729/704

Interval information

Ratio

729/704

Factorization

2^-6 × 3⁶ × 11^-1

Monzo

[-6 6 0 0 -1⟩

Size in cents

60.41206¢

Names

Alpharabian infraaugmented prime,
Alpharabian infraapotomic quartertone,
undecimal major diesis

FJS name

[math]\displaystyle{ \text{A1}_{11} }[/math]

Special properties

reduced

Tenney height (log₂ nd)

18.9692

Weil height (log₂ max(n, d))

19.0196

Wilson height (sopfr(nd))

41

Open this interval in xen-calc

729/704, the Alpharabian infraaugmented prime or Alpharabian infraapotomic quartertone is a type of quartertone that differs from 33/32 by 243/242, and is itself the interval left over after subtracting 33/32 from 2187/2048. While many may be accustomed to thinking of 33/32 and 729/704 as "semiaugmented primes", this analysis is only completely accurate when 243/242 is tempered out. This interval differs from the simpler 28/27 by the symbiotic comma. This interval is referred to in the Huygens-Fokker Foundation's interval list as the undecimal major diesis.

729/704

See also