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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]]. | 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 [[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. | |||
{{chord edo approximation}} | |||
== Audio of close voicings == | == Audio of close voicings == | ||
[[File:SculpEufaDem4-5-6-7-onD.mp3|none|thumb|4:5:6:7, Root position]] | [[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: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: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]] | ||
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| 4:5:6:7 | | 4:5:6:7 | ||
| | | basic | ||
| Isodifferential | | Isodifferential | ||
|- | |- | ||
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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. | 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| | Plausible [[chord homonym|homonyms]]: none. | ||
Notable extensions (7-limit): | Notable extensions (7-limit): | ||
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* [[5:6:7]] | * [[5:6:7]] | ||
[[Category:Dominant seventh chords|#]] | |||
[[Category:German sixth chords|#]] <!-- 1-digit first number --> | [[Category:German sixth chords|#]] <!-- 1-digit first number --> | ||