9/7
| 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.