16/11: Difference between revisions
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{{Infobox Interval | |||
| Name = undecimal subfifth, undecimal semidiminished fifth, subharmonic semidiminished fifth, Axirabian paraminor fifth, just paraminor fifth, undecimal minor fifth | |||
| Color name = 1u5, lu 5th | |||
| Sound = jid_16_11_pluck_adu_dr220.mp3 | |||
}} | |||
{{Wikipedia|Major fourth and minor fifth}} | |||
In [[11-limit]] [[just intonation]], '''16/11''' is an '''undecimal subfifth''' measuring about 648.7{{cent}}. 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{{cent}}) to exactly between a [[3/2|perfect fifth]] and [[1024/729|diminished fifth]], the latter of which is the ''diminished'' version of the [[Pythagorean tuning|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 [[11/9|undecimal neutral third]] and [[12/11|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'''. | |||
== Approximation == | |||
{{Interval edo approximation|16/11}} | |||
== See also == | |||
* [[11/8]] – its [[octave complement]] | |||
* [[33/32]] – its [[fifth complement]] | |||
* [[Gallery of just intervals]] | |||
* [[Iceface tuning]] | |||
[[Category:Fifth]] | |||
[[Category:Subfifth]] | |||
[[Category:Alpharabian]] | |||
[[Category:Over-11 intervals]] | |||
Latest revision as of 13:06, 3 November 2025
| Interval information |
undecimal semidiminished fifth,
subharmonic semidiminished fifth,
Axirabian paraminor fifth,
just paraminor fifth,
undecimal minor fifth
reduced subharmonic
[sound info]
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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 1\2 | 600.00 | -48.68 | -8.11 |
| 11 | 6\11 | 654.55 | +5.86 | +5.37 |
| 13 | 7\13 | 646.15 | -2.53 | -2.74 |
| 24 | 13\24 | 650.00 | +1.32 | +2.64 |
| 26 | 14\26 | 646.15 | -2.53 | -5.48 |
| 35 | 19\35 | 651.43 | +2.75 | +8.01 |
| 37 | 20\37 | 648.65 | -0.03 | -0.10 |
| 39 | 21\39 | 646.15 | -2.53 | -8.22 |
| 48 | 26\48 | 650.00 | +1.32 | +5.27 |
| 50 | 27\50 | 648.00 | -0.68 | -2.84 |
| 61 | 33\61 | 649.18 | +0.50 | +2.53 |
| 63 | 34\63 | 647.62 | -1.06 | -5.58 |
| 72 | 39\72 | 650.00 | +1.32 | +7.91 |
| 74 | 40\74 | 648.65 | -0.03 | -0.21 |
| 76 | 41\76 | 647.37 | -1.31 | -8.32 |