729/704: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = Alpharabian infraaugmented prime, Alpharabian infraapotomic quartertone, undecimal major diesis
| Name = Alpharabian infra-augmented prime, Alpharabian infra-apotomic quartertone, undecimal major diesis
| Color name = L1u1, lalu 1sn, Lalu comma
| Color name = L1u1, lalu 1sn, Lalu comma
}}
}}


'''729/704''', conventionally named the '''undecimal major diesis'''<ref>[http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list]</ref>, is a [[medium comma]] measuring about 60.4{{cent}}. In [[Alpharabian tuning]], it is called the '''Alpharabian infraaugmented prime''' or '''Alpharabian infraapotomic quartertone'''.
'''729/704''', conventionally named the '''undecimal major diesis'''<ref>[http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list]</ref>, is a [[medium comma]] measuring about 60.4{{cent}}. 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]].
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]].

Revision as of 18:19, 6 May 2023

Interval information
Ratio 729/704
Factorization 2-6 × 36 × 11-1
Monzo [-6 6 0 0 -1
Size in cents 60.41206¢
Names Alpharabian infra-augmented prime,
Alpharabian infra-apotomic 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
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

References