128/121
Ratio | 128/121 |
Factorization | 2^{7} × 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 (log_{2} 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.