16/11: Difference between revisions

(8 intermediate revisions by 5 users not shown)

Line 1:

{{Infobox Interval

~~| Icon =~~

| Name = undecimal subfifth, undecimal semidiminished fifth, subharmonic semidiminished fifth, Axirabian paraminor fifth, just paraminor fifth, undecimal minor fifth

~~| Ratio = 16/11~~

~~| Monzo = 4 0 0 0 -1~~

~~| Cents = 648.68206~~

| Name = undecimal subfifth, ~~ minor~~ fifth, ~~ ~~Axirabian paraminor fifth, ~~ ~~just paraminor fifth

| Color name = 1u5, lu 5th

~~| FJS name = P511~~

| Sound = jid_16_11_pluck_adu_dr220.mp3

}}

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 ~~it's~~ own right being like neither a perfect fifth nor the tritone. ~~Accordingly, this~~ interval~~, or rather the tempered version found in~~ [[~~24edo~~]], ~~was dubbed~~ the '''~~minor fifth~~'~~'' by~~ [[~~Ivan Wyschnegradsky~~]]~~, and, given its connections to~~ [[~~Alpharabian tuning~~]], ~~it can also~~ be ~~somewhat similarly dubbed~~ the '''~~Axirabian paraminor fifth''' or even the '''just paraminor~~ 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.

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'''.

== See also ==

Line 20:

* [[Iceface tuning]]

[[Category:~~11-limit]]~~

[[Category:Fifth]]

~~[[Category:Interval ratio]]~~

~~[[Category:Just interval~~]]

[[Category:Subfifth]]

~~[[Category:Fifth]]~~

[[Category:Alpharabian]]

[[Category:Over-11]]

[[Category:Over-11 intervals]]

~~[[Category:Octave-reduced subharmonics]]~~

~~[[Category:Todo:expand~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = undecimal subfifth, undecimal semidiminished fifth, subharmonic semidiminished fifth, Axirabian paraminor fifth, just paraminor fifth, undecimal minor fifth
-| Ratio = 16/11
-| Monzo = 4 0 0 0 -1
-| Cents = 648.68206
-| Name = undecimal subfifth, <br>minor fifth, <br>Axirabian paraminor fifth, <br>just paraminor fifth
 | Color name = 1u5, lu 5th
-| FJS name = P5<sub>11</sub>
 | 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¢. 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 it's own right being like neither a perfect fifth nor the tritone.  Accordingly, this interval, or rather the tempered version found in [[24edo]], was dubbed the '''minor fifth''' by [[Ivan Wyschnegradsky]], and, given its connections to [[Alpharabian tuning]], it can also be somewhat similarly dubbed the '''Axirabian paraminor fifth''' or even the '''just paraminor 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.
+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'''.
 == See also ==
@@ Line 20: / Line 20: @@
 * [[Iceface tuning]]
-[[Category:11-limit]]
+[[Category:Fifth]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
 [[Category:Subfifth]]
-[[Category:Fifth]]
 [[Category:Alpharabian]]
-[[Category:Over-11]]
+[[Category:Over-11 intervals]]
-[[Category:Octave-reduced subharmonics]]
-[[Category:Todo:expand]]