135/112

135/112, conventionally known as the septimal wide minor third or marvel-ptolemaic minor third, is a 7-limit interval that 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 an aberschisma. This gives rise to the more precise name aberschismic augmented second. In fact it forms the difference between 9/7 and 16/15.

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, aberschismic 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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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