7/6: Difference between revisions

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In [[7-limit]] [[just intonation]], '''7/6''' is the '''subminor third''' <ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal minor third'''. At about 267 cents, it is smaller than both the [[5-limit]] minor third ([[6/5]], ~316 cents) and the familiar [[12edo]] minor third (300 cents). In contrast to [[5/4]] and [[6/5]], 7/6 is noticeably more consonant than it's counterpart [[9/7]], and a 6:7:9 ~~minor~~ triad can sound very stable compared to 14:18:21 .

In [[7-limit]] [[just intonation]], '''7/6''' is the '''subminor third''' <ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal minor third'''. At about 267 cents, it is smaller than both the [[5-limit]] minor third ([[6/5]], ~316 cents) and the familiar [[12edo]] minor third (300 cents). In contrast to [[5/4]] and [[6/5]], 7/6 is noticeably more consonant than it's counterpart [[9/7]], and a [[6:7:9]] subminor triad can sound very stable compared to a [[14:18:21]] supermajor triad. It can also be used with [[8/7]] in a [[6:7:8]] triad dividing [[4/3]] rather than [[3/2]], though this chord is better voiced as 4:6:7.

== Approximation ==

== Temperaments ==

7/6 can be used as a generator for several temperaments, most notably [[orwell]], where two subminor thirds reach [[11/8]], three reach [[8/5]], and seven reach [[3/2]]. It also generates [[septimin]].

It is almost perfectly approximated by [[9edo|2\9]], and is represented as such in the [[septiennealimmal clan]], including [[ennealimmal]].

== See also ==

* [[12/7]] – its [[octave complement]]

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 {{Wikipedia|Septimal minor third}}
-In [[7-limit]] [[just intonation]], '''7/6''' is the '''subminor third''' <ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal minor third'''. At about 267 cents, it is smaller than both the [[5-limit]] minor third ([[6/5]], ~316 cents) and the familiar [[12edo]] minor third (300 cents). In contrast to [[5/4]] and [[6/5]], 7/6 is noticeably more consonant than it's counterpart [[9/7]], and a 6:7:9 minor triad can sound very stable compared to 14:18:21 .
+In [[7-limit]] [[just intonation]], '''7/6''' is the '''subminor third''' <ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal minor third'''. At about 267 cents, it is smaller than both the [[5-limit]] minor third ([[6/5]], ~316 cents) and the familiar [[12edo]] minor third (300 cents). In contrast to [[5/4]] and [[6/5]], 7/6 is noticeably more consonant than it's counterpart [[9/7]], and a [[6:7:9]] subminor triad can sound very stable compared to a [[14:18:21]] supermajor triad. It can also be used with [[8/7]] in a [[6:7:8]] triad dividing [[4/3]] rather than [[3/2]], though this chord is better voiced as 4:6:7.
+== Approximation ==
+{{Interval edo approximation|7/6}}
+== Temperaments ==
+/6 can be used as a generator for several temperaments, most notably [[orwell]], where two subminor thirds reach [[11/8]], three reach [[8/5]], and seven reach [[3/2]]. It also generates [[septimin]].
+It is almost perfectly approximated by [[9edo|2\9]], and is represented as such in the [[septiennealimmal clan]], including [[ennealimmal]].
 == See also ==
 * [[12/7]] – its [[octave complement]]