German sixth chord: Difference between revisions
Per discussion, list the 5-limit chord separately. |
m →In meantone: 75/64~125/108 could be useful too |
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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 | 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 | ||
* (Meantone) 1 – 5/4 – 3/2 – 125/72 with steps 5/4, 6/5, 75/64 | * (Meantone) 1 – 5/4 – 3/2 – 125/72 with steps 5/4, 6/5, 75/64. | ||
Note the ~125/72 is simultaneously ~225/128. | Note the ~125/72 is simultaneously ~225/128, and the ~75/64 is simultaneously ~125/108. | ||
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]]: | 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]]: | ||