729/704: Difference between revisions

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Additional name found in the Huygens-Fokker Foundation's interval list
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== See also ==
== See also ==
* [[1408/729]] – its [[octave complement]]
* [[1408/729]] – its [[octave complement]]
* [[Alpharabian tuning]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]

Revision as of 23:59, 20 November 2021

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.

See also