44/35: Difference between revisions

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{{Infobox Interval| Name = valinorsmic major third}}
{{Infobox Interval
44/35, the '''valinorsmic major third''', is an [[11-limit]] interval that is close to a [[12edo]] major third, and which 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.
| Name = fwiwismic major third
}}
'''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.
 
== Terminology ==
It could also be called ''valinorsmic major third'' if viewed as [[fudging]] from [[5/4]] instead.
 
== See also ==
* [[35/22]] – its [[octave complement]]
 
[[Category:Fwiwismic]]

Latest revision as of 09:27, 13 March 2026

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
Open this interval in xen-calc

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.

Terminology

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

See also