9/7: Difference between revisions
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{{Wikipedia|Septimal major third}} | {{Wikipedia|Septimal major third}} | ||
In [[just intonation]], '''9/7''' is the '''supermajor third''' 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-limit pentad 4:5:6:7:9 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. | In [[just intonation]], '''9/7''' is the '''supermajor third'''<ref>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-limit pentad 4:5:6:7:9 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{{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. | ||
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* [[28/27]] – its [[fourth complement]] | * [[28/27]] – its [[fourth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== References == | |||
<references /> | |||
[[Category:Third]] | [[Category:Third]] | ||
Revision as of 14:41, 16 April 2025
| Interval information |
septimal major third
[sound info]
In just intonation, 9/7 is the supermajor third[1] or septimal major 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 pentad 4:5:6:7:9 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-odd-limit pentad above and certain subsets of it give more opportunity for 9/7 to be heard as consonant.
In Ancient Greek music, 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 ¢ sharp of 9/7.
See also
- 14/9 – its octave complement
- 7/6 – its fifth complement
- 28/27 – its fourth complement
- Gallery of just intervals
References
- ↑ Hermann L. F. von Helmholtz (1875). On the sensations of tone as a physiological basis for the theory of music, p. 284.