896/891 - Revision history

Hotcrystal0: 14/11 and 13/11

2026-03-05T17:40:11Z

14/11 and 13/11

← Older revision		Revision as of 17:40, 5 March 2026
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	The pentacircle comma can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo\| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo\| 5 -3 0 0 1 -1 }}).		The pentacircle comma can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo\| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo\| 5 -3 0 0 1 -1 }}).

	364/363 is the minor minthma or gentle comma, which is the difference between (14/11 × [[13/11]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)		364/363 is the minor minthma or gentle comma, which is the difference between a stack of 14/11 and [[13/11]] ([[182/121]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)

	352/351 is the major minthma. Tempering it out means 13/11 is equated with the pythagorean minor third, [[32/27]]. Tempering out 352/351 also makes [[11/9]] and [[16/13]] fifth complements of each other.		352/351 is the major minthma. Tempering it out means 13/11 is equated with the pythagorean minor third, [[32/27]]. Tempering out 352/351 also makes [[11/9]] and [[16/13]] fifth complements of each other.

Overthink: cleanup

2026-02-08T17:22:04Z

cleanup

← Older revision		Revision as of 17:22, 8 February 2026
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	}}		}}

	The '''pentacircle comma''' or '''undecimal semicomma''', '''896/891''' (9.68796 [[cent]]s), is an [[11-limit]] [[comma]] with monzo {{monzo\|7 -4 0 1 -1}}. It is similar to the Didymus or syntonic comma, [[81/80]], in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is [[5/4]], while with the pentacircle comma, the major third is [[14/11]]. It also equates [[33/32]] and [[28/27]].		The '''pentacircle comma''' or '''undecimal semicomma''', '''896/891''' (9.68796 [[cent]]s), is an [[11-limit]] [[comma]] with monzo {{monzo\|7 -4 0 1 -1}}. It is similar to the Didymus or syntonic comma, [[81/80]], in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is [[5/4]], while with the pentacircle comma, the major third is [[14/11]]. Tempering it out also equates [[33/32]] and [[28/27]].

	~~Pentacircle~~ is ~~tempered out by the following edos, using their patent vals:~~ {{~~EDOs~~\|5, 12, 17, 19, 22, 24, 27, 29, 36, 41, 44, 46, 51, 58, 60, 63, 65, 68, 80, 82, 85, 87, 90, 92, 104, 109, 114, 121, 123, 126, 128, 131, 133, 136, 138, 145, 150, 155, 167, 169, 172, 174, 177, 184, 189, 191, 196, 201, 208, 213, 218, 230, 232, 237, 242, 254, 259, 271, 278, 283, and 295}}.		The pentacircle comma can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo\| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo\| 5 -3 0 0 1 -1 }}).

	~~Pentacircle can be factored into two~~ [[13~~-limit~~]] [[~~superparticular~~]] ~~commas, [[~~364/363~~]] (which~~ is ~~{{monzo\| 2 -1 0 1 -2 1 }})~~ and [[~~352/351~~]] (~~which is {{monzo\|~~ 5 -3 ~~0 0 1 -1 }}~~).		364/363 is the minor minthma or gentle comma, which is the difference between (14/11 × [[13/11]]) and [[3/2]]. If 364/363 is tempered out, a 14/11 major third and a 13/11 minor third become [[fifth complement]]s; that is, they add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)

	~~364~~/~~363~~ is the ~~gentle comma, which is the difference between (14/11 ×~~ 13/11~~) and 3~~/2. ~~If both pentacircle and 364/363 are tempered~~ out ~~(which implies that~~ 352/351 is also ~~tempered out, of course), a 14~~/~~11 major third~~ and a 13~~/11 minor third together add up to a perfect~~ fifth. ~~(This isn't necessary for traditional minor and major thirds, because 5/4 × 6/5 = 3/2.)~~		352/351 is the major minthma. Tempering it out means 13/11 is equated with the pythagorean minor third, [[32/27]]. Tempering out 352/351 also makes [[11/9]] and [[16/13]] fifth complements of each other.

	~~352/351 is the minthma:~~ see the ~~article~~ on [[~~minthmic~~ chords]].		Each of these commas has their own essentially tempered chords; see the articles on [[pentacircle chords]], [[minor minthmic chords]], and [[major minthmic chords]].

	~~Finally~~, ~~see the article on~~ [[~~Pentacircle~~ chords]].

	~~Example scales:~~ [[~~Cantonpenta~~]] ~~is a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the pentacircle comma~~.

	== 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 '''11/7 kleisma''', or '''11/7k''' for short, because the simplest interval it notates is 11/7, as for example in A-F{{nbhsp}}{{sagittal \| )!( }}. The upward version is called '''7/11k''' or '''11/7k 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 '''11/7 kleisma''', or '''11/7k''' for short, because the simplest interval it notates is 11/7, as for example in A-F{{nbhsp}}{{sagittal \| )!( }}. The upward version is called '''7/11k''' or '''11/7k up''' and is represented by {{sagittal\| )\|( }}.

			== Temperaments ==
			Tempering out 896/891 in the 11-limit leads to the [[rank-4]] [[pentacircle]] temperament. This temperament naturally extends to the 13-limit via 352/351 and 364/363. Tridecimal pentacircle is supported by the following edos, using their patent vals: {{EDOs\|17, 22, 24, 29, 41, 46, 58, 63, 65, 80, 87, 92, 104, 109, 121}}, etc. The [[2.3.7.11.13 subgroup\|2.3.7.11.13-]][[subgroup]] version of this temperament is known as [[parapyth]], and the 2.3.11/7.13/7-subgroup version of it is known as [[pepperoni]].

