736/729 - Revision history

Fredg999: Fix typo

2025-07-29T20:15:30Z

Fix typo

← Older revision		Revision as of 20:15, 29 July 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic [[23/16]] exceeds the [[729/512\|Pythagorean ~~augemented~~ fourth (729/512)]].		'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic [[23/16]] exceeds the [[729/512\|Pythagorean augmented fourth (729/512)]].

	== Notation ==		== Notation ==

FloraC: +short explanation on its look in HEJI and hopefully this helps to understand the current name

2024-11-28T17:59:35Z

+short explanation on its look in HEJI and hopefully this helps to understand the current name

← Older revision		Revision as of 17:59, 28 November 2024
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	== Notation ==		== Notation ==
	This interval is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.		This interval is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval. The symbols being used in Helmholtz-Ellis notation are virtually identical to up and down arrows, and the authors attribute them to [[James Tenney]] and {{w\|John Cage}}, who have possibly used them for [[72edo\|1\72]].

	=== Sagittal notation ===		=== Sagittal notation ===

FloraC: +significance in FJS and misc. rework

2024-11-28T17:12:02Z

+significance in FJS and misc. rework

← Older revision		Revision as of 17:12, 28 November 2024
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	{{Infobox Interval		{{Infobox Interval
	\|Ratio = 736/729		\| Ratio = 736/729
	\|Name = 23-limit Tenney/Cage comma (HEJI)		\| Name = 23-limit Tenney/Cage comma (HEJI)
	\|Color name = s23o2, satwetho 2nd		\| Color name = s23o2, satwetho 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 ~~(the 23rd harmonic)~~ exceeds the Pythagorean augemented fourth (729/512)~~. It is significant in [[Helmholtz-Ellis notation~~]] ~~as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval~~.		'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which the octave-reduced 23rd harmonic [[23/16]] exceeds the [[729/512\|Pythagorean augemented fourth (729/512)]].

	== Sagittal notation ==		== Notation ==
			This interval is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

			=== Sagittal notation ===
	In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.

	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]

BudjarnLambeth at 01:02, 16 November 2024

2024-11-16T01:02:03Z

← Older revision		Revision as of 01:02, 16 November 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.

			[[Category:Commas named after music theorists]]
			[[Category:Commas named after composers]]

Dave Keenan: /* Sagittal notation */ Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.

2024-10-10T07:10:15Z

Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Gave the truly-simplest (2,3-free) interval in addition to the octave-reduced interval. Replaced hair-space with nbhsp template call.

← Older revision		Revision as of 07:10, 10 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest ~~ratio~~ it notates is 16~~:23~~, as for example in F:B~~ ~~{{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest interval it notates is 23/1 (equiv. 23/16), as for example in F-B{{nbhsp}}{{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.

Dave Keenan: /* Sagittal notation */ Added downward version

2024-10-09T13:34:37Z

Sagittal notation: Added downward version

← Older revision		Revision as of 13:34, 9 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest ratio it notates is 16:23, as for example in F:B{{sagittal \| \|~ }}.		In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest ratio it notates is 16:23, as for example in F:B {{sagittal \| \|~ }}. The downward version is called '''1/23C''' or '''23C down''' and is represented by {{sagittal\| !~ }}.

Cmloegcmluin: add section for this comma's use in Sagittal notation

2024-10-09T05:18:27Z

add section for this comma's use in Sagittal notation

← Older revision		Revision as of 05:18, 9 October 2024
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	}}		}}
	'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.		'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

			== Sagittal notation ==
			In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal \| \|~ }} and is called the '''23 comma''', or '''23C''' for short, because the simplest ratio it notates is 16:23, as for example in F:B{{sagittal \| \|~ }}.

BudjarnLambeth: | Comma = yes

2024-01-20T06:48:48Z

| Comma = yes

← Older revision		Revision as of 06:48, 20 January 2024
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	\|Name = 23-limit Tenney/Cage comma (HEJI)		\|Name = 23-limit Tenney/Cage comma (HEJI)
	\|Color name = s23o2, satwetho 2nd		\|Color name = s23o2, satwetho 2nd
			\| Comma = yes
	}}		}}
	'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.		'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

Francium: Added Infobox Interval

2023-09-24T10:09:48Z

Added Infobox Interval

← Older revision		Revision as of 10:09, 24 September 2023
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	{~~\| class="wikitable"~~		{{Infobox Interval
	\|+Interval ~~information~~		\|Ratio = 736/729
	\|Ratio		\|Name = 23-limit Tenney/Cage comma (HEJI)
	\|736/729		\|Color name = s23o2, satwetho 2nd
	\|-		}}
	~~\|[[Smonzos and svals\|Subgroup monzo]]~~
	~~\|2.3.23 [5 -6 1⟩~~
	\|-
	~~\|Size in [[Cent\|cents]]~~
	~~\|16.544342¢~~
	\|-
	~~\|Names~~
	\|23-limit Tenney/Cage comma (HEJI)
	\|}
	'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.		'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.

Stephen Weigel: I added a page explaining that this comma is used in HEJI.

2023-09-24T03:05:30Z

I added a page explaining that this comma is used in HEJI.

New page

{| class="wikitable"
|+Interval information
|Ratio
|736/729
|-
|[[Smonzos and svals|Subgroup monzo]]
|2.3.23 [5 -6 1⟩
|-
|Size in [[Cent|cents]]
|16.544342¢
|-
|Names
|23-limit Tenney/Cage comma (HEJI)
|}
'''736/729''', the '''23-limit Tenney/Cage comma''', is a 2.3.23 subgroup comma. It is the amount by which 23/16 (the 23rd harmonic) exceeds the Pythagorean augemented fourth (729/512). It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 23-limit (vicesimotertial) interval.