16/11

Interval information

Ratio	16/11
Factorization	24 × 11-1
Monzo	[4 0 0 0 -1⟩
Size in cents	648.6821¢
Names	undecimal subfifth, undecimal semidiminished fifth, subharmonic semidiminished fifth, Axirabian paraminor fifth, just paraminor fifth, undecimal minor fifth
Color name	1u5, lu 5th
FJS name	[math]\displaystyle{ \text{P5}_{11} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	7.45943
Weil height (log2 max(n, d))	8
Wilson height (sopfr(nd))	19
[sound info]
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Major fourth and minor fifth

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 version of the Pythagorean diatonic generator, therefore may be called the subharmonic/undecimal semidiminished fifth

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.

Terminology

The naming pattern from undecimal neutral third and undecimal neutral second and their octave-complements can be rigorously generalized and results in the somewhat unconventional subharmonic/undecimal neutral fifth. 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. 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 also

• 11/8 – its octave complement
• 33/32 – its fifth complement
• Gallery of just intervals
• Iceface tuning