	== See also ==		== See also ==
	* [[Pentacircle clan]], the clan of rank-3 temperaments where it is tempered out		* [[Pentacircle clan]], the clan of rank-3 temperaments where it is tempered out
	* [[Small comma]]		* [[Small comma]]
			* [[Cantonpenta]], a scale that tempers out the pentacircle comma

	[[Category:Pentacircle]]		[[Category:Pentacircle]]
	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

Hotcrystal0: Hotcrystal0 moved page Pentacircle comma to 896/891 over redirect: The ratio numbers don’t have that many digits

2026-01-08T18:43:31Z

Hotcrystal0 moved page Pentacircle comma to 896/891 over redirect: The ratio numbers don’t have that many digits

← Older revision	Revision as of 18:43, 8 January 2026
(No difference)

Squib at 17:24, 21 September 2025

2025-09-21T17:24:07Z

← Older revision		Revision as of 17:24, 21 September 2025
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	}}		}}

	The '''pentacircle comma''' or '''undecimal semicomma''', '''896/891''' (9.68796 [[cent]]s), is an [[11-limit]] [[comma]] with monzo {{monzo\|7 -4 0 1 -1}}. It is similar to the Didymus or syntonic comma, [[81/80]], in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is [[5/4]], while with the pentacircle comma, the major third is [[14/11]].		The '''pentacircle comma''' or '''undecimal semicomma''', '''896/891''' (9.68796 [[cent]]s), is an [[11-limit]] [[comma]] with monzo {{monzo\|7 -4 0 1 -1}}. It is similar to the Didymus or syntonic comma, [[81/80]], in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is [[5/4]], while with the pentacircle comma, the major third is [[14/11]]. It also equates [[33/32]] and [[28/27]].

	Pentacircle is tempered out by the following edos, using their patent vals: {{EDOs\|5, 12, 17, 19, 22, 24, 27, 29, 36, 41, 44, 46, 51, 58, 60, 63, 65, 68, 80, 82, 85, 87, 90, 92, 104, 109, 114, 121, 123, 126, 128, 131, 133, 136, 138, 145, 150, 155, 167, 169, 172, 174, 177, 184, 189, 191, 196, 201, 208, 213, 218, 230, 232, 237, 242, 254, 259, 271, 278, 283, and 295}}.		Pentacircle is tempered out by the following edos, using their patent vals: {{EDOs\|5, 12, 17, 19, 22, 24, 27, 29, 36, 41, 44, 46, 51, 58, 60, 63, 65, 68, 80, 82, 85, 87, 90, 92, 104, 109, 114, 121, 123, 126, 128, 131, 133, 136, 138, 145, 150, 155, 167, 169, 172, 174, 177, 184, 189, 191, 196, 201, 208, 213, 218, 230, 232, 237, 242, 254, 259, 271, 278, 283, and 295}}.

BudjarnLambeth at 02:00, 16 November 2024

2024-11-16T02:00:40Z

← Older revision		Revision as of 02:00, 16 November 2024
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	[[Category:Pentacircle]]		[[Category:Pentacircle]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named for their regular temperament properties]]

BudjarnLambeth at 13:20, 3 November 2024

2024-11-03T13:20:36Z

← Older revision		Revision as of 13:20, 3 November 2024
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	[[Category:Pentacircle]]		[[Category:Pentacircle]]
			[[Category:Commas with unknown etymology]]

Dave Keenan: /* Sagittal notation */ Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Replaced hair-space with nbhsp template call.

2024-10-10T07:04:30Z

Sagittal notation: Changed "simplest ratio" to "simplest interval". Changed colons to slashes and dash. Replaced hair-space with nbhsp template call.

← Older revision		Revision as of 07:04, 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 '''11/7 kleisma''', or '''11/7k''' for short, because the simplest ~~ratio~~ it notates is 7~~:11~~, as for example in A:F~~ ~~{{sagittal \| )!( }}. The upward version is called '''7/11k''' or '''11/7k 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 '''11/7 kleisma''', or '''11/7k''' for short, because the simplest interval it notates is 11/7, as for example in A-F{{nbhsp}}{{sagittal \| )!( }}. The upward version is called '''7/11k''' or '''11/7k up''' and is represented by {{sagittal\| )\|( }}.

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

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

2024-10-09T13:31:59Z

Sagittal notation: Added upward version

← Older revision		Revision as of 13:31, 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 '''11/7 kleisma''', or '''11/7k''' for short, because the simplest ratio it notates is 7:11, as for example in A:F{{sagittal \| )!( }}.		In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )!( }} and is called the '''11/7 kleisma''', or '''11/7k''' for short, because the simplest ratio it notates is 7:11, as for example in A:F {{sagittal \| )!( }}. The upward version is called '''7/11k''' or '''11/7k up''' and is represented by {{sagittal\| )\|( }}.

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

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

2024-10-09T05:18:30Z

add section for this comma's use in Sagittal notation

← Older revision		Revision as of 05:18, 9 October 2024
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	Example scales: [[Cantonpenta]] is a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the pentacircle comma.		Example scales: [[Cantonpenta]] is a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the pentacircle comma.

			== Sagittal notation ==
			In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal \| )!( }} and is called the '''11/7 kleisma''', or '''11/7k''' for short, because the simplest ratio it notates is 7:11, as for example in A:F{{sagittal \| )!( }}.

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

TallKite: added color name

2022-12-29T03:18:45Z

added color name

← Older revision		Revision as of 03:18, 29 December 2022
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	\| Ratio = 896/891		\| Ratio = 896/891
	\| Name = pentacircle comma, undecimal semicomma		\| Name = pentacircle comma, undecimal semicomma
			\| Color name = s1uz2, Saluzo comma
	\| Comma = yes		\| Comma = yes
	}}		}}