Xenharmonic Wiki

9/7: Difference between revisions

← Older edit
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
reworked: simplified links; introduced infobox interval
Overthink (talk | contribs)
autopatrolled
2,671 edits
space out links
 
(31 intermediate revisions by 13 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Icon = [[File:glyph_9_7.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| Name = supermajor third, septimal major third
| Ratio = 9/7
| Color name = r3, ru 3rd
| Monzo = 0 2 0 -1
| Cents = 435.08410
| Name = supermajor third
| Sound = jid_9_7_pluck_adu_dr220.mp3
| Sound = jid_9_7_pluck_adu_dr220.mp3
| Color name =
}}
}}
{{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.


In [[Just intonation|Just Intonation]], 9/7 is a supermajor third of approximately 435.1¢, 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-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]]. 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.


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¢ 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]] hexad above and 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}}


== See also ==
== See also ==
* [[Gallery of Just Intervals]]
* [[14/9]] – its [[octave complement]]
* [http://en.wikipedia.org/wiki/Septimal_major_third Septimal major third] (Wikipedia)
* [[7/6]] – its [[fifth complement]]
* [[28/27]] – its [[fourth complement]]
* [[Gallery of just intervals]]
 
== References ==
<references />


[[Category:7-limit]]
[[Category:Third]]
[[Category:interval]]
[[Category:Major third]]
[[Category:just_interval]]
[[Category:Supermajor third]]
[[Category:major_third]]
[[Category:Over-7 intervals]]
[[Category:ratio]]
[[Category:supermajor]]
Retrieved from "https://en.xen.wiki/w/9/7"