729/704
Jump to navigation
Jump to search
| 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.