4:5:6:7: Difference between revisions

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'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh ]]), and also for the German augmented sixth chord in [[septimal meantone]].

'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh]]), and also for the German augmented sixth chord in [[septimal meantone]].

It is a [[dyadic chord]] in the [[~~odd limit|~~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 ''~~harmonic~~ 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 the ~~harmonic sixth~~ chord.

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]].

== ~~Rotations around the octave~~ ==

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.

[[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"]]

== Audio of close voicings ==

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

[[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]]

[[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]]

== Notable voicings ==

Sorted by [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively. This list is only a brief overview, see [[Voicings of 4:5:6:7]] for a more comprehensive list.

{| class="wikitable"

|+

! Voices

! [[EFR]]

! [[Kite's thoughts on hi-lo notation|Hi-lo name]]

! Special properties

|-

| rowspan="5" |4 voices

| 1:3:5:7

| hi37loR

| AOV, [[Isodifferential chord|isodifferential]]

|-

| 2:3:5:7

| hi37

| CAOV

|-

| 3:4:5:7

| lo5

|

|-

| 4:5:6:7

| basic

| Isodifferential

|-

| 4:6:7:10

| hi3

|

|}

== Related chords ==

~~Chords related to this triad~~ (5-limit ~~except where noted~~):

Melodic inversion: 1/(7:6:5:4) = [[60:70:84:105]] = 1–7/6–7/5–7/4, and its homonym 1/(12:10:8:7) = [[70:84:105:120]] = 1–6/5–3/2–12/7.

Plausible [[chord homonym|homonyms]]: none.

Notable extensions (7-limit):

* [[4:5:6:7:9]] – adds 9/4

* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord

* [[~~2:3~~:5:7]] ~~- open voicing~~

Notable restrictions:

* [[60:70:~~84:105~~]] ~~- chord inversion~~

* [[4:5:6]]

* [[4:5:6:7:9]] ~~- adds 9/4 (two octave spanning pentad)~~

* [[4:5:7]]

* [[12:14:~~18:21~~]] ~~- substitutes 5/4 with 7/6~~

* [[4:6:7]]

* [[5:6:7]]

[[Category:Dominant seventh chords|#]]

[[Category:German sixth chords|#]]

@@ Line 1: / Line 1: @@
 {{Infobox Chord|4:5:6:7|ColorName=yo zo-7 or y,z7, har-7 or h7}}
 {{Wikipedia|Harmonic seventh chord}}
-'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh ]]), and also for the German augmented sixth chord in [[septimal meantone]].
+'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh]]), and also for the German augmented sixth chord in [[septimal meantone]].
-It is a [[dyadic chord]] in the [[odd limit|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 ''harmonic 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 the harmonic sixth chord.
+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]].
-== Rotations around the octave ==
+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.
-[[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"]]
+{{chord edo approximation}}
-[[Category:Dominant seventh chords|#]]
-[[File:SculpEufaDem6-7-8-10-onD.mp3|none|thumb|6:7:8:10 "2nd inversion"]]
+== Audio of close voicings ==
-[[File:SculpEufaDem7-8-10-12-onD.mp3|none|thumb|7:8:10:12 "3rd inversion"]]
+[[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]]
+[[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]]
+== Notable voicings ==
+Sorted by [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively. This list is only a brief overview, see [[Voicings of 4:5:6:7]] for a more comprehensive list.
+{| class="wikitable"
+|+
+! Voices
+! [[EFR]]
+! [[Kite's thoughts on hi-lo notation|Hi-lo name]]
+! Special properties
+|-
+| rowspan="5" |4 voices
+| 1:3:5:7
+| hi37loR
+| AOV, [[Isodifferential chord|isodifferential]]
+|-
+| 2:3:5:7
+| hi37
+| CAOV
+|-
+| 3:4:5:7
+| lo5
+|
+|-
+| 4:5:6:7
+| basic
+| Isodifferential
+|-
+| 4:6:7:10
+| hi3
+|
+|}
 == Related chords ==
-Chords related to this triad (5-limit except where noted):
+Melodic inversion: 1/(7:6:5:4) = [[60:70:84:105]] = 1–7/6–7/5–7/4, and its homonym 1/(12:10:8:7) = [[70:84:105:120]] = 1–6/5–3/2–12/7.
+Plausible [[chord homonym|homonyms]]: none.
+Notable extensions (7-limit):
+* [[4:5:6:7:9]] – adds 9/4
+* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord
-* [[2:3:5:7]] - open voicing
+Notable restrictions:
-* [[60:70:84:105]] - chord inversion
+* [[4:5:6]]
-* [[4:5:6:7:9]] - adds 9/4 (two octave spanning pentad)
+* [[4:5:7]]
-* [[12:14:18:21]] - substitutes 5/4 with 7/6<!-- 1-digit first number -->
+* [[4:6:7]]
+* [[5:6:7]]
+[[Category:Dominant seventh chords|#]]
 [[Category:German sixth chords|#]] <!-- 1-digit first number -->