128/121: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = Axirabian limma, Axirabian artomean minor second, Axirabian diatonic semitone, octave-reduced 121st subharmonic

~~| Ratio = 128/121~~

| Color name = 1uu2, lulu 2nd

~~| Monzo = 7 0 0 0 -2~~

~~| Cents = 97.36412~~

| Name = ~~Alpharabian~~ diatonic semitone, ~~<br>~~ octave-reduced 121st subharmonic

| Color name =

~~| FJS name = M2<sub>121</sub>~~

| Sound = Ji-128-121-csound-foscil-220hz.mp3

| Comma = yes

}}

'''128/121''', the '''~~Alpharabian~~ diatonic semitone'''~~, or~~ '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.~~36412~~ cents. ~~As the name "Alpharabian diatonic semitone" suggests, it~~ acts as the diatonic counterpart to the [[1089/1024]], with the two intervals adding up to a [[9/8]] whole tone.

'''128/121''', the '''Axirabian limma''', otherwise known as the '''Axirabian artomean minor second''', the '''Axirabian diatonic semitone''' and the '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.4 cents. It acts as the diatonic counterpart to the [[1089/1024]], with the two intervals adding up to a [[9/8]] whole tone. Furthermore its status as a diatonic semitone can be verified by the fact that just as a diatonic semitone and a chromatic semitone add up to make a whole tone, a similar pairing of quartertones- namely [[4096/3993]] and [[33/32]]- add up to 128/121. By tempering [[243/242]], the Axirabian limma can be made equal to the Pythagorean limma, allowing an 11-limit extension to standard pythagorean tuning.

In [[12edo]], it is tempered out despite being almost as large as an entire standard semitone, since 12edo's patent val maps [[11/8]] to the 600{{cent}} tritone, which results in [[16/11]] also getting mapped to 600{{cent}}.

== See also ==

* [[121/64]] – its [[octave complement]]

* [[Gallery of just intervals]]

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

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

[[Category:Semitone]]

[[Category:Alpharabian]]

[[Category:Commas named after polymaths]]

[[Category:~~Todo:add color name~~]]

[[Category:Commas named after their interval size]]

[[Category:~~Todo:expand~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = Axirabian limma, Axirabian artomean minor second, Axirabian diatonic semitone, octave-reduced 121st subharmonic
-| Ratio = 128/121
+| Color name = 1uu2, lulu 2nd
-| Monzo = 7 0 0 0 -2
-| Cents = 97.36412
-| Name = Alpharabian diatonic semitone, <br> octave-reduced 121st subharmonic
-| Color name =
-| FJS name = M2<sub>121</sub>
 | Sound = Ji-128-121-csound-foscil-220hz.mp3
+| Comma = yes
 }}
-'''128/121''', the '''Alpharabian diatonic semitone''', or '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.36412 cents.  As the name "Alpharabian diatonic semitone" suggests, it acts as the diatonic counterpart to the [[1089/1024]], with the two intervals adding up to a [[9/8]] whole tone.
+'''128/121''', the '''Axirabian limma''', otherwise known as the '''Axirabian artomean minor second''', the '''Axirabian diatonic semitone''' and the '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.4 cents.  It acts as the diatonic counterpart to the [[1089/1024]], with the two intervals adding up to a [[9/8]] whole tone.  Furthermore its status as a diatonic semitone can be verified by the fact that just as a diatonic semitone and a chromatic semitone add up to make a whole tone, a similar pairing of quartertones- namely [[4096/3993]] and [[33/32]]- add up to 128/121. By tempering [[243/242]], the Axirabian limma can be made equal to the Pythagorean limma, allowing an 11-limit extension to standard pythagorean tuning.
+In [[12edo]], it is tempered out despite being almost as large as an entire standard semitone, since 12edo's patent val maps [[11/8]] to the 600{{cent}} tritone, which results in [[16/11]] also getting mapped to 600{{cent}}.
+== See also ==
+* [[121/64]] – its [[octave complement]]
+* [[Gallery of just intervals]]
-[[Category:11-limit]]
-[[Category:Interval ratio]]
 [[Category:Semitone]]
 [[Category:Alpharabian]]
+[[Category:Commas named after polymaths]]
-[[Category:Todo:add color name]]
+[[Category:Commas named after their interval size]]
-[[Category:Todo:expand]]