Half-diminished seventh chord: Difference between revisions

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In the [[7-limit]]:

* [[5:6:7:9]]

* [[5:6:7:9]] is a highly [[concordant]] 7-limit interpretation of the half-diminished seventh, found in the [[Ringer_scale|Ringer 5]] scale and [[Euler-Fokker genus|genus]]32{{dot}}5{{dot}}7, and tempered together with 45:54:64:81 in archytas temperament.

* [[20:24:28:35]]

* [[20:24:28:35]] is a [[condissonant]] chord found in genus 3{{dot}}5{{dot}}7, and tempered together with 45:54:64:80 in archytas temperament.

* [[35:42:50:63]]

* [[35:42:50:63]] is a [[condissonant]] chord found in genus 32{{dot}}52{{dot}}7, and tempered together with 25:30:36:45 in starling temperament.

In the [[5-limit]]:

* [[25:30:36:45]]

* [[25:30:36:45]] is found on iiiø7 ({{Frac|5|4}}) and viø7 ({{Frac|5|3}}) in the [[duodene]].

* [[45:54:64:80]]

* [[45:54:64:80]] found on viiø7 ({{Frac|15|8}}) in Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common 5-limit diatonic. It is also found on Vø7 ({{Frac|3|2}}) in the [[duodene]].

* [[45:54:64:81]], another [[preimage]] of the meantone half-diminished seventh chord, is found in [[Euler-Fokker genus|genus]] 34{{dot}}5, and tempered together with 5:6:7:9 in archytas temperament.

* [[135:160:192:240]]

* [[135:160:192:240]] is found on iiø7 ({{Frac|9|8}}) and ♯ivø7 ({{Frac|45|32}}) in the [[duodene]].

[[Category:Half-diminished seventh chords| ]]

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[[Category:9-odd-limit chords]]

[[Category:Essentially tempered chords]]

~~{{stub}}~~

@@ Line 24: / Line 24: @@
 In the [[7-limit]]:
-* [[5:6:7:9]]
+* [[5:6:7:9]] is a highly [[concordant]] 7-limit interpretation of the half-diminished seventh, found in the [[Ringer_scale|Ringer 5]] scale and [[Euler-Fokker genus|genus]]3<sup>2</sup>{{dot}}5{{dot}}7, and tempered together with 45:54:64:81 in archytas temperament.
-* [[20:24:28:35]]
+* [[20:24:28:35]] is a [[condissonant]] chord found in genus 3{{dot}}5{{dot}}7, and tempered together with 45:54:64:80 in archytas temperament.
-* [[35:42:50:63]]
+* [[35:42:50:63]] is a [[condissonant]] chord found in genus 3<sup>2</sup>{{dot}}5<sup>2</sup>{{dot}}7, and tempered together with 25:30:36:45 in starling temperament.
 In the [[5-limit]]:
-* [[25:30:36:45]]
+* [[25:30:36:45]] is found on iii<sup>ø7</sup> ({{Frac|5|4}}) and vi<sup>ø7</sup> ({{Frac|5|3}}) in the [[duodene]].
-* [[45:54:64:80]]
+* [[45:54:64:80]] found on vii<sup>ø7</sup> ({{Frac|15|8}}) in Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common 5-limit diatonic. It is also found on V<sup>ø7</sup> ({{Frac|3|2}}) in the [[duodene]].
 * [[45:54:64:81]], another [[preimage]] of the meantone half-diminished seventh chord, is found in [[Euler-Fokker genus|genus]] 3<sup>4</sup>{{dot}}5, and tempered together with 5:6:7:9 in archytas temperament.
-* [[135:160:192:240]]
+* [[135:160:192:240]] is found on ii<sup>ø7</sup> ({{Frac|9|8}}) and ♯iv<sup>ø7</sup> ({{Frac|45|32}}) in the [[duodene]].
 [[Category:Half-diminished seventh chords| ]]
@@ Line 39: / Line 39: @@
 [[Category:9-odd-limit chords]]
 [[Category:Essentially tempered chords]]
-{{stub}}