11/9: Difference between revisions
Changing some of the nomenclature concerning Alpharabian tuning |
m Misc. edits, categories |
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{{Infobox Interval | {{Infobox Interval | ||
| 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]] [[ | 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 | * [[Gallery of just intervals]] | ||
* [[Iceface tuning]] | * [[Iceface tuning]] | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category: | [[Category:Third]] | ||
[[Category:Neutral third]] | [[Category:Neutral third]] | ||
[[Category:Alpharabian]] | [[Category:Alpharabian]] | ||