French sixth chord: Difference between revisions
add links and categories for meantone chords |
→In temperaments: clarify conventional / septimal meantone distinction; refer to starling instead of marvel for the general essentially-tempered chord (marvel doesn't get that close!) |
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However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], and the augmented fourth is only a few cents shy of [[7/5]], so the meantone French sixth chord can be considered to also approximate the [[septimal meantone]] chord: | However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], and the augmented fourth is only a few cents shy of [[7/5]], so the meantone French sixth chord can be considered to also approximate the [[septimal meantone]] chord: | ||
* ([[ | * ([[Septimal meantone chords|Septimal meantone]]) 1 – 5/4 – 7/5 – 7/4 | ||
or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9 | or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[10/9]], in septimal meantone (and, more generally, in [[starling]] temperaments) this chord is an [[essentially tempered chord]] in the [[9-odd-limit]]. | ||
<!-- Note: The close approximation of the 7-limit chord is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. --> | <!-- Note: The close approximation of the 7-limit chord is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. --> | ||