11/7 - Revision history

Squib: removed duplicate text

2026-02-03T00:34:44Z

removed duplicate text

← Older revision		Revision as of 00:34, 3 February 2026
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	In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].

	In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the Pythagorean ([[3-limit]]) minor sixth of [[128/81]] (about 792.2{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a minor sixth, hence the names. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].

	However, it is only flat of the [[128/81\|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.		However, it is only flat of the [[128/81\|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.

	It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].		It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].

	== Approximation ==		== Approximation ==

FloraC: Rework

2026-01-16T09:12:03Z

Rework

← Older revision		Revision as of 09:12, 16 January 2026
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	}}		}}

	In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].		In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].

	In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the Pythagorean ([[3-limit]]) minor sixth of [[128/81]] (about 792.2¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a minor sixth, hence the names.		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the Pythagorean ([[3-limit]]) minor sixth of [[128/81]] (about 792.2{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a minor sixth, hence the names. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].

	It is flat of the ~~5-limit minor sixth of~~ [[8/5]] (about ~~813~~.7¢) by [[56/~~55]]. It is sharp of the 7-limit subminor sixth of [[14~~/9]] ~~(about 764.9¢) by~~ a ~~mothwellsma~~, ~~[[99/98]]~~. ~~And finally~~, it is ~~sharp of the classic augmented fifth of [[25~~/~~16]]~~ (about ~~772~~.6¢) by a ~~valinorsma, [[176/175]]~~.		However, it is only flat of the [[128/81\|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891\|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.

	~~As 11~~/7 is 22/21 (about 80.5¢) ~~above~~ the ~~perfect~~ fifth~~, it can be resolved down~~ by a ~~step from 11/7 to 3~~/2.		It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|11/7}}		{{Interval edo approximation\|11/7}}

	~~<references/>~~		== Proximity with acoustic pi ==
			[[22/7]], one octave higher, is a fraction convergent to the continued fraction of acoustic pi. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.
	== Proximity with π ==
	[[22/7]], one octave higher, is a fraction convergent to the continued fraction of π. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.

	== See also ==		== See also ==
	* [[14/11]] – its octave complement		* [[14/11]] – its [[octave complement]]
			* [[21/11]] – its [[twelfth complement]]
	* [[Ed11/7]]		* [[Ed11/7]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:07:47Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:07, 3 November 2025
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	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 11/7}}		{{Interval edo approximation\|11/7}}

	<references/>		<references/>

Pailiaq at 07:36, 3 November 2025

2025-11-03T07:36:09Z

@@ Line 13: / Line 13: @@
 As 11/7 is 22/21 (about 80.5¢) above the perfect fifth, it can be resolved down by a step from 11/7 to 3/2.
-== Approximations by edos ==
+== Approximation ==
+ {{Interval_Edo_Approximation | 11/7}}
 <references/>

Eufalesio: Made 22/7 to properly talk about pi approximants

2025-11-01T19:07:37Z

Made 22/7 to properly talk about pi approximants

← Older revision		Revision as of 19:07, 1 November 2025
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	<references/>		<references/>

	== Proximity with π/2 ==		== Proximity with π ==
	~~(11~~/7~~)/(~~π~~/2) =~~ 22/7π is an [[unnoticeable comma]] of only 0.7 cents.		[[22/7]], one octave higher, is a fraction convergent to the continued fraction of π. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.

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

BudjarnLambeth: Category:Taxicab-2 intervals

2024-12-01T23:01:08Z

Category:Taxicab-2 intervals

← Older revision		Revision as of 23:01, 1 December 2024
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	[[Category:Subminor sixth]]		[[Category:Subminor sixth]]
	[[Category:Pentacircle]]		[[Category:Pentacircle]]
			[[Category:Taxicab-2 intervals]]

BudjarnLambeth: /* See also */ link

2024-10-26T23:57:04Z

FloraC: Rework; +"pentacircle minor sixth" and reasons; -"undecimal augmented fifth" (its octave complement isn't "undecimal diminished fourth" yet)

2024-10-25T09:08:54Z

Rework; +"pentacircle minor sixth" and reasons; -"undecimal augmented fifth" (its octave complement isn't "undecimal diminished fourth" yet)

← Older revision		Revision as of 09:08, 25 October 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = undecimal minor sixth, ~~undecimal augmented fifth~~		\| Name = undecimal minor sixth, pentacircle minor sixth
	\| Color name = 1or5, loru 5th		\| Color name = 1or5, loru 5th
	\| Sound = jid_11_7_pluck_adu_dr220.mp3		\| Sound = jid_11_7_pluck_adu_dr220.mp3
	}}		}}

	In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the ~~undecimal~~ major third.		In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].

