729/484: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Aura (talk | contribs)
Created page with "{{Infobox Interval | Name = Alpharabian wide fifth | Color name = | Sound = }} '''729/484''', the '''Alpharabian wide fifth''' (709.09¢), is 243/242 (7.1¢) above the..."
 
mention 121/81
 
(5 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Name = Alpharabian wide fifth
| Name = Alpharabian wide fifth
| Color name =  
| Color name = L1uu5, lalulu 5th
| Sound =  
| Sound =  
}}
}}


'''729/484''', the '''Alpharabian wide fifth''' (709.09¢), is [[243/242]] (7.1¢) above the just fifth [[3/2]].  It is the interval created by stacking two [[27/22]] neutral thirds, and can be considered a [[superpyth]] fifth.
'''729/484''', the '''Alpharabian wide fifth''' (709.09¢), is [[243/242]] (7.1¢) above the just fifth [[3/2]].  It is the interval created by stacking two [[27/22]] neutral thirds, and can be considered a [[superpyth]] fifth.  Oddly enough, it is only about 0.003 [[cent]]s away from [[22edo]]'s approximation of the perfect fifth. This gives [[44edo]] a very accurate 27/22 approximation, even though 27/22 is not actually mapped to that interval. The first multiple of 44edo to map it consistently is [[176edo]].


== See also ==
== See also ==
* [[968/729]] - its [[octave complement]]
* [[968/729]] - its [[octave complement]]
* [[121/81]] - the Alpharabian narrow fifth
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]

Latest revision as of 00:48, 18 March 2026

Interval information
Ratio 729/484
Factorization 2-2 × 36 × 11-2
Monzo [-2 6 0 0 -2
Size in cents 709.0941¢
Name Alpharabian wide fifth
Color name L1uu5, lalulu 5th
FJS name [math]\displaystyle{ \text{A5}_{11,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 18.4286
Weil norm (log2 max(n, d)) 19.0196
Wilson norm (sopfr(nd)) 44
Open this interval in xen-calc

729/484, the Alpharabian wide fifth (709.09¢), is 243/242 (7.1¢) above the just fifth 3/2. It is the interval created by stacking two 27/22 neutral thirds, and can be considered a superpyth fifth. Oddly enough, it is only about 0.003 cents away from 22edo's approximation of the perfect fifth. This gives 44edo a very accurate 27/22 approximation, even though 27/22 is not actually mapped to that interval. The first multiple of 44edo to map it consistently is 176edo.

See also