Talk:Fifth complement: Difference between revisions

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== Naming and origin ==

Oh is it really me who coined this term? By analogy of octave complement and in the desire to contrast major and minor keys, the concept should date back to classical era. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:38, 8 September 2020 (UTC)

: It's possible that this term existed before. But I don't remember that I heard or read of it. I also searched the web for it, no success so far. I admit that it's not such a huge step but this is typical for retrospection. The fifth is absolutely important for classical Western music but there is no fifth equivalence ... :) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:35, 8 September 2020 (UTC)

== Eleventh complement ==

The fifth complement is only applicable to intervals that are smaller than the fifth. Their [[octave complement]]s don't have an equivalent. Because the octave complement can also be interpreted as mirroring on the [[unison]] axis, the [[wikipedia:multiplicative inverse|multiplicative inverse]] of an interval can be taken (turning upward into downward intervals). Here we find the perfect downward fifth (2/3) which is octave-reduced into the fourth (<code>(2/3) * ([[2/1]]) → [[4/3]]</code>). The perfect eleventh ([[FJS]]:'''P11''', [[8/3]]) shares the same interval class but has the advantage that octave-reduction is already included if it is used as the completion target for intervals greater than [[3/2]] (see for example <code>[[8/3]]) / ([[5/3]]) → ([[8/5]]</code>). That's why I suggest to add the [[eleventh complement]] to the concept of [[fifth complement]]. In may opinion both should be described in the same article (preferably '''Fifth complement''') with a [[Help:redirect|redirect]] added to the '''Eleventh complement''' lemma. As a consequence "normal" interval pages tend to build link rings of four like this <ref>'''Legend''' a, b, c, d: intervals c8: octave complement c5: fifth complement c11: eleventh complement</ref>:

a ↔c8 b ↔c5 c ↔c8 d ↔c11 a

--[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:42, 29 September 2020 (UTC)

: Maybe an image would make the relations much more obvious but I currently don't have the time to create it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:47, 29 September 2020 (UTC)

: I see the point, but this is just one of the directions in looking for harmonic resources. It doesn't make much sense to those who prefer tritave complements to fifths complements. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:06, 30 September 2020 (UTC)

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+__TOC__
+== Naming and origin ==
 Oh is it really me who coined this term? By analogy of octave complement and in the desire to contrast major and minor keys, the concept should date back to classical era. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:38, 8 September 2020 (UTC)
 : It's possible that this term existed before. But I don't remember that I heard or read of it. I also searched the web for it, no success so far. I admit that it's not such a huge step but this is typical for retrospection. The fifth is absolutely important for classical Western music but there is no fifth equivalence ... :) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:35, 8 September 2020 (UTC)
+== Eleventh complement ==
+The fifth complement is only applicable to intervals that are smaller than the fifth. Their [[octave complement]]s don't have an equivalent. Because the octave complement can also be interpreted as mirroring on the [[unison]] axis, the [[wikipedia:multiplicative inverse|multiplicative inverse]] of an interval can be taken (turning upward into downward intervals). Here we find the perfect downward fifth (2/3) which is octave-reduced into the fourth (<code>(2/3) * ([[2/1]]) &rarr; [[4/3]]</code>). The perfect eleventh ([[FJS]]:'''P11''', [[8/3]]) shares the same interval class but has the advantage that octave-reduction is already included if it is used as the completion target for intervals greater than [[3/2]] (see for example <code>[[8/3]]) / ([[5/3]]) &rarr; ([[8/5]]</code>). That's why I suggest to add the [[eleventh complement]] to the concept of [[fifth complement]]. In may opinion both should be described in the same article (preferably '''Fifth complement''') with a [[Help:redirect|redirect]] added to the '''Eleventh complement''' lemma. As a consequence "normal" interval pages tend to build link rings of four like this <ref><small><u>'''Legend'''</u> <br> a, b, c, d: intervals <br> c8: octave complement <br> c5: fifth complement <br> c11: eleventh complement</small></ref>:
+ a &harr;<sup>c8</sup> b &harr;<sup>c5</sup> c &harr;<sup>c8</sup> d &harr;<sup>c11</sup> a
+<references/>
+--[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:42, 29 September 2020 (UTC)
+: Maybe an image would make the relations much more obvious but I currently don't have the time to create it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:47, 29 September 2020 (UTC)
+: I see the point, but this is just one of the directions in looking for harmonic resources. It doesn't make much sense to those who prefer tritave complements to fifths complements. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:06, 30 September 2020 (UTC)