715/714 - Revision history

FloraC at 15:05, 22 March 2026

2026-03-22T15:05:59Z

← Older revision		Revision as of 15:05, 22 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[~~unnoticeable comma\|unnoticeable~~]] [[~~superparticular~~]] ~~comma~~ with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:		'''715/714''', the '''september comma''' or '''septembrisma''' is an [[unnoticeable comma\|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:
	* the subfourths [[17/13]] and [[55/42]];		* the subfourths [[17/13]] and [[55/42]];
	* the superminor sixths [[21/13]] and [[55/34]];		* the superminor sixths [[21/13]] and [[55/34]];

FloraC: + see also

2026-03-22T15:00:48Z

+ see also

← Older revision		Revision as of 15:00, 22 March 2026
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	== Etymology ==		== Etymology ==
	The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name.		The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name.

			== See also ==
			* [[List of superparticular intervals]]

	[[Category:September]]		[[Category:September]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]
	[[Category:Commas with names disavowed by the original namer]]		[[Category:Commas with names disavowed by the original namer]]

FloraC: Update data

2026-03-22T14:59:51Z

Update data

← Older revision		Revision as of 14:59, 22 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}

	'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma\|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:		'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma\|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:
	* the subfourths [[17/13]] and [[55/42]]		* the subfourths [[17/13]] and [[55/42]];
	* the superminor sixths [[21/13]] and [[55/34]]		* the superminor sixths [[21/13]] and [[55/34]];
	* the semitones [[68/65]] and [[22/21]].		* the semitones [[68/65]] and [[22/21]].

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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 17-limit gives the rank-6 '''september ~~temperament~~''', and enables the [[~~September chords\|related~~ essentially tempered chords]].		Tempering out this comma in the 17-limit gives the rank-6 '''september''' temperament, and enables the related [[essentially tempered chord]]s – [[september chords]].

	=== September ===		=== September ===
	[[Subgroup]]: ~~Full~~ 17-~~limit~~		[[Subgroup]]: 2.3.5.7.11.13.17

			[[Mapping]]:
			{\| class="right-all"
			\|-
			\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ]]
			\|}
			: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[~~Comma basis~~]]: ~~715~~/~~714~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0409{{c}}, ~3/2 = 702.0169{{c}}, ~5/4 = 386.0109{{c}}, ~7/4 = 969.0667{{c}}, ~11/8 = 550.7048{{c}}, ~13/8 = 839.8438{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0260{{c}}, ~5/4 = 385.0429{{c}}, ~7/4 = 969.0934{{c}}, ~11/8 = 550.7520{{c}}, ~13/8 = 839.8854{{c}}

	~~[[Mapping]]: [⟨1 0 0 0 0 0 -~~1], ~~⟨0 1 0 0 0 0 -1]~~, ~~⟨0 0 1 0 0 0 1]~~, ~~⟨0 0 0 1 0 0 -1]~~, ~~⟨0 0 0 0 1 0 1]~~, ~~⟨0 0 0 0 0 1 1]]~~		{{Optimal ET sequence\|legend=1\| 22f, 26, 27eg, 29g, 31, 38df, 41, 46, 60e, 65d, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 634g, 706f }} *

	[[~~Optimal tuning~~]] ~~(POTE)~~: ~~~2 = 1＼1, ~3/2 = 701.9930, ~5/4 = 385.9978, ~7/4 = 969.0337, ~11/8 = 550.6860, ~13/8 = 839.8152~~		<nowiki>*</nowiki> [[optimal patent val]]: [[843edo\|843]]

	[[~~Optimal ET sequence~~]]: ~~{{Optimal ET sequence\|19, 26, 31, 41, 46, 68, 72, 103, 111, 121, 140, 183, 224, 270, 364, 436, 547, 843}}~~		[[Badness]] (Sintel): 0.292

	== Etymology ==		== Etymology ==

Xenllium at 09:51, 23 March 2025

2025-03-23T09:51:56Z

@@ Line 37: / Line 37: @@
 == Temperaments ==
 Tempering out this comma in the 17-limit gives the rank-6 '''september temperament''', and enables the [[September chords|related essentially tempered chords]].
 == Etymology ==

BudjarnLambeth at 01:52, 16 November 2024

2024-11-16T01:52:09Z

← Older revision		Revision as of 01:52, 16 November 2024
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	[[Category:September]]		[[Category:September]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]
	[[Category:Commas with names disavowed by the original namer~~\|Category:Commas with names disavowed by the original name~~]]		[[Category:Commas with names disavowed by the original namer]]

BudjarnLambeth at 01:51, 16 November 2024

2024-11-16T01:51:53Z

← Older revision		Revision as of 01:51, 16 November 2024
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	[[Category:September]]		[[Category:September]]
			[[Category:Commas named for the intervals they stack]]
			[[Category:Commas with names disavowed by the original namer\|Category:Commas with names disavowed by the original name]]

Francium: Added color name

2023-09-07T18:17:07Z

Added color name

← Older revision		Revision as of 18:17, 7 September 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = september comma, septembrisma		\| Name = september comma, septembrisma
			\| Color name = 17u3o1ory-2, sutholoruyo negative 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}

Inthar: Added a note that Scott disavowed the name.

2023-07-24T18:22:40Z

Added a note that Scott disavowed the name.

← Older revision		Revision as of 18:22, 24 July 2023
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	== Etymology ==		== Etymology ==
	The september comma was named by [[Scott Dakota]] in 2021.		The september comma was named by [[Scott Dakota]] in 2021; however, Scott Dakota has disavowed this name.

	[[Category:September]]		[[Category:September]]

Inthar at 14:50, 24 July 2023

2023-07-24T14:50:17Z

← Older revision		Revision as of 14:50, 24 July 2023
Line 6:		Line 6:
	'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma\|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:		'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma\|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:
	* the subfourths [[17/13]] and [[55/42]]		* the subfourths [[17/13]] and [[55/42]]
	* the ~~supraminor~~ sixths [[21/13]] and [[55/34]]		* the superminor sixths [[21/13]] and [[55/34]]
	* the semitones [[68/65]] and [[22/21]].		* the semitones [[68/65]] and [[22/21]].

Inthar: Added MC- and HCJI intervals related by this comma.

2023-07-24T14:49:55Z

Added MC- and HCJI intervals related by this comma.

← Older revision		Revision as of 14:49, 24 July 2023
Line 4:		Line 4:
	}}		}}

	'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma\|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''.		'''715/714''', the '''september comma''' or '''septembrisma''' is a [[17-limit]] [[unnoticeable comma\|unnoticeable]] [[superparticular]] comma with a size of approximately 2.42 [[cent]]s. It is also described as the ''septendecimal bridge comma''. It is the gap between:
			* the subfourths [[17/13]] and [[55/42]]
			* the supraminor sixths [[21/13]] and [[55/34]]
			* the semitones [[68/65]] and [[22/21]].

	== Commatic relations ==		== Commatic relations ==
	This comma ~~identifies itself~~ as the difference between the following superparticular pairs:		This comma appears as the difference between the following superparticular pairs:
	* [[120/119]] and [[144/143]]		* [[120/119]] and [[144/143]]
	* [[154/153]] and [[196/195]]		* [[154/153]] and [[196/195]]