4:5:6:7: Difference between revisions

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It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126|1–9/7–3/2–9/5]].

Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], resolving to the [[4:5:6]] chord on the tonic.

Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[16/15|15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The 15/16 can step up by 16/15 to reach [[1/1]], and the 21/16 down by [[21/20]] to reach 5/4, resolving to the [[4:5:6]] chord on the tonic.

== Audio of close voicings ==

[[File:SculpEufaDem4-5-6-7-onD.mp3|none|thumb|4:5:6:7, Root position]]

[[File:SculpEufaDem5-6-7-8-onD.mp3|none|thumb|5:6:7:8, 1st inversion]]

~~[[Category:Dominant seventh chords|#]]~~

[[File:SculpEufaDem6-7-8-10-onD.mp3|none|thumb|6:7:8:10, 2nd inversion]]

[[File:SculpEufaDem7-8-10-12-onD.mp3|none|thumb|7:8:10:12, 3rd inversion]]

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* [[5:6:7]]

[[Category:Dominant seventh chords|#]]

[[Category:German sixth chords|#]]

@@ Line 5: / Line 5: @@
 It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126|1–9/7–3/2–9/5]].
-Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], resolving to the [[4:5:6]] chord on the tonic.
+Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[16/15|15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The 15/16 can step up by 16/15 to reach [[1/1]], and the 21/16 down by [[21/20]] to reach 5/4, resolving to the [[4:5:6]] chord on the tonic.
 == Audio of close voicings ==
 [[File:SculpEufaDem4-5-6-7-onD.mp3|none|thumb|4:5:6:7, Root position]]
 [[File:SculpEufaDem5-6-7-8-onD.mp3|none|thumb|5:6:7:8, 1st inversion]]
-[[Category:Dominant seventh chords|#]]
 [[File:SculpEufaDem6-7-8-10-onD.mp3|none|thumb|6:7:8:10, 2nd inversion]]
 [[File:SculpEufaDem7-8-10-12-onD.mp3|none|thumb|7:8:10:12, 3rd inversion]]
@@ Line 61: / Line 60: @@
 * [[5:6:7]]
+[[Category:Dominant seventh chords|#]]
 [[Category:German sixth chords|#]] <!-- 1-digit first number -->