81/65

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]\text{M3}_{5,13}[/math]
Special properties	reduced
Tenney height (log2 nd)	12.3622
Weil height (log2 max(n, d))	12.6797
Wilson height (sopfr(nd))	30
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.03705 bits
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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

• 65/54 – its fifth complement

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