16/11: Difference between revisions

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{{Infobox Interval

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

| Name = 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

| Sound = jid_16_11_pluck_adu_dr220.mp3

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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. ~~Accordingly~~, ~~this interval can also~~ be called the '''undecimal ~~minor~~ fifth''' ~~since~~ the ~~tempered version found in~~ [[~~24edo~~]]~~, was dubbed the "minor fifth" by~~ [[~~Ivan Wyschnegradsky~~]]. 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 [[User:Aura/Aura's Ideas on Functional Harmony #History|the history of Aura's Ideas on Functional Harmony]] for explanation of the modified names.

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{{cent}}) to exactly between a [[3/2|perfect fifth]] and [[1024/729|diminished fifth]], the latter of which is the ''diminished'' (a.k.a. ''imperfect'') version of the [[Pythagorean tuning|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 [[11/9|undecimal neutral third]] and [[12/11|undecimal neutral second]] and [[11/8|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 [[User:Aura/Aura's Ideas on Functional Harmony #History|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.

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 {{Infobox Interval
-| Name = undecimal subfifth, undecimal minor fifth, Axirabian paraminor fifth, just paraminor fifth
+| Name = 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
 | Sound = jid_16_11_pluck_adu_dr220.mp3
@@ Line 6: / Line 6: @@
 {{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 its own right being like neither a perfect fifth nor the tritone.  Accordingly, this interval can also be called the '''undecimal minor fifth''' since the tempered version found in [[24edo]], was dubbed the "minor fifth" by [[Ivan Wyschnegradsky]].  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 [[User:Aura/Aura's Ideas on Functional Harmony #History|the history of Aura's Ideas on Functional Harmony]] for explanation of the modified names.
+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{{cent}}) to exactly between a [[3/2|perfect fifth]] and [[1024/729|diminished fifth]], the latter of which is the ''diminished'' (a.k.a. ''imperfect'') version of the [[Pythagorean tuning|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 [[11/9|undecimal neutral third]] and [[12/11|undecimal neutral second]] and [[11/8|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 [[User:Aura/Aura's Ideas on Functional Harmony #History|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.