German sixth chord: Difference between revisions

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simultaneously represents both [[72:90:108:125]] (with steps 5/4, 6/5, and [[125/108]]) and [[128:160:192:225]] (with steps 5/4, 6/5, and [[75/64]]).

However, in the historically prevalent [[quarter-comma meantone]], the augmented ~~seventh~~ is tuned only a few cents shy of a just [[7/4]], so the meantone German sixth chord can be considered to approximate the ''harmonic seventh chord'' as in [[septimal meantone]]:

However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], so the meantone German sixth chord can be considered to approximate the ''harmonic seventh chord'' as in [[septimal meantone]]:

* (~~Meantone~~) 1 – 5/4 – 3/2 – 7/4

* (Septimal meantone) 1 – 5/4 – 3/2 – 7/4

representing [[4:5:6:7]] (with steps 5/4, 6/5, and 7/6).

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In the [[5-limit]]:

* [[128:160:192:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted on ♭VI in the [[duodene]].

* [[128:160:192:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]].

[[Category:Just intonation chords]]

[[Category:~~Tetrads~~]]

[[Category:German sixth chords| ]]

@@ Line 11: / Line 11: @@
 simultaneously represents both [[72:90:108:125]] (with steps 5/4, 6/5, and [[125/108]]) and [[128:160:192:225]] (with steps 5/4, 6/5, and [[75/64]]).
-However, in the historically prevalent [[quarter-comma meantone]], the augmented seventh is tuned only a few cents shy of a just [[7/4]], so the meantone German sixth chord can be considered to approximate the ''harmonic seventh chord'' as in [[septimal meantone]]:
+However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], so the meantone German sixth chord can be considered to approximate the ''harmonic seventh chord'' as in [[septimal meantone]]:
-* (Meantone) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;3/2&thinsp;–&thinsp;7/4
+* (Septimal meantone) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;3/2&thinsp;–&thinsp;7/4
 representing [[4:5:6:7]] (with steps 5/4, 6/5, and 7/6).
@@ Line 22: / Line 22: @@
 In the [[5-limit]]:
-* [[128:160:192:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted on ♭VI in the [[duodene]].
+* [[128:160:192:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]].
 [[Category:Just intonation chords]]
-[[Category:Tetrads]]
+[[Category:German sixth chords| ]] <!-- main article -->