11/9: Difference between revisions

Line 4:

| Monzo = 0 -2 0 0 1

| 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

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

Line 10:

}}

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]].

@@ Line 4: / Line 4: @@
 | Monzo = 0 -2 0 0 1
 | 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
 | FJS name = m3<sup>11</sup>
@@ Line 10: / Line 10: @@
 }}
-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]].