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Interval information
Ratio 128/121
Factorization 27 × 11-2
Monzo [7 0 0 0 -2
Size in cents 97.364115¢
Names Axirabian limma,
Axirabian artomean minor second,
Axirabian diatonic semitone,
octave-reduced 121st subharmonic
Color name 1uu2, lulu 2nd
FJS name [math]\text{M2}_{11,11}[/math]
Special properties reduced
Tenney height (log2 nd) 13.9189
Weil height (log2 max(n, d)) 14
Wilson height (sopfr (nd)) 36
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.29426 bits
Comma size medium

[sound info]
open this interval in xen-calc

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 ¢ tritone, which results in 16/11 also getting mapped to 600 ¢.

See also