12/11

Interval information

Ratio	12/11
Factorization	22 × 3 × 11-1
Monzo	[2 1 0 0 -1⟩
Size in cents	150.6371¢
Name	undecimal neutral second
Color name	1u2, lu 2nd
FJS name	[math]\displaystyle{ \text{M2}_{11} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	7.04439
Weil height (log2 max(n, d))	7.16993
Wilson height (sopfr(nd))	18
[sound info]
Open this interval in xen-calc

The (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.

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 and valentine.