44/35

44/35, the fwiwismic major third, is an 11-limit interval that is close to a 12edo major third. It differs from 81/64, the Pythagorean major third, by 2835/2816, the fwiwisma. It also differs from 5/4 by 176/175, the valinorsma. It is the product of 11/10 and 8/7, intervals that are commonly used as stand-ins for the cube roots of 4/3 and 3/2 respectively, so appears as 1/3 of an octave in systems that carve both 4/3 and 3/2 in thirds, such as 15edo, 72edo, 87edo, and 159edo. It is 441/440 flat of 63/50, a 7-limit interval often representing 1/3 of an octave, in fact much more accurately than 44/35.

Interval information

Ratio	44/35
Factorization	22 × 5-1 × 7-1 × 11
Monzo	[2 0 -1 -1 1⟩
Size in cents	396.1783¢
Name	fwiwismic major third
FJS name	[math]\displaystyle{ \text{m3}^{11}_{5,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	10.5887
Weil norm (log2 max(n, d))	10.9189
Wilson norm (sopfr(nd))	27
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Terminology

It could also be called valinorsmic major third if viewed as fudging from 5/4 instead.

See also

• 35/22 – its octave complement