9/7: Difference between revisions

| Sound = jid_9_7_pluck_adu_dr220.mp3

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.  

 

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.

 

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).

 

== Approximation ==

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

 

{{Interval edo approximation|9/7}}

 

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

* [[7/6]] – its [[fifth complement]]

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

 

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