11/9: Difference between revisions

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~~'''~~11/9~~'''~~

{{Infobox Interval

|0 -2 0 0 1~~>~~

| Icon =

| Ratio = 11/9

| Monzo = 0 -2 0 0 1

| Cents = 347.40794

| Name = undecimal neutral third

| Sound = jid_11_9_pluck_adu_dr220.mp3

}}

347.~~40794 cents~~

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 persony (others include [[16/13]], [[27/22]], [[49/40]] and [[60/49]]). It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]].

[[~~File:jid_11_9_pluck_adu_dr220.mp3~~]] [[~~:File:jid_11_9_pluck_adu_dr220~~.~~mp3~~|~~sound sample~~]]

In the 11-limit theyxad 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. Persony 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 [[~~11-limit|11-limit]] [[Just_intonation|~~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 persony (others include [[16/13|16/13]], [[27/22|27/22]], [[49/40|49/40]] and [[60/49|60/49]]). It is nearly halfway between two intervals of [[12edo|12edo]], implying that it is both very xenharmonic and well-represented in [[24edo|24edo]].

:''See also [[Gallery of Just Intervals]]''

In the 11-limit theyxad 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. Persony temperaments, including [[17edo|17edo]], [[24edo|24edo]], [[31edo|31edo]], [[41edo|41edo]], [[58edo|58edo]], [[72edo|72edo]], [[130edo|130edo]], [[202edo|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]].

[[Category:11-limit]]

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~ [[Category:11-limit]]

[[Category:interval]]

[[Category:neutral_3rd]]

@@ Line 1: / Line 1: @@
-'''11/9'''
+{{Infobox Interval
-|0 -2 0 0 1&gt;
+| Icon =
+| Ratio = 11/9
+| Monzo = 0 -2 0 0 1
+| Cents = 347.40794
+| Name = undecimal neutral third
+| Sound = jid_11_9_pluck_adu_dr220.mp3
+}}
-.40794 cents
+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 persony (others include [[16/13]], [[27/22]], [[49/40]] and [[60/49]]). It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]].
-[[File:jid_11_9_pluck_adu_dr220.mp3]] [[:File:jid_11_9_pluck_adu_dr220.mp3|sound sample]]
+In the 11-limit theyxad 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. Persony 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 [[11-limit|11-limit]] [[Just_intonation|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 persony (others include [[16/13|16/13]], [[27/22|27/22]], [[49/40|49/40]] and [[60/49|60/49]]). It is nearly halfway between two intervals of [[12edo|12edo]], implying that it is both very xenharmonic and well-represented in [[24edo|24edo]].
+:''See also [[Gallery of Just Intervals]]''
-In the 11-limit theyxad 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. Persony temperaments, including [[17edo|17edo]], [[24edo|24edo]], [[31edo|31edo]], [[41edo|41edo]], [[58edo|58edo]], [[72edo|72edo]], [[130edo|130edo]], [[202edo|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]].
+[[Category:11-limit]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:11-limit]]
 [[Category:interval]]
 [[Category:neutral_3rd]]