128/121: Difference between revisions

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

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'''128/121''', the '''Axirabian limma''', otherwise known as both the '''Axirabian diatonic semitone''' and the '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.4 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. 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 Alpharabian 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 it's patent val.

'''128/121''', the '''Axirabian limma''', otherwise known as both the '''Axirabian diatonic semitone''' and the '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.4 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. 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 Alpharabian 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 it's patent val.

== See also ==

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 | Sound = Ji-128-121-csound-foscil-220hz.mp3
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-'''128/121''', the '''Axirabian limma''', otherwise known as both the '''Axirabian diatonic semitone''' and the '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.4 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.  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 Alpharabian 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 it's patent val.
+'''128/121''', the '''Axirabian limma''', otherwise known as both the '''Axirabian diatonic semitone''' and the '''octave-reduced 121st subharmonic''', is an [[11-limit]] semitone with a value of roughly 97.4 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.  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 Alpharabian 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 it's patent val.
 == See also ==