128/121: Difference between revisions

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'''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. ~~Despite being nearly the size of a~~ [[12edo]] ~~semitone~~, it is tempered out in 12edo~~, which~~ maps ~~both~~ [[11/8]] ~~and~~ [[16/11]] to ~~the half octave period in its patent val~~.

'''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 ==

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[[Category:Semitone]]

[[Category:Alpharabian]]

[[Category:Commas named after polymaths]]

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

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-'''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. Despite being nearly the size of a [[12edo]] semitone, it is tempered out in 12edo, which maps both [[11/8]] and [[16/11]] to the half octave period in its patent val.
+'''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 ==
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 [[Category:Semitone]]
 [[Category:Alpharabian]]
+[[Category:Commas named after polymaths]]
+[[Category:Commas named after their interval size]]