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
Color name	L1u1, lalu 1sn, Lalu comma
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
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729/704, conventionally named the undecimal major diesis, is a medium comma measuring about 60.4 ¢. In Alpharabian tuning, it is called the Alpharabian infraaugmented prime or Alpharabian infraapotomic quartertone.

It 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.

See also

• 1408/729 – its octave complement
• Gallery of just intervals