	~~11/7 is flat of the Pythagorean minor sixth of~~ [[~~128/81~~]] ~~(about 792.2¢~~) by a ~~pentacircle comma,~~ [[~~896~~/~~891~~]]~~. It is flat of the 5-limit minor sixth~~ of [[8/5]] (~~about 813.7¢~~) by [[56/55]]~~. It is sharp~~ of the ~~7-limit subminor sixth of~~ [[~~14/9~~]] ~~(about 764.9¢) by a mothwellsma,~~ [[~~99/98~~]]. ~~And finally~~, it is ~~sharp~~ of the ~~classic augmented fifth~~ of [[25/16]] (about ~~772~~.6¢) by a ~~valinorsma,~~ [[~~176~~/~~175~~]].		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2\|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the Pythagorean ([[3-limit]]) minor sixth of [[128/81]] (about 792.2¢) by a [[896/891\|pentacircle comma (896/891)]], which makes it function more often as a minor sixth, hence the names.

	11/7 is [[22/21]] (about 80.5¢) ~~above the~~ [[3/2]] ~~perfect fifth~~, ~~allowing~~ the ~~possibility~~ of ~~a resolution down~~ by a ~~step from 11~~/~~7 to 3/2~~.		It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7¢) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9¢) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6¢) by a valinorsma, [[176/175]].

	~~== Approximations~~ by ~~EDOs ==~~		As 11/7 is 22/21 (about 80.5¢) above the perfect fifth, it can be resolved down by a step from 11/7 to 3/2.

	Following [[~~EDO~~]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the ~~EDO~~ representation is sharp (↑) or flat (↓).		== Approximations by edos ==

			Following [[edo]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (↑) or flat (↓).

	{\| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"		{\| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
	\|-		\|-
	! [[~~EDO~~]]		! [[Edo]]
	! class="unsortable" \| deg\edo		! class="unsortable" \| deg\edo
	! Absolute <br> error ([[Cent\|¢]])		! Absolute <br> error ([[Cent\|¢]])
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	== Proximity with π/2 ==		== Proximity with π/2 ==
	(11/7)/(π/2) = 22/7π is an [[unnoticeable comma]] of only +0.7 cents.		(11/7)/(π/2) = 22/7π is an [[unnoticeable comma]] of only 0.7 cents.

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

FloraC: Recategorize

2024-09-30T08:42:53Z

Recategorize

← Older revision		Revision as of 08:42, 30 September 2024
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	* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example		* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example

	[[Category:Over-7]]		[[Category:Over-7 intervals]]
	[[Category:Sixth]]		[[Category:Sixth]]
	[[Category:Minor sixth]]		[[Category:Minor sixth]]
	[[Category:Subminor sixth]]		[[Category:Subminor sixth]]
	[[Category:Pentacircle]]		[[Category:Pentacircle]]

Cmloegcmluin: /* Proximity with π/2 */ it's fine to include 22/7π now, but without also preserving the original formulation in terms of 11/7, it's not obvious why this fact is in this article

2023-03-07T17:17:08Z

Proximity with π/2: it's fine to include 22/7π now, but without also preserving the original formulation in terms of 11/7, it's not obvious why this fact is in this article

← Older revision		Revision as of 17:17, 7 March 2023
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	== Proximity with π/2 ==		== Proximity with π/2 ==
	22/7π is an [[unnoticeable comma]] of only +0.7 cents.		(11/7)/(π/2) = 22/7π is an [[unnoticeable comma]] of only +0.7 cents.

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

← Older revision		Revision as of 23:57, 26 October 2024
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	== See also ==		== See also ==
	* [[14/11]] – its octave complement		* [[14/11]] – its octave complement
			* [[Ed11/7]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example		* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example