11/9: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = undecimal neutral third, Alpharabian artoneutral third

~~| Ratio = 11/9~~

~~| Monzo = 0 -2 0 0 1~~

~~| Cents = 347.40794~~

| Name = undecimal neutral third, ~~<br>~~ Alpharabian artoneutral third

| Color name = 1o3, ilo 3rd

~~| FJS name = m3<sup>11</sup>~~

| Sound = jid_11_9_pluck_adu_dr220.mp3

}}

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]]. 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 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]].

== Approximation ==

== See also ==

* [[7edo]]

* [[24edo]]

* [[18/11]] – its [[octave complement]]

* [[27/22]] – its [[fifth complement]]

* [[12/11]] – its [[fourth complement]]

* [[Gallery of ~~Just Intervals~~]]

* [[Gallery of just intervals]]

* [[Iceface tuning]]

[[Category:~~11-limit]]~~

[[Category:Third]]

~~[[Category:Just interval]]~~

~~[[Category:Interval ratio~~]]

[[Category:Neutral third]]

~~[[Category:Third]]~~

[[Category:Alpharabian]]

[[Category:~~Listen]]~~

[[Category:Tritave-reduced harmonics]]

~~[[Category:Untwelve]]~~

~~[[Category:Pages with internal sound examples~~]]

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 {{Infobox Interval
-| Icon =
+| Name = undecimal neutral third, Alpharabian artoneutral third
-| Ratio = 11/9
-| Monzo = 0 -2 0 0 1
-| Cents = 347.40794
-| Name = undecimal neutral third, <br> Alpharabian artoneutral third
 | Color name = 1o3, ilo 3rd
-| FJS name = m3<sup>11</sup>
 | Sound = jid_11_9_pluck_adu_dr220.mp3
 }}
-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]]. 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 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]].
+== Approximation ==
+{{Interval edo approximation|11/9}}
 == See also ==
+* [[7edo]]
 * [[24edo]]
 * [[18/11]] – its [[octave complement]]
 * [[27/22]] – its [[fifth complement]]
 * [[12/11]] – its [[fourth complement]]
-* [[Gallery of Just Intervals]]
+* [[Gallery of just intervals]]
 * [[Iceface tuning]]
-[[Category:11-limit]]
+[[Category:Third]]
-[[Category:Just interval]]
-[[Category:Interval ratio]]
 [[Category:Neutral third]]
-[[Category:Third]]
 [[Category:Alpharabian]]
-[[Category:Listen]]
+[[Category:Tritave-reduced harmonics]]
-[[Category:Untwelve]]
-[[Category:Pages with internal sound examples]]