36/35 - Revision history

FloraC: Re-organize following 15/14

2026-05-01T12:21:40Z

Re-organize following 15/14

← Older revision		Revision as of 12:21, 1 May 2026
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			{{Interwiki
			\| en = 36/35
			\| de = 36/35
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = septimal quartertone, mint comma		\| Name = septimal quartertone, mint comma
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	{{Wikipedia\|Septimal quarter tone}}		{{Wikipedia\|Septimal quarter tone}}

	'''36/35''', the '''septimal quartertone''' (~48.8{{cent~~}}) is~~ the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]]~~, and~~ [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].		'''36/35''', the '''septimal quartertone''' is a [[7-limit]] interval with a size of about 48.8 [[cent]]s. It arises as the difference between various 7-limit [[interval quality\|qualities]] of seconds, thirds, sixths, and sevenths: between supermajor and classical major, and between subminor and classical minor. These are the pairs of intervals separated by 36/35:
			* [[28/27]] and [[16/15]]
			* [[10/9]] and [[8/7]]
			* [[7/6]] and [[6/5]]
			* [[5/4]] and [[9/7]]
			* [[14/9]] and [[8/5]]
			* [[5/3]] and [[12/7]]
			* [[7/4]] and [[9/5]]
			* [[15/8]] and [[27/14]]

			It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as ([[64/63]])⋅([[81/80]]) and as ([[66/65]])⋅([[78/77]]); it is also ([[45/44]])⋅([[176/175]]), ([[51/50]])⋅([[120/119]]), ([[128/125]])⋅([[225/224]]), ([[50/49]])⋅([[126/125]]) and ([[56/55]])⋅([[99/98]]).

	== Temperaments ==		== Temperaments ==
	When treated as a generator, it is almost a fourth of the septimal whole tone [[28/25]], differing by a [[wizma]]. This allows it to be used as a generator for ~~an extension~~ of [[~~Hemimean family\|~~hemimean]] called [[sengagen]], where 5/4, 7/5 and 7/4 map to 8, 12 and 20 quartertones respectively.		When treated as a generator, it is almost a fourth of the septimal whole tone [[28/25]], differing by a [[wizma]]. This allows it to be used as a generator for a temperament of [[hemimean]] called [[sengagen]], where 5/4, 7/5 and 7/4 map to 8, 12 and 20 quartertones respectively.

	When treated as a comma to be tempered out, it is known as the '''mint comma''', and tempering it out leads to the [[mint]] temperament. See [[~~mint~~ family]], the family of rank-3 temperaments where it is tempered out, and [[~~mint~~ temperaments]], the collection of rank-2 temperaments where it is tempered out.		When treated as a comma to be tempered out, it is known as the '''mint comma''', and tempering it out leads to the [[mint]] temperament. See [[Mint family]] for the family of rank-3 temperaments where it is tempered out, and [[Mint temperaments]] for the collection of rank-2 temperaments where it is tempered out.

	== Etymology ==		== Etymology ==
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	== ~~Notes~~ ==		== References ==

	[[Category:Quartertone]]		[[Category:Quartertone]]
	[[Category:Mint]]		[[Category:Mint]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]
	~~<!-- interwiki -->~~
	~~[[de:36/35]]~~

Eufalesio: Added generator possibility

2025-11-21T11:11:15Z

Added generator possibility

← Older revision		Revision as of 11:11, 21 November 2025
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	== Temperaments ==		== Temperaments ==
			When treated as a generator, it is almost a fourth of the septimal whole tone [[28/25]], differing by a [[wizma]]. This allows it to be used as a generator for an extension of [[Hemimean family\|hemimean]] called [[sengagen]], where 5/4, 7/5 and 7/4 map to 8, 12 and 20 quartertones respectively.

	When treated as a comma to be tempered out, it is known as the '''mint comma''', and tempering it out leads to the [[mint]] temperament. See [[mint family]], the family of rank-3 temperaments where it is tempered out, and [[mint temperaments]], the collection of rank-2 temperaments where it is tempered out.		When treated as a comma to be tempered out, it is known as the '''mint comma''', and tempering it out leads to the [[mint]] temperament. See [[mint family]], the family of rank-3 temperaments where it is tempered out, and [[mint temperaments]], the collection of rank-2 temperaments where it is tempered out.

FloraC: /* Notation */ expand on Johnston notation

2024-11-13T11:24:34Z

Notation: expand on Johnston notation

← Older revision		Revision as of 11:24, 13 November 2024
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	== Notation ==		== Notation ==
	=== Ben Johnston's notation ===		=== Ben Johnston's notation ===
	[[Ben Johnston's notation]] ~~denotes~~ this interval with "~~<span style="display: inline-block; transform: rotate(180deg)">~~7~~</span>~~" (a turned 7), and the reciprocal 35/36 with an ordinary 7.		In [[Ben Johnston's notation]], this interval is denoted with "{{invert\|7}}" (a turned "7"), and the reciprocal 35/36 with an ordinary "7". If the base note is C, then [[7/4]] is reprented by C–Bb7.

