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, 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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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 an aberdiesis (3645/3584), i.e. a syntonic comma (81/80) plus a marvel comma (225/224). This interval functionally doubles as a type of augmented second, sharp of the Pythagorean augmented second (19683/16384) by an aberschisma (5120/5103). This gives rise to the more precise name aberschismic augmented second. In fact it forms the difference between 9/7 and 16/15.

This interval has the distinction of being almost half of a undecimal semidiminished fifth (16/11) – in fact, a stack of two 135/112's differs from 16/11 by a "reef comma" (200704/200475), which is 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