11/9 - Revision history

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

2025-11-03T13:05:26Z

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

← Older revision		Revision as of 13:05, 3 November 2025
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	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 11/9}}		{{Interval edo approximation\|11/9}}
	== See also ==		== See also ==
	* [[7edo]]		* [[7edo]]

Pailiaq at 07:07, 3 November 2025

2025-11-03T07:07:09Z

← Older revision		Revision as of 07:07, 3 November 2025
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	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].
	== Approximation ==		== Approximation ==
	{{Interval_Edo_Approximation \| 11/9}		{{Interval_Edo_Approximation \| 11/9}}
	== See also ==		== See also ==
	* [[7edo]]		* [[7edo]]

Pailiaq at 07:06, 3 November 2025

2025-11-03T07:06:41Z

← Older revision		Revision as of 07:06, 3 November 2025
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	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].
			== Approximation ==
			{{Interval_Edo_Approximation \| 11/9}
	== See also ==		== See also ==
	* [[7edo]]		* [[7edo]]

Fitzgerald Lee at 08:49, 5 August 2025

2025-08-05T08:49:54Z

← Older revision		Revision as of 08:49, 5 August 2025
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	}}		}}

	In [[11-limit]] [[just intonation]], '''11/9''' is a [[neutral third]] of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but it is only one of many, of which others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]. As this is the smaller of the two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. As it is nearly halfway between two intervals of [[12edo]], it implies that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.		In [[11-limit]] [[just intonation]], '''11/9''' is a [[neutral third]] of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but it is only one of many, of which others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]. As this is the smaller of the two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. Since it is nearly halfway between two intervals of [[12edo]], it implies that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.

	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].

Fitzgerald Lee: changed phrasing, replaced big edo examples with small edo exmaples

2025-08-05T08:30:44Z

changed phrasing, replaced big edo examples with small edo exmaples

← Older revision		Revision as of 08:30, 5 August 2025
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	}}		}}

	In [[11-limit]] [[just intonation]], '''11/9''' is a ~~'''~~neutral third~~'''~~ of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but ~~of course,~~ only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], ~~implying~~ that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the ~~5th~~ creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.		In [[11-limit]] [[just intonation]], '''11/9''' is a [[neutral third]] of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but it is only one of many, of which others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]. As this is the smaller of the two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. As it is nearly halfway between two intervals of [[12edo]], it implies that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.

	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic ~~11th~~ and the harmonic ~~9th~~. A triad can also be built with a 3/2 ~~fifth~~ and 11/9 ~~third: this would be~~ 18:22:27. This introduces a second neutral third, 27/22, which ~~together make a perfect fifth~~. Many temperaments, including [[~~17edo]], [[24edo~~]], [[~~31edo~~]], [[~~41edo~~]], [[~~58edo~~]], [[~~72edo~~]], [[~~130edo~~]], [[~~202edo~~]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds~~, allowing either~~ interval to be stacked ~~on top of itself~~ to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of ~~them~~ leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].

	== See also ==		== See also ==
			* [[7edo]]
	* [[24edo]]		* [[24edo]]
	* [[18/11]] – its [[octave complement]]		* [[18/11]] – its [[octave complement]]

CompactStar at 01:02, 7 May 2023

2023-05-07T01:02:11Z

← Older revision		Revision as of 01:02, 7 May 2023
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	[[Category:Neutral third]]		[[Category:Neutral third]]
	[[Category:Alpharabian]]		[[Category:Alpharabian]]
			[[Category:Tritave-reduced harmonics]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T11:29:04Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 11:29, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 11/9~~		\| Name = undecimal neutral third, Alpharabian artoneutral third
	~~\| Monzo = 0 -2 0 0 1~~
	~~\| Cents = 347.40794~~
	\| Name = undecimal neutral third, ~~<br>~~ Alpharabian artoneutral third
	\| Color name = 1o3, ilo 3rd		\| Color name = 1o3, ilo 3rd
	~~\| FJS name = m3<sup>11</sup>~~
	\| Sound = jid_11_9_pluck_adu_dr220.mp3		\| Sound = jid_11_9_pluck_adu_dr220.mp3
	}}		}}
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	* [[Iceface tuning]]		* [[Iceface tuning]]

