9/7: Difference between revisions

(32 intermediate revisions by 13 users not shown)

Line 1:

{| ~~class~~=~~"wikitable"~~

{{Infobox Interval

|-

| Name = supermajor third, septimal major third

| Color name = r3, ru 3rd

|-

| Sound = jid_9_7_pluck_adu_dr220.mp3

~~| | JI glyph for~~ 9/7

}}

|}

In [[just intonation]], '''9/7''' is the '''supermajor 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 major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The [[9-odd-limit]] harmonic ninth chord, a [[pentad]] with ratios [[4:5:6:7:9]], includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way [[9/8]] behaves as ratios of [[9/1|9]] all share this quality.

~~'''~~9/7~~'''~~

A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be [[14:18:21]]. This triad can be very effective in music, but in this context, the modern ear accustomed to [[12edo]] thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.

~~|0 2 0~~ -~~1>~~

~~435~~.~~08410 cents~~

In [[Ancient Greek music]], {{w|Archytas}} used the 9/7 interval in his [[tetrachord]] tunings (in all three genera), for the interval between the ''parhypate'' (second degree) and ''mese'' (fourth degree).

[[~~File:jid_9_7_pluck_adu_dr220.mp3~~]] ~~[[:File:jid_9_7_pluck_adu_dr220~~.~~mp3|sound sample]]~~

== Approximation ==

In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.

~~In [[Just_intonation~~|~~Just Intonation]],~~ 9/7 is a supermajor third of approximately 435.1¢, characteristic of [[7-limit|7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit hexad 4:5:6:7:8:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.

~~A just chord can be built with this wide third in place of the more traditional~~ [[5/~~4|5/4~~]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400¢ is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its ~~own right. Because 9/~~7 ~~is a ratio of 9, it shares sonority qualities with 9~~/~~8 much more than 5~~/~~4. Chords such as the~~ [[~~9-limit|9-limit~~]] ~~hexad above and subsets~~ of ~~it give more opportunity for 9/7 to be heard as consonant.~~

== See also ==

* [[14/9]] – its [[octave complement]]

* [[7/6]] – its [[fifth complement]]

* [[28/27]] – its [[fourth complement]]

* [[Gallery of just intervals]]

~~See also:~~

== References ==

~~[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~

[[Category:Third]]

[[Category:Major third]]

~~[http://en.wikipedia.org/wiki/Septimal_major_third Septimal major third] (Wikipedia)~~

[[Category:Supermajor third]]

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

[[Category:Over-7 intervals]]

[[Category:~~interval~~]]

[[Category:~~just_interval~~]]

[[Category:~~major_third]]~~

~~[[Category:ratio]]~~

~~[[Category:supermajor~~]]

@@ Line 1: / Line 1: @@
-{| class="wikitable"
+{{Infobox Interval
-|-
+| Name = supermajor third, septimal major third
-| | [[File:glyph_9_7.png|alt=glyph 9 7.png|101x137px|glyph 9 7.png]]
+| Color name = r3, ru 3rd
-|-
+| Sound = jid_9_7_pluck_adu_dr220.mp3
-| | JI glyph for 9/7
+}}
-|}
+{{Wikipedia|Septimal major third}}
+In [[just intonation]], '''9/7''' is the '''supermajor 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 major third''' of approximately 435.1{{cent}}, characteristic of [[7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The [[9-odd-limit]] harmonic ninth chord, a [[pentad]] with ratios [[4:5:6:7:9]], includes a septimal supermajor third between the seventh and the ninth. The interval has an interesting "neutral" quality to it similar to the way [[9/8]] behaves as ratios of [[9/1|9]] all share this quality.
-'''9/7'''
+A just chord can be built with this wide third in place of the more traditional [[5/4]]. This supermajor triad would be [[14:18:21]]. This triad can be very effective in music, but in this context, the modern ear accustomed to [[12edo]] thirds of 400{{cent}} is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the 9-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.
-|0 2 0 -1&gt;
-.08410 cents
+In [[Ancient Greek music]], {{w|Archytas}} used the 9/7 interval in his [[tetrachord]] tunings (in all three genera), for the interval between the ''parhypate'' (second degree) and ''mese'' (fourth degree).
-[[File:jid_9_7_pluck_adu_dr220.mp3]] [[:File:jid_9_7_pluck_adu_dr220.mp3|sound sample]]
+== Approximation ==
+In [[11edo]], 4\11 is about 1.3{{cent}} sharp of 9/7.
-In [[Just_intonation|Just Intonation]], 9/7 is a supermajor third of approximately 435.1¢, characteristic of [[7-limit|7-limit]] and beyond. On its own, it has a very strident quality, but in the context of a chord, it can sound perfectly consonant. The 9-limit hexad 4:5:6:7:8:9 includes a septimal supermajor third between the 7th and the 9th. The interval has an interesting neutral quality to it similar to the way 9/8 behaves as ratios of nine all share this quality.
+{{Interval edo approximation|9/7}}
-A just chord can be built with this wide third in place of the more traditional [[5/4|5/4]]. This supermajor triad would be 14:18:21. This triad can be very effective in music, but in this context, the modern ear accustomed to 12edo thirds of 400¢ is likely to hear 9/7 as a mistuned major third instead of a new class of interval in its own right. Because 9/7 is a ratio of 9, it shares sonority qualities with 9/8 much more than 5/4. Chords such as the [[9-limit|9-limit]] hexad above and subsets of it give more opportunity for 9/7 to be heard as consonant.
+== See also ==
+* [[14/9]] – its [[octave complement]]
+* [[7/6]] – its [[fifth complement]]
+* [[28/27]] – its [[fourth complement]]
+* [[Gallery of just intervals]]
-See also:
+== References ==
+<references />
-[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
+[[Category:Third]]
+[[Category:Major third]]
-[http://en.wikipedia.org/wiki/Septimal_major_third Septimal major third] (Wikipedia)
+[[Category:Supermajor third]]
-[[Category:7-limit]]
+[[Category:Over-7 intervals]]
-[[Category:interval]]
-[[Category:just_interval]]
-[[Category:major_third]]
-[[Category:ratio]]
-[[Category:supermajor]]