4:5:6:7: Difference between revisions

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'''4:5:6:7''', the ''harmonic seventh chord'', is a [[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 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 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.

[[Category:Dominant seventh chords|#]]

[[Category:German sixth chords|#]]

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 '''4:5:6:7''', the ''harmonic seventh chord'', is a [[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 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 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.
 [[Category:Dominant seventh chords|#]] <!-- 1-digit first number -->
 [[Category:German sixth chords|#]] <!-- 1-digit first number -->