9/7

Interval information

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]\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 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 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

• 14/9 – its octave complement
• 7/6 – its fifth complement
• 11edo has a good approximation: 4\11
• Gallery of Just Intervals
• Septimal major third - Wikipedia