From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 128/121
Factorization 27 × 11-2
Monzo [7 0 0 0 -2
Size in cents 97.364115¢
Names Axirabian limma,
Axirabian diatonic semitone,
octave-reduced 121st subharmonic
Color name 1uu2, lulu 2nd
FJS name [math]\text{M2}_{11,11}[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 n⋅d) 13.9189
Weil height (max(n, d)) 128
Benedetti height (n⋅d) 15488
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.64887 bits

[sound info]
open this interval in xen-calc

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 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.

See also