729/490: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
m Remove name pointing to fourth for consistency
Copied some more info from 729/490
Line 11: Line 11:
'''729/490''', the '''sensamagic fifth''' is a [[7-limit]] ratio of about 687 cents, flat of a just fifth [[3/2]] by a sensamagic comma [[245/243]].  
'''729/490''', the '''sensamagic fifth''' is a [[7-limit]] ratio of about 687 cents, flat of a just fifth [[3/2]] by a sensamagic comma [[245/243]].  


It arises in just intonation scales often as the octave complement of [[980/729]].  
It arises in just intonation as the difference between the semidimished fourth [[35/27]] and the supermajor seventh [[27/14]], making it a critical tempering target in the [[Canovian chord]]. However, its distinction from 3/2 is emphasised in the [[canou family]] of temperaments, through its accessibility by two steps of the [[81/70]]-generator.  


== See also ==
== See also ==
Line 21: Line 21:
[[Category:Interval]]
[[Category:Interval]]
[[Category:Ratio]]
[[Category:Ratio]]
[[Category:Fifth]]
[[Category:Augmented fourth]]
[[Category:Augmented fourth]]
[[Category:Sensamagic]]
[[Category:Sensamagic]]
[[Category:Canou]]

Revision as of 04:19, 17 November 2020

Interval information
Ratio 729/490
Factorization 2-1 × 36 × 5-1 × 7-2
Monzo [-1 6 -1 -2
Size in cents 687.7645¢
Name sensamagic fifth
Color name rrg4, rurugu 4th
FJS name [math]\displaystyle{ \text{A4}_{5,49} }[/math]
Special properties reduced
Tenney norm (log2 nd) 18.4464
Weil norm (log2 max(n, d)) 19.0196
Wilson norm (sopfr(nd)) 39
Open this interval in xen-calc

729/490, the sensamagic fifth is a 7-limit ratio of about 687 cents, flat of a just fifth 3/2 by a sensamagic comma 245/243.

It arises in just intonation as the difference between the semidimished fourth 35/27 and the supermajor seventh 27/14, making it a critical tempering target in the Canovian chord. However, its distinction from 3/2 is emphasised in the canou family of temperaments, through its accessibility by two steps of the 81/70-generator.

See also