4:5:6:7: Difference between revisions

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Added voicings and rotations
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[[File:SculpEufaDem6-7-8-10-onD.mp3|none|thumb|6:7:8:10 "2nd 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"]]
[[File:SculpEufaDem7-8-10-12-onD.mp3|none|thumb|7:8:10:12 "3rd inversion"]]
== Voicings and rotations around two octaves ==
{| class="wikitable sortable" style="text-align:center;"
|+
! style="width:120px;" {{diagonal split header|Rotation|Voicing}}
! style="width:120px;" | Root
! style="width:120px;" | '3
! style="width:120px;" | '5
! style="width:120px;" | '7
! style="width:120px;" | '3'5
! style="width:120px;" | '3'7
! style="width:120px;" | '''<nowiki/>'5'7'''
! style="width:120px;" | '3'5'7
|-
! style="width:120px;" | On 1
| data-sort-value="004-005-006-007" | ''4:5:6:7''
| data-sort-value="004-005-007-012" | 4:5:7:12
| data-sort-value="004-006-007-010" | 4:6:7:10
| data-sort-value="004-005-006-014" | 4:5:6:14
| data-sort-value="004-007-010-012" | 4:7:10:12
| data-sort-value="004-005-012-014" | 4:5:12:14
| data-sort-value="002-003-005-007" | 2:3:5:7
| data-sort-value="002-005-006-007" | 2:5:6:7
|-
! style="width:120px;" | On 3
| data-sort-value="006-007-016-020" | 6:7:16:20
| data-sort-value="003-004-005-007" | 3:4:5:7
| data-sort-value="006-007-010-016" | 6:7:10:16
| data-sort-value="003-007-008-010" | 3:7:8:10
| data-sort-value="003-004-007-010" | 3:4:7:10
| data-sort-value="006-007-008-010" | ''6:7:8:10''
| data-sort-value="003-005-007-008" | 3:5:7:8
| data-sort-value="006-007-008-020" | 6:7:8:20
|-
! style="width:120px;" | On 5
| data-sort-value="005-006-007-016" | 5:6:7:16
| data-sort-value="005-007-012-016" | 5:7:12:16
| data-sort-value="005-008-012-014" | 5:8:12:14
| data-sort-value="005-006-014-016" | 5:6:14:16
| data-sort-value="005-006-008-014" | 5:6:8:14
| data-sort-value="005-012-014-016" | 5:12:14:16
| data-sort-value="005-007-008-012" | 5:7:8:12
| data-sort-value="005-006-007-008" | ''5:6:7:8''
|-
! style="width:120px;" | On 7
| data-sort-value="007-016-020-024" | 7:16:20:24
| data-sort-value="007-012-016-020" | 7:12:16:20
| data-sort-value="007-010-016-024" | 7:10:16:24
| data-sort-value="007-008-010-012" | ''7:8:10:12''
| data-sort-value="007-010-012-016" | 7:10:12:16
| data-sort-value="007-008-010-024" | 7:8:10:24
| data-sort-value="007-008-012-020" | 7:8:12:20
| data-sort-value="007-008-020-024" | 7:8:20:24
|}
Enumerations in italics map to an existing octave-reduced rotation.


== Related chords ==
== Related chords ==
Chords related to this triad (7-limit except where noted):
Chords related to this triad (7-limit except where noted):


* [[2:3:5:7]] - open voicing
* [[60:70:84:105]] - chord inversion
* [[60:70:84:105]] - chord inversion
* [[4:5:6:7:9]] - adds 9/4 (two octave spanning pentad)
* [[4:5:6:7:9]] - adds 9/4 (two octave spanning pentad)

Revision as of 13:31, 10 November 2025

Chord information
Harmonics 4:5:6:7
Subharmonics 1/(105:84:70:60)
Intervals from root 1/1–5/4–3/2–7/4
Cents from root 0¢–386¢–702¢–969¢
Step intervals 5/4, 6/5, 7/6
Step cents 386¢, 316¢, 267¢
Color names yo zo-7 or y,z7
har-7 or h7
Prime limit 7
Genus 3⋅5⋅7 (105)
Intervallic odd limit 7
Otonal odd limit 7
Utonal odd limit 105
Consistent edos (d ≥ 2) 31edo*, 41edo*, 68edo*, 72edo*
English Wikipedia has an article on:

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 7-odd-limit, with its most complex interval a 7/5 tritone. It is the 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 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 the subharmonic sixth chord.

Rotations around the octave

4:5:6:7 "Root position"
5:6:7:8 "1st inversion"
6:7:8:10 "2nd inversion"
7:8:10:12 "3rd inversion"

Voicings and rotations around two octaves

Voicing
Rotation
 Root '3 '5 '7 '3'5 '3'7 '5'7 '3'5'7
On 1 4:5:6:7 4:5:7:12 4:6:7:10 4:5:6:14 4:7:10:12 4:5:12:14 2:3:5:7 2:5:6:7
On 3 6:7:16:20 3:4:5:7 6:7:10:16 3:7:8:10 3:4:7:10 6:7:8:10 3:5:7:8 6:7:8:20
On 5 5:6:7:16 5:7:12:16 5:8:12:14 5:6:14:16 5:6:8:14 5:12:14:16 5:7:8:12 5:6:7:8
On 7 7:16:20:24 7:12:16:20 7:10:16:24 7:8:10:12 7:10:12:16 7:8:10:24 7:8:12:20 7:8:20:24

Enumerations in italics map to an existing octave-reduced rotation.

Related chords

Chords related to this triad (7-limit except where noted):

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