	~~[[Category:11-limit]]~~
	[[Category:Third]]		[[Category:Third]]
	[[Category:Neutral third]]		[[Category:Neutral third]]
	[[Category:Alpharabian]]		[[Category:Alpharabian]]

Fredg999: Misc. edits, categories

2022-02-22T17:22:08Z

Misc. edits, categories

← Older revision		Revision as of 17:22, 22 February 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 11/9		\| Ratio = 11/9
	\| Monzo = 0 -2 0 0 1		\| Monzo = 0 -2 0 0 1
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	}}		}}

	In [[11-limit]] [[~~Just Intonation~~]], '''11/9''' is a '''neutral third''' of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the 5th creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.		In [[11-limit]] [[just intonation]], '''11/9''' is a '''neutral third''' of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the 5th creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.

	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds, allowing either interval to be stacked on top of itself to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds, allowing either interval to be stacked on top of itself to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].
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	* [[27/22]] – its [[fifth complement]]		* [[27/22]] – its [[fifth complement]]
	* [[12/11]] – its [[fourth complement]]		* [[12/11]] – its [[fourth complement]]
	* [[Gallery of ~~Just Intervals~~]]		* [[Gallery of just intervals]]
	* [[Iceface tuning]]		* [[Iceface tuning]]

	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:~~Just interval]]~~		[[Category:Third]]
	~~[[Category:Interval ratio~~]]
	[[Category:Neutral third]]		[[Category:Neutral third]]
	~~[[Category:Third]]~~
	[[Category:Alpharabian]]		[[Category:Alpharabian]]
	~~[[Category:Listen]]~~
	~~[[Category:Untwelve]]~~
	~~[[Category:Pages with internal sound examples]]~~

Aura: Changing some of the nomenclature concerning Alpharabian tuning

2022-01-29T23:36:09Z

Changing some of the nomenclature concerning Alpharabian tuning

← Older revision		Revision as of 23:36, 29 January 2022
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	\| Monzo = 0 -2 0 0 1		\| Monzo = 0 -2 0 0 1
	\| Cents = 347.40794		\| Cents = 347.40794
	\| Name = undecimal neutral third, <br> ~~lesser~~ Alpharabian ~~neutral~~ third		\| Name = undecimal neutral third, <br> Alpharabian artoneutral third
	\| Color name = 1o3, ilo 3rd		\| Color name = 1o3, ilo 3rd
	\| FJS name = m3<sup>11</sup>		\| FJS name = m3<sup>11</sup>
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	}}		}}

	In [[11-limit]] [[Just Intonation]], '''11/9''' is a '''neutral third''' of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''~~lesser~~ Alpharabian ~~neutral~~ third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the 5th creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.		In [[11-limit]] [[Just Intonation]], '''11/9''' is a '''neutral third''' of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the 5th creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.

	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds, allowing either interval to be stacked on top of itself to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds, allowing either interval to be stacked on top of itself to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].

Morion: Clarified information.

2022-01-01T02:14:25Z

Clarified information.

← Older revision		Revision as of 02:14, 1 January 2022
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	In [[11-limit]] [[Just Intonation]], '''11/9''' is a '''neutral third''' of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''lesser Alpharabian neutral third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the 5th creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.		In [[11-limit]] [[Just Intonation]], '''11/9''' is a '''neutral third''' of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]). As this is the smaller of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''lesser Alpharabian neutral third''' in [[Alpharabian tuning]]. It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the 5th creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.

	In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds, allowing ~~one neutral third~~ interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].		In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle\|miracle]], [[Breedsmic temperaments #Harry\|harry]], and [[Schismatic family #Sesquiquartififths\|sesquart]], conflate these two neutral thirds, allowing either interval to be stacked on top of itself to generate a perfect fifth. 11/9 differs from 27/22 by [[243/242]], but also from 49/40 by [[441/440]] and 60/49 by [[540/539]], with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder\|jove]].

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