12/11
Ratio | 12/11 |
Factorization | 2^{2} × 3 × 11^{-1} |
Monzo | [2 1 0 0 -1⟩ |
Size in cents | 150.63706¢ |
Names | undecimal neutral second, Alpharabian tendoneutral second |
Color name | 1u2, lu 2nd |
FJS name | [math]\text{M2}_{11}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 7.04439 |
Weil height (log_{2} max(n, d)) | 7.16993 |
Wilson height (sopfr (nd)) | 18 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.24375 bits |
[sound info] | |
open this interval in xen-calc |
12/11, the undecimal neutral second or (lesser) neutral second, is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In just intonation it is represented by the superparticular ratio 12/11, and is about 150.6 cents large. One step of 8edo is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^{8}/2 = [15 8 0 0 -8⟩. It follows that EDOs which are multiples of 8, such as 16edo and 24edo, will also represent this interval well. In Alpharabian tuning it is known as the Alpharabian tendoneutral second.
12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include 15edo, 22edo, 31edo, orwell, porcupine, mohajira, valentine, etc.