9/7
| Ratio | 9/7 |
| Factorization | 32 × 7-1 |
| Monzo | [0 2 0 -1⟩ |
| Size in cents | 435.0841¢ |
| Names | supermajor third, septimal major third |
| Color name | r3, ru 3rd |
| FJS name | [math]\text{M3}_{7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 5.97728 |
| Weil height (log2 max(n, d)) | 6.33985 |
| Wilson height (sopfr (nd)) | 13 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.57105 bits |
[sound info] | |
| open this interval in xen-calc | |
In just intonation, 9/7 is the supermajor third 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