9/7: Difference between revisions

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reworked: simplified links; introduced infobox interval
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{| class="wikitable"
{{Infobox Interval
|-
| Icon = [[File:glyph_9_7.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| | [[File:glyph_9_7.png|alt=glyph 9 7.png|101x137px|glyph 9 7.png]]
| Ratio = 9/7
|-
| Monzo = 0 2 0 -1
| | JI glyph for 9/7
| Cents = 435.08410
|}
| Name = supermajor third
| Sound = jid_9_7_pluck_adu_dr220.mp3
| Color name =
}}


'''9/7'''
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.
|0 2 0 -1&gt;


435.08410 cents
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.


[[File:jid_9_7_pluck_adu_dr220.mp3]] [[:File:jid_9_7_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[Gallery of Just Intervals]]
* [http://en.wikipedia.org/wiki/Septimal_major_third Septimal major third] (Wikipedia)


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:
[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
[http://en.wikipedia.org/wiki/Septimal_major_third Septimal major third] (Wikipedia)
[[Category:7-limit]]
[[Category:7-limit]]
[[Category:interval]]
[[Category:interval]]

Revision as of 22:39, 17 October 2018

Interval information
Ratio 9/7
Factorization 32 × 7-1
Monzo [0 2 0 -1
Size in cents 435.0841¢
Name supermajor third
FJS name [math]\displaystyle{ \text{M3}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 5.97728
Weil norm (log2 max(n, d)) 6.33985
Wilson norm (sopfr(nd)) 13

[sound info]
Open this interval in xen-calc

In 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¢ 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.

See also