French sixth chord: Difference between revisions

Line 9:

* (Meantone) 1 – 5/4 – 25/18 – 125/72

represents a range of JI interpretations including both [[72:90:100:125]] and [[128:160:180:225]].

represents a range of JI interpretations including both [[72:90:100:125]] (step sizes 5/4, 10/9, and 5/4) and [[128:160:180:225]] (step sizes 5/4, 9/8, and 5/4).

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 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:

* (Meantone) 1 – 5/4 – 7/5 – 7/4

~~representing~~ [[20:25:28:35]].

or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]], in septimal meantone (and, more generally, in [[marvel]] temperaments) this chord is an [[essentially tempered chord]] in the [[9-odd-limit]].

@@ Line 9: / Line 9: @@
 * (Meantone) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;25/18&thinsp;–&thinsp;125/72
-represents a range of JI interpretations including both [[72:90:100:125]] and [[128:160:180:225]].
+represents a range of JI interpretations including both [[72:90:100:125]] (step sizes 5/4, 10/9, and 5/4) and [[128:160:180:225]] (step sizes 5/4, 9/8, and 5/4).
-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 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:
 * (Meantone) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;7/5&thinsp;–&thinsp;7/4
-representing [[20:25:28:35]].
+or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]], in septimal meantone (and, more generally, in [[marvel]] 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. -->