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 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 (log_{2} nd) | 13.9189 |
Weil height (log_{2} 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 ¢.