135/112

Interval information

Ratio	135/112
Factorization	2-4 × 33 × 5 × 7-1
Monzo	[-4 3 1 -1⟩
Size in cents	323.3528¢
Names	septimal wide minor third, marvel-ptolemaic minor third, hemifamity augmented second
Color name	ry2, ruyo 2nd
FJS name	[math]\displaystyle{ \text{A2}^{5}_{7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	13.8842
Weil norm (log2 max(n, d))	14.1536
Wilson norm (sopfr(nd))	29
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135/112, the septimal wide minor third, or marvel-ptolemaic minor third, is a 7-limit interval that forms the difference between 9/7 and 16/15. It is sharp of the Pythagorean minor third by 3645/3584, i.e. a syntonic comma plus a marvel comma. This interval functionally doubles as a type of augmented second, sharp of the Pythagorean augmented second by 5120/5103. This gives rise to the name hemifamity augmented second.

This interval has the distinction of being almost half of a 16/11 semidiminished fifth – in fact, a stack of two 135/112's differs from 16/11 by 200704/200475, a comma less than two cents in size. Because of the relationship between 135/112 and 16/11, one can easily form a triad consisting of 1–135/112–16/11, to which one can then add 135/77 as a seventh.

See also

• 224/135 – its octave complement
• 56/45 – its fifth complement
• Gallery of just intervals