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

BudjarnLambeth at 00:10, 4 November 2024

2024-11-04T00:10:54Z

← Older revision		Revision as of 00:10, 4 November 2024
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	[[Category:Quartertone]]		[[Category:Quartertone]]
	[[Category:Mint]]		[[Category:Mint]]
	[[Category:Commas named for ~~their regular temperament properties~~]]		[[Category:Commas named for the intervals they stack]]
	<!-- interwiki -->		<!-- interwiki -->
	[[de:36/35]]		[[de:36/35]]

BudjarnLambeth at 07:29, 3 November 2024

2024-11-03T07:29:23Z

← Older revision		Revision as of 07:29, 3 November 2024
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	[[Category:Quartertone]]		[[Category:Quartertone]]
	[[Category:Mint]]		[[Category:Mint]]
			[[Category:Commas named for their regular temperament properties]]
	<!-- interwiki -->		<!-- interwiki -->
	[[de:36/35]]		[[de:36/35]]

FloraC: Improve sectioning

2024-10-10T09:02:08Z

Improve sectioning

← Older revision		Revision as of 09:02, 10 October 2024
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	'''36/35''', the '''septimal quartertone''' (~48.8{{cent}}) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].		'''36/35''', the '''septimal quartertone''' (~48.8{{cent}}) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].

	~~[[Ben Johnston's notation]] denotes this interval with "<span style="display: inline-block; transform: rotate(180deg)">7</span>" (a turned 7), and the reciprocal 35/36 with an ordinary 7.~~

	== Temperaments ==		== Temperaments ==
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	The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group \| ''Quartonic'']</ref>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.		The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group \| ''Quartonic'']</ref>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.

	== Sagittal notation ==		== Notation ==
			=== Ben Johnston's notation ===
			[[Ben Johnston's notation]] denotes this interval with "<span style="display: inline-block; transform: rotate(180deg)">7</span>" (a turned 7), and the reciprocal 35/36 with an ordinary 7.

			=== Sagittal notation ===
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest interval it notates is 35/1 = 5×7 (equiv. 35/16), as for example in C-D{{nbhsp}}{{sagittal \| \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal\| /\|) }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest interval it notates is 35/1 = 5×7 (equiv. 35/16), as for example in C-D{{nbhsp}}{{sagittal \| \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal\| /\|) }}.

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.

2024-10-10T07:24:11Z

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 07:24, 10 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest ~~ratio~~ it notates is 16~~:35~~, as for example in C:D~~ ~~{{sagittal \| \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal\| /\|) }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest interval it notates is 35/1 = 5×7 (equiv. 35/16), as for example in C-D{{nbhsp}}{{sagittal \| \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal\| /\|) }}.

	== See also ==		== See also ==

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

2024-10-09T12:48:29Z

Sagittal notation: Added upward version

← Older revision		Revision as of 12:48, 9 October 2024
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	== Sagittal notation ==		== Sagittal notation ==
	In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest ratio it notates is 16:35, as for example in C:D{{sagittal \| \!) }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest ratio it notates is 16:35, as for example in C:D {{sagittal \| \!) }}. The upward version is called '''1/35M''' or '''35M up''' and is represented by {{sagittal\| /\|) }}.

	== See also ==		== See also ==

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

2024-10-09T05:17:36Z

add section for this comma's use in Sagittal notation

← Older revision		Revision as of 05:17, 9 October 2024
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	== Etymology ==		== Etymology ==
	The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group \| ''Quartonic'']</ref>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.		The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group \| ''Quartonic'']</ref>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.

			== Sagittal notation ==
			In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| \!) }} and is called the '''35 medium diesis''', or '''35M''' for short, because the simplest ratio it notates is 16:35, as for example in C:D{{sagittal \| \!) }}.

	== See also ==		== See also ==

FloraC: /* Etymology */ on "quartonic"

2023-12-05T15:51:58Z

Etymology: on "quartonic"

← Older revision		Revision as of 15:51, 5 December 2023
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	== Etymology ==		== Etymology ==
	The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group \| ''Quartonic'']</ref>.		The name ''mint comma'' was given by [[Mike Battaglia]] in 2012, for <u>min</u>or <u>t</u>hird because "it mixes 7/6 and 6/5 together into one minty interval"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103732.html Yahoo! Tuning Group \| ''Quartonic'']</ref>. Before that, it had been known as the ''quartonic comma'', which refers to another comma today.

	== See also ==		== See also ==