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Interval information
Ratio 729/704
Factorization 2-6 × 36 × 11-1
Monzo [-6 6 0 0 -1
Size in cents 60.412063¢
Names Alpharabian infra-augmented prime,
Alpharabian infra-apotomic quartertone,
undecimal major diesis
Color name L1u1, lalu 1sn, Lalu comma
FJS name [math]\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
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~4.75958 bits
Comma size medium
S-expression S92 × S10
open this interval in xen-calc

729/704, conventionally named the undecimal major diesis[1], is a medium comma measuring about 60.4 ¢. In Alpharabian tuning, it is called the Alpharabian infra-augmented prime or Alpharabian infra-apotomic 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