121/81: Difference between revisions

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mention 729/484
 
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{{Infobox Interval
{{Infobox Interval
| Name = Alpharabian narrow fifth
| Name = Alpharabian narrow fifth
| Color name = 1uu5, lulu 5th
| Color name = 1oo5, lolo 5th
| Sound =  
| Sound =  
}}
}}


'''121/81''', the '''Alpharabian narrow fifth''' (694.8¢), is [[243/242]] (7.1¢) below the just fifth [[3/2]].  It is the interval created by stacking two [[11/9]] neutral thirds, and can be considered a [[meantone]] fifth.
'''121/81''', the '''Alpharabian narrow fifth''' (694.8¢), is a rastma [[243/242]] (7.1¢) below the just fifth [[3/2]].  It is the interval created by stacking two [[11/9]] neutral thirds, and can be considered a [[meantone]] fifth. It differs from the marvellous fifth [[112/75]] by [[3025/3024]]. Since [[38edo]] represents 11/9 near perfectly, it also represents this near perfectly as well.
 
When treated as a meantone fifth, it is incredibly close to [[1/3-comma meantone]], three of these intervals differing from [[5/3]] by only the [[parimo]].


== See also ==
== See also ==
* [[162/121]] - its [[octave complement]]
* [[162/121]] - its [[octave complement]]
* [[729/484]] - the Alpharabian wide fifth
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
[[Category:Fifth]]

Latest revision as of 00:49, 18 March 2026

Interval information
Ratio 121/81
Factorization 3-4 × 112
Monzo [0 -4 0 0 2
Size in cents 694.8159¢
Name Alpharabian narrow fifth
Color name 1oo5, lolo 5th
FJS name [math]\displaystyle{ \text{d5}^{11,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 13.2587
Weil norm (log2 max(n, d)) 13.8377
Wilson norm (sopfr(nd)) 34
Open this interval in xen-calc

121/81, the Alpharabian narrow fifth (694.8¢), is a rastma 243/242 (7.1¢) below the just fifth 3/2. It is the interval created by stacking two 11/9 neutral thirds, and can be considered a meantone fifth. It differs from the marvellous fifth 112/75 by 3025/3024. Since 38edo represents 11/9 near perfectly, it also represents this near perfectly as well.

When treated as a meantone fifth, it is incredibly close to 1/3-comma meantone, three of these intervals differing from 5/3 by only the parimo.

See also