81/65: Difference between revisions

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{{Infobox interval|81/65|Name=Quasimagical major third}}
{{Infobox interval|81/65|Name=Quasimagical major third}}
'''81/65''', the '''quasimagical major third''', is a [[13-limit]] [[major third]] measuring about 381 [[cent]]s. It is the interval between [[9/5]] and [[13/9]], and is notable for approximating the major third found in [[magic]] temperament, where five such major thirds stack to [[3/1]]. It is a more accurate approximation of this generator than [[5/4]] is, and being no-twos, appears in [[tritave]]-based systems as 1\[[5edt]] as well.
'''81/65''', the '''quasimagical major third''', is a [[13-limit]] [[major third]] measuring about 381 [[cent]]s. It is the interval between [[9/5]] and [[13/9]], and differs from [[5/4]] by the comma [[325/324]], the marveltwin comma. It is notable for approximating the major third found in [[magic]] temperament, where five such major thirds stack to [[3/1]]. It is a more accurate approximation of this generator than 5/4 is, and being no-twos, appears in [[tritave]]-based systems as 1\[[5edt]] as well.


== See also ==
== See also ==

Latest revision as of 15:54, 6 March 2025

Interval information
Ratio 81/65
Factorization 34 × 5-1 × 13-1
Monzo [0 4 -1 0 0 -1
Size in cents 380.9786¢
Name Quasimagical major third
FJS name [math]\displaystyle{ \text{M3}_{5,13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.3622
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 30
Open this interval in xen-calc

81/65, the quasimagical major third, is a 13-limit major third measuring about 381 cents. It is the interval between 9/5 and 13/9, and differs from 5/4 by the comma 325/324, the marveltwin comma. It is notable for approximating the major third found in magic temperament, where five such major thirds stack to 3/1. It is a more accurate approximation of this generator than 5/4 is, and being no-twos, appears in tritave-based systems as 1\5edt as well.

See also

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