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~~

| Color name = z3, zo 3rd

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

~~| Cents = 266.87091~~

| Name = septimal minor third

| Sound = jid_7_6_pluck_adu_dr220.mp3

}}

In [[7-limit~~|7-limit~~]] ~~Just Intonation~~, 7:6 is the septimal minor third. At about 267 cents, it is smaller than both the [[~~5-limit|~~5-limit]] minor third ([[~~6/5|~~6/5]], ~316 cents) and the familiar [[~~12edo|~~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]].

[~~http://en~~.~~wikipedia.org~~/~~wiki~~/~~Septimal_minor_third http:~~/~~/en.wikipedia.org/wiki/Septimal_minor_third~~] [[~~Category:7-limit~~]]

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

[[~~Category:~~interval]]

== See also ==

[[~~Category:just_interval~~]]

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

[[~~Category:minor_third~~]]

* [[9/7]] – its [[fifth complement]]

[[Category:~~ratio~~]]

* [[8/7]] – its [[fourth complement]]

[[Category:~~superparticular~~]]

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

[[Category:third]]

* [[Gallery of just intervals]]

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

== References ==

[[Category:Third]]

[[Category:Minor third]]

[[Category:Subminor third]]

[[Category:Over-3 intervals]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph = [[File:Ji_glyph_7_6.png|x48px]]
+| Name = subminor third, septimal minor third
-| Ratio = 7/6
+| Color name = z3, zo 3rd
-| Monzo = -1 -1 0 1
-| Cents = 266.87091
-| Name = septimal minor third
 | Sound = jid_7_6_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Septimal minor third}}
-In [[7-limit|7-limit]] Just Intonation, 7:6 is the septimal minor third. At about 267 cents, it is smaller than both the [[5-limit|5-limit]] minor third ([[6/5|6/5]], ~316 cents) and the familiar [[12edo|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]].
-[http://en.wikipedia.org/wiki/Septimal_minor_third http://en.wikipedia.org/wiki/Septimal_minor_third]      [[Category:7-limit]]
+It is almost perfectly approximated by [[9edo|2\9]], and is represented as such in the [[septiennealimmal clan]], including [[ennealimmal]].
-[[Category:interval]]
+== See also ==
-[[Category:just_interval]]
+* [[12/7]] – its [[octave complement]]
-[[Category:minor_third]]
+* [[9/7]] – its [[fifth complement]]
-[[Category:ratio]]
+* [[8/7]] – its [[fourth complement]]
-[[Category:superparticular]]
+* [[7/3]] – the interval plus one [[octave]] may sound even more [[consonant]]
-[[Category:third]]
+* [[Gallery of just intervals]]
-[[Category:todo:expand]]
+== References ==
+<references />
+[[Category:Third]]
+[[Category:Minor third]]
+[[Category:Subminor third]]
+[[Category:Over-3 intervals]]
+{{Todo| expand }}