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m the reason i'm removing these JI glyphs is that there can be no complete, systematic system of JI glyphs for all JI intervals, thus they aren't very useful. They aren't used in practice in the community, either. |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = supermajor third, septimal major third | |||
| Name = supermajor third, | |||
| Color name = r3, ru 3rd | | Color name = r3, ru 3rd | ||
| Sound = jid_9_7_pluck_adu_dr220.mp3 | | Sound = jid_9_7_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{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. | |||
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}} | |||
== See also == | == See also == | ||
* [[14/9]] – its [[octave complement]] | * [[14/9]] – its [[octave complement]] | ||
* [[7/6]] – its [[fifth complement]] | * [[7/6]] – its [[fifth complement]] | ||
* [[ | * [[28/27]] – its [[fourth complement]] | ||
* [[Gallery of just intervals]] | |||
* [[ | |||
== References == | |||
<references /> | |||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Major third]] | [[Category:Major third]] | ||
[[Category:Supermajor third]] | [[Category:Supermajor third]] | ||
[[Category:Over-7 intervals]] | |||
[[Category:Over-7]] | |||
Latest revision as of 04:08, 12 March 2026
| 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-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 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.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 1\3 | 400.00 | -35.08 | -8.77 |
| 8 | 3\8 | 450.00 | +14.92 | +9.94 |
| 11 | 4\11 | 436.36 | +1.28 | +1.17 |
| 14 | 5\14 | 428.57 | -6.51 | -7.60 |
| 22 | 8\22 | 436.36 | +1.28 | +2.35 |
| 25 | 9\25 | 432.00 | -3.08 | -6.43 |
| 33 | 12\33 | 436.36 | +1.28 | +3.52 |
| 36 | 13\36 | 433.33 | -1.75 | -5.25 |
| 44 | 16\44 | 436.36 | +1.28 | +4.69 |
| 47 | 17\47 | 434.04 | -1.04 | -4.08 |
| 55 | 20\55 | 436.36 | +1.28 | +5.86 |
| 58 | 21\58 | 434.48 | -0.60 | -2.91 |
| 66 | 24\66 | 436.36 | +1.28 | +7.04 |
| 69 | 25\69 | 434.78 | -0.30 | -1.73 |
| 77 | 28\77 | 436.36 | +1.28 | +8.21 |
| 80 | 29\80 | 435.00 | -0.08 | -0.56 |
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.