7/6: Difference between revisions

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{{Infobox Interval

~~| JI glyph = [[File:Ji_glyph_7_6.png|x48px]]~~

| Name = subminor third, septimal minor third

~~| Ratio = 7/6~~

~~| Monzo = -1 -1 0 1~~

~~| Cents = 266.87091~~

| Name = septimal minor third

| Color name = z3, zo 3rd

| Sound = jid_7_6_pluck_adu_dr220.mp3

}}

In [[7-limit]] ~~Just Intonation~~, '''7/6''' is the '''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 [[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 ==

* [[~~Gallery of Just Intervals~~]]

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

* [[12/7]] - its [[~~inverse interval~~]]

* [[9/7]] – its [[fifth complement]]

* [[7/3]] - the interval plus one [[octave]] ~~sounds~~ even more [[consonant]]

* [[8/7]] – its [[fourth complement]]

* [~~http://en.wikipedia.org/wiki/Septimal_minor_third http://en.wikipedia.org/wiki/Septimal_minor_third~~]

* [[7/3]] – the interval plus one [[octave]] may sound even more [[consonant]]

* [[Gallery of just intervals]]

~~[[Category:7-limit]]~~

== References ==

~~[[Category:Interval]]~~

[[Category:~~Just interval~~]]

[[Category:Third]]

[[Category:Minor third]]

[[Category:~~Ratio~~]]

[[Category:Subminor third]]

[[Category:~~Superparticular~~]]

[[Category:Over-3 intervals]]

~~[[Category:Third]]~~

~~[[Category:todo:~~expand]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph = [[File:Ji_glyph_7_6.png|x48px]]
+| Name = subminor third, septimal minor third
-| Ratio = 7/6
-| Monzo = -1 -1 0 1
-| Cents = 266.87091
-| Name = septimal minor third
 | Color name = z3, zo 3rd
 | Sound = jid_7_6_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Septimal minor third}}
-In [[7-limit]] Just Intonation, '''7/6''' is the '''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 [[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 ==
-* [[Gallery of Just Intervals]]
+* [[12/7]] – its [[octave complement]]
-* [[12/7]] - its [[inverse interval]]
+* [[9/7]] – its [[fifth complement]]
-* [[7/3]] - the interval plus one [[octave]] sounds even more [[consonant]]
+* [[8/7]] – its [[fourth complement]]
-* [http://en.wikipedia.org/wiki/Septimal_minor_third http://en.wikipedia.org/wiki/Septimal_minor_third]
+* [[7/3]] – the interval plus one [[octave]] may sound even more [[consonant]]
+* [[Gallery of just intervals]]
-[[Category:7-limit]]
+== References ==
-[[Category:Interval]]
+<references />
-[[Category:Just interval]]
+[[Category:Third]]
 [[Category:Minor third]]
-[[Category:Ratio]]
+[[Category:Subminor third]]
-[[Category:Superparticular]]
+[[Category:Over-3 intervals]]
-[[Category:Third]]
+{{Todo| expand }}
-[[Category:todo:expand]]