12/7

Interval information

Ratio	12/7
Factorization	22 × 3 × 7-1
Monzo	[2 1 0 -1⟩
Size in cents	933.1291¢
Names	supermajor sixth, septimal major sixth
Color name	r6, ru 6th
FJS name	[math]\displaystyle{ \text{M6}_{7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	6.39232
Weil height (log2 max(n, d))	7.16993
Wilson height (sopfr(nd))	14
[sound info]
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In 7-limit Just Intonation, 12/7 is the supermajor sixth or septimal major sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of 5/3 by 36/35 -- the septimal quartertone -- a superparticular interval of about 48.8¢. It differs from the Pythagorean major sixth of 27/16 by 64/63 -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- 7/4, about 968.8¢ -- by 49/48 -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of 7/6.

See also

• 7/6 -- its octave complement
• Gallery of Just Intervals
• Septimal major sixth - Wikipedia
• an alternative sound sample