4:5:7: Difference between revisions

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+ a possible name, + link to inverse
Note the utility of 4:7:10
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'''4:5:7''', the ''fifthless harmonic seventh chord'', is a [[7-limit]] chord found as a subset of the harmonic seventh chord, [[4:5:6:7]]. It is used as a tuning target for the [[Italian sixth chord|Italian augmented sixth chord]] in [[septimal meantone]].
'''4:5:7''', the ''fifthless harmonic seventh chord'', is a [[7-limit]] chord found as a subset of the harmonic seventh chord, [[4:5:6:7]]. It is used as a tuning target for the [[Italian sixth chord|Italian augmented sixth chord]] in [[septimal meantone]].
The open voicing '''4:7:10''' may be used as a fundamental consonance of the [[2.5.7 subgroup]]. It inverts to 14:20:35 with the middle voice contrasting by [[49/40]].


== Rotations around the octave ==
== Rotations around the octave ==
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== Related chords ==
== Related chords ==
Chords related to this triad (5-limit except where noted):  
Chords related to this triad (5-limit except where noted):  
* 4:7:10 – open voicing
* [[4:6:7]] – no-fives version
* [[4:6:7]] – no-fives version
* [[4:5:6:7]] – full tetrad
* [[4:5:6:7]] – full tetrad

Revision as of 08:13, 17 March 2026

Chord information
Harmonics 4:5:7
Subharmonics 1/(35:28:20)
Intervals from root 1/15/47/4
Cents from root 386¢969¢
Step intervals 5/4, 7/5
Step cents 386¢, 583¢
Color names yo zo-7 no-5 or y,z7no5
har-7 no-5 or h7no5
Prime limit 7
Genus 57 (35)
Intervallic odd limit 7
Otonal odd limit 7
Utonal odd limit 35
Consistent edos (d ≥ 2) 6edo*, 10edo*, 16edo*, 21edo*, …

4:5:7, the fifthless harmonic seventh chord, is a 7-limit chord found as a subset of the harmonic seventh chord, 4:5:6:7. It is used as a tuning target for the Italian augmented sixth chord in septimal meantone.

The open voicing 4:7:10 may be used as a fundamental consonance of the 2.5.7 subgroup. It inverts to 14:20:35 with the middle voice contrasting by 49/40.

Rotations around the octave

4:5:7 "Root position"
5:7:8 "1st inversion"
7:8:10 "2nd inversion"

Related chords

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