128/121

Interval information

Ratio	128/121
Factorization	27 × 11-2
Monzo	[7 0 0 0 -2⟩
Size in cents	97.36412¢
Names	Axirabian limma, Axirabian diatonic semitone, octave-reduced 121st subharmonic
FJS name	[math]\displaystyle{ \text{M2}_{121} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	13.9189
Weil height (log2 max(n, d))	14
Wilson height (sopfr(nd))	36
[sound info]
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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 its patent val.

See also

• 121/64 – its octave complement