729/704
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Ratio | 729/704 |
Factorization | 2^{-6} × 3^{6} × 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 (log_{2} nd) | 18.9692 |
Weil height (log_{2} max(n, d)) | 19.0196 |
Wilson height (sopfr (nd)) | 41 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.39245 bits |
Comma size | medium |
S-expression | S9^{2} × 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.