German sixth chord: Difference between revisions

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== In meantone ==

If we stick to the [[5-limit]], which traditional tonal harmony mainly concerns, the augmented sixth represents both [[125/72]] and [[225/128]]. It is treated as a rare and special dissonance, especially when used on the sixth degree. ~~However, most [[meantone]] tunings has the augmented sixth placed near [[7/4]]. In the historically-prevalent [[quarter-comma meantone]], for example, it~~ 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]]:~~

If we stick to the [[5-limit]], which traditional tonal harmony mainly concerns, the augmented sixth represents both [[125/72]] and [[225/128]]. It is treated as a rare and special dissonance, especially when used on the sixth degree. The chord is

* 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6.

* (Meantone) 1 – 5/4 – 3/2 – 125/72 with steps 5/4, 6/5, 75/64

Note the ~125/72 is simultaneously ~225/128.

However, most [[meantone]] tunings has the augmented sixth placed near [[7/4]]. In the historically-prevalent [[quarter-comma meantone]], for example, it 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]]:

* (Meantone) 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6.

== In just intonation ==

Because the German sixth chord is often built on the sixth degree of a minor scale, the [[128:160:192:225]] found on the ♭VI of the [[duodene]] is a good candidate for its interpretation in the 5-limit.

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 == In meantone ==
-If we stick to the [[5-limit]], which traditional tonal harmony mainly concerns, the augmented sixth represents both [[125/72]] and [[225/128]]. It is treated as a rare and special dissonance, especially when used on the sixth degree. However, most [[meantone]] tunings has the augmented sixth placed near [[7/4]]. In the historically-prevalent [[quarter-comma meantone]], for example, it 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]]:
+If we stick to the [[5-limit]], which traditional tonal harmony mainly concerns, the augmented sixth represents both [[125/72]] and [[225/128]]. It is treated as a rare and special dissonance, especially when used on the sixth degree. The chord is
-* 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;3/2&thinsp;–&thinsp;7/4 with steps 5/4, 6/5, 7/6.
+* (Meantone) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;3/2&thinsp;–&thinsp;125/72 with steps 5/4, 6/5, 75/64
+Note the ~125/72 is simultaneously ~225/128.
+However, most [[meantone]] tunings has the augmented sixth placed near [[7/4]]. In the historically-prevalent [[quarter-comma meantone]], for example, it 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]]:
+* (Meantone) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;3/2&thinsp;–&thinsp;7/4 with steps 5/4, 6/5, 7/6.
 == In just intonation ==
 Because the German sixth chord is often built on the sixth degree of a minor scale, the [[128:160:192:225]] found on the ♭VI of the [[duodene]] is a good candidate for its interpretation in the 5-limit.