| 23 -1 -1 }}		\| {{Monzo\| 23 -1 -1 }}
	\|		\|
	\|}		\|}

Line 108:		Line 108:
	[[Category:Lists of commas]]		[[Category:Lists of commas]]
	[[Category:Octave-reduced subharmonics]]		[[Category:Octave-reduced subharmonics]]
	{{~~todo~~\|~~complete table\|review\|correct maths\|comment=check and complete the Index column~~}}		{{Todo\|explain its xenharmonic value}}

Eliora: explain relevance of octave-reduced subharmonic quality

2024-09-29T21:00:45Z

explain relevance of octave-reduced subharmonic quality

← Older revision		Revision as of 21:00, 29 September 2024
Line 1:		Line 1:
	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>. As such, they are also by definition [[octave-reduced]] [[subharmonic]]s.

	Mersenne prime commas equate a specific prime harmonic with the octave, so they are generally not of interest to EDO theory, with the possible exception of certain equal divisions of a compressed octave.		Mersenne prime commas equate a specific prime harmonic with the octave, so they are generally not of interest to EDO theory, with the possible exception of certain equal divisions of a compressed octave.

BudjarnLambeth: /* List of Mersenne commas */ corrected names

2024-09-29T03:53:44Z

List of Mersenne commas: corrected names

← Older revision		Revision as of 03:53, 29 September 2024
Line 42:		Line 42:
	\| 2.3.11.31		\| 2.3.11.31
	\|{{monzo\| 10 -1 -1 -1 }}		\|{{monzo\| 10 -1 -1 -1 }}
	\|~~Kilobyte comma~~		\|Kibisma
	\|-		\|-
	\|11		\|11
Line 81:		Line 81:
	\|-		\|-
	\|20		\|20
	\|[[~~Megabyte comma\|~~1048576/1048575]]		\|[[1048576/1048575]]
	\|2.3.5.11.31.41		\|2.3.5.11.31.41
	\|{{monzo\| 20 -1 -2 -1 -1 -1 }}		\|{{monzo\| 20 -1 -2 -1 -1 -1 }}
	\|~~Megabyte comma~~		\|Mebisma
	\|-		\|-
	\|21		\|21

Lucius Chiaraviglio: /* List of Mersenne commas */ Fix formatting around the link to Megabyte comma

2024-09-22T22:09:26Z

List of Mersenne commas: Fix formatting around the link to Megabyte comma

← Older revision		Revision as of 22:09, 22 September 2024
Line 81:		Line 81:
	\|-		\|-
	\|20		\|20
	\|[[[[Megabyte comma\|1048576/1048575]]]]		\|[[Megabyte comma\|1048576/1048575]]
	\|2.3.5.11.31.41		\|2.3.5.11.31.41
	\|{{monzo\| 20 -1 -2 -1 -1 -1 }}		\|{{monzo\| 20 -1 -2 -1 -1 -1 }}

Lucius Chiaraviglio: /* List of Mersenne commas */ Clarity rewrite; add missing indices; fix broken link to Megabyte comma.

2024-09-22T22:08:29Z

List of Mersenne commas: Clarity rewrite; add missing indices; fix broken link to Megabyte comma.

← Older revision		Revision as of 22:08, 22 September 2024
Line 1:		Line 1:
	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 ~~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~~.		Mersenne prime commas equate a specific prime harmonic with the octave, so they are generally not of interest to EDO theory, with the possible exception of certain equal divisions of a compressed octave.

	== List of Mersenne commas ==		Mersenne composite commas, on the other hand, can have other uses, and the table below includes such notable examples of these as the [[64/63\|Septimal comma]]. Mersenne composite numbers can be found in The On-Line Encyclopedia of Integer Sequences (OEIS) at [[oeis:A135972\|sequence A135972]].

