16/11
| Ratio | 16/11 |
| Factorization | 24 × 11-1 |
| Monzo | [4 0 0 0 -1⟩ |
| Size in cents | 648.68206¢ |
| Names | undecimal subfifth, undecimal neutral fifth, subharmonic neutral fifth, subharmonic semidiminished fifth, subharmonic semiperfect fifth, Axirabian paraminor fifth, just paraminor fifth, undecimal minor fifth |
| Color name | 1u5, lu 5th |
| FJS name | [math]\text{P5}_{11}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 7.45943 |
| Weil height (log2 max(n, d)) | 8 |
| Wilson height (sopfr (nd)) | 19 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.61194 bits |
[sound info] | |
| open this interval in xen-calc | |
In 11-limit just intonation, 16/11 is an undecimal subfifth measuring about 648.7¢. It is the inversion of 11/8, the undecimal superfourth. While the name "undecimal subfifth" suggests some variation of a perfect fifth, the subfifth is generally considered an interval in its own right being like neither a perfect fifth nor the tritone. This interval is close (~3 ¢) to exactly between a perfect fifth and diminished fifth, the latter of which is the diminished (a.k.a. imperfect) version of the Pythagorean diatonic generator, therefore may be called the subharmonic semidiminished/semiperfect fifth, or subharmonic/undecimal neutral fifth if you prefer to generalise the naming pattern from undecimal neutral third and undecimal neutral second and harmonic neutral fourth and their octave-complements (which is also rigorous). Furthermore, given its connections to Alpharabian tuning, it can also be somewhat similarly dubbed the Axirabian paraminor fifth or even the just paraminor fifth- see the history of Aura's Ideas on Functional Harmony for explanation of the modified names. This interval has also been termed the undecimal minor fifth since the tempered version found in 24edo was dubbed the "minor fifth" by Ivan Wyschnegradsky, although this may be confusing in diatonic contexts.
The character of this interval is something very unique in that it produces a sound of overtones that resembles that of a large bell. Furthermore, the hands of a good composer, 16/11 has decent potential as the interval between the root and fifth of a chord. That said, even the best triads that utilize it in this capacity- such as 44:55:64- must be handled with some measure of care as the rather dissonant nature of this interval provides a sense of tension, albeit less so than with diminished triads.