			==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		!S. Monzo
	! Comments		!Comments
	\|-		\|-
	\| 4		\| 4
	\| [[16/15]]		\|[[16/15]]
	\| 2.3.5		\|2.3.5
	\| {{monzo\| 4 -1 -1 }}		\|{{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 }}		\|{{monzo\| 6 -2 -1 }}
	\| Septimal comma		\| Septimal comma (Archytas comma)
	\|-		\|-
	\| 8		\|8
	\| [[256/255]]		\|[[256/255]]
	\| 2.3.5.17		\|2.3.5.17
	\| {{monzo\| 8 -1 -1 -1 }}		\|{{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 }}		\|{{monzo\| 9 -1 -1 }}
	\|		\|
	\|-		\|-
	\| 10		\|10
	\| [[1024/1023]]		\|[[1024/1023]]
	\| 2.3.11.31		\| 2.3.11.31
	\| {{monzo\| 10 -1 -1 -1 }}		\|{{monzo\| 10 -1 -1 -1 }}
	\| Kilobyte comma		\|Kilobyte comma
	\|-		\|-
	\| 11		\|11
	\| [[2048/2047]]		\|[[2048/2047]]
	\| 2.23.89		\|2.23.89
	\| {{monzo\| 11 -1 -1 }}		\|{{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 }}		\|{{monzo\| 12 -2 -1 -1 -1 }}
	\| Schismina		\|Schismina
	\|-		\|-
	\|		\|14
	\| [[16384/16383]]		\|[[16384/16383]]
	\| 2.3.43.127		\|2.3.43.127
	\| {{monzo\| 14 -1 -1 -1 }}		\|{{monzo\| 14 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|15
	\| [[32768/32767]]		\|[[32768/32767]]
	\| 2.7.31.151		\| 2.7.31.151
	\| {{monzo\| 15 -1 -1 -1 }}		\|{{monzo\| 15 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|16
	\| [[65536/65535]]		\|[[65536/65535]]
	\| 2.3.5.17.257		\|2.3.5.17.257
	\| {{monzo\| 16 -1 -1 -1 -1 }}		\|{{monzo\| 16 -1 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|19
	\| [[262144/262143]]		\|[[262144/262143]]
	\| 2.3.7.19.73		\|2.3.7.19.73
	\| {{monzo\| 18 -3 -1 -1 -1 }}		\|{{monzo\| 18 -3 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|20
	\| [[1048576/1048575]]		\|[[[[Megabyte comma\|1048576/1048575]]]]
	\| 2.3.5.11.31.41		\|2.3.5.11.31.41
	\| {{monzo\| 20 -1 -2 -1 -1 -1 }}		\|{{monzo\| 20 -1 -2 -1 -1 -1 }}
	\|		\|Megabyte comma
	\|-		\|-
	\|		\|21
	\| [[2097152/2097151]]		\|[[2097152/2097151]]
	\| 2.7.127.337		\|2.7.127.337
	\| {{monzo\| 21 -2 -1 -1 }}		\|{{monzo\| 21 -2 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|22
	\| [[4194304/4194303]]		\|[[4194304/4194303]]
	\| 2.3.23.89.683		\|2.3.23.89.683
	\| {{monzo\| 22 -1 -1 -1 -1 }}		\|{{monzo\| 22 -1 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|23
	\| [[8388608/8388607]]		\|[[8388608/8388607]]
	\| 2.47.178481		\|2.47.178481
	\| {{monzo\| 23 -1 -1 }}		\|{{monzo\| 23 -1 -1 }}
	\|		\|
	\|}		\|}

BudjarnLambeth at 06:26, 22 September 2024

2024-09-22T06:26:11Z

← Older revision		Revision as of 06:26, 22 September 2024
Line 106:		Line 106:
	[[Category:Lists of commas]]		[[Category:Lists of commas]]
	[[Category:Octave-reduced subharmonics]]		[[Category:Octave-reduced subharmonics]]
	{{todo\|complete table\|review\|comment=check and complete the Index column}}		{{todo\|complete table\|review\|correct maths\|comment=check and complete the Index column}}

BudjarnLambeth at 06:24, 22 September 2024

2024-09-22T06:24:26Z

← Older revision		Revision as of 06:24, 22 September 2024
Line 56:		Line 56:
	\|		\|
	\| [[16384/16383]]		\| [[16384/16383]]
	\|		\| 2.3.43.127
	\|		\| {{monzo\| 14 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[32768/32767]]		\| [[32768/32767]]
	\|		\| 2.7.31.151
	\|		\| {{monzo\| 15 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[65536/65535]]		\| [[65536/65535]]
	\|		\| 2.3.5.17.257
	\|		\| {{monzo\| 16 -1 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[262144/262143]]		\| [[262144/262143]]
	\|		\| 2.3.7.19.73
	\|		\| {{monzo\| 18 -3 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[1048576/1048575]]		\| [[1048576/1048575]]
	\|		\| 2.3.5.11.31.41
	\|		\| {{monzo\| 20 -1 -2 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[2097152/2097151]]		\| [[2097152/2097151]]
	\|		\| 2.7.127.337
	\|		\| {{monzo\| 21 -2 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[4194304/4194303]]		\| [[4194304/4194303]]
	\|		\| 2.3.23.89.683
	\|		\| {{monzo\| 22 -1 -1 -1 -1 }}
	\|		\|
	\|-		\|-
	\|		\|
	\| [[8388608/8388607]]		\| [[8388608/8388607]]
	\|		\| 2.47.178481
	\|		\| {{monzo\| 23 -1 -1 }}
	\|		\|
	\|}		\|}
Line 106:		Line 106:
	[[Category:Lists of commas]]		[[Category:Lists of commas]]
	[[Category:Octave-reduced subharmonics]]		[[Category:Octave-reduced subharmonics]]
	{{todo\|complete table\|review\|comment=check ~~math~~}}		{{todo\|complete table\|review\|comment=check and complete the Index column}}

BudjarnLambeth: /* List of Mersenne commas */ Expanded table

2024-09-22T06:11:58Z

List of Mersenne commas: Expanded table

@@ Line 53: / Line 53: @@
 | {{monzo| 12 -2 -1 -1 -1 }}
 | Schismina
 |}
@@ Line 58: / Line 106: @@
 [[Category:Lists of commas]]
 [[Category:Octave-reduced subharmonics]]

BudjarnLambeth: /* List of Mersenne commas */

2024-09-22T06:01:08Z

List of Mersenne commas

← Older revision		Revision as of 06:01, 22 September 2024
Line 40:		Line 40:
	\| 2.3.11.31		\| 2.3.11.31
	\| {{monzo\| 10 -1 -1 -1 }}		\| {{monzo\| 10 -1 -1 -1 }}
	\| Kilobyte ~~commas~~		\| Kilobyte comma
	\|-		\|-
	\| 11		\| 11