1331/1296: Difference between revisions

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Created page with "{{Infobox Interval | Ratio = 1331/1296 | Monzo = -4 -4 0 0 3 | Cents = 46.13382 | Name = Alpharabian parachromatic semilimma | Color name = | FJS name = | Sound = }} '''409..."
 
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{{Infobox Interval
{{Infobox Interval
| Ratio = 1331/1296
| Name = Alpharabian parachromatic semilimma, Alpharabian semilimmic ultraprime
| Monzo = -4 -4 0 0 3
| Color name = 1o<sup>3</sup>1, trilo 1sn, Trilo comma
| Cents = 46.13382
| Name = Alpharabian parachromatic semilimma
| Color name =  
| FJS name =
| Sound =
}}
}}


'''4096/3993''', the '''Alpharabian parachromatic semilimma''', is a quartertone in the [[11-limit]], specifically the 2.3.11 [[subgroup]], that differs from the simpler [[33/32]] by the [[rastma]], and is also the interval separating [[81/64]] and [[1331/1024]]. It is of further note that this interval is only just slightly more than half of [[256/243]]- the Pythagorean limma- being separated from the nearby [[4096/3993]], the interval forming the other part of the Pythagorean limma, by the [[nexus comma]].
'''1331/1296''', the '''Alpharabian parachromatic semilimma''' or '''Alpharabian semilimmic ultraprime''', is a [[quartertone]] in the [[11-limit]], specifically the 2.3.11 [[subgroup]], that differs from the simpler [[33/32]] by the [[rastma]], and is also the interval separating [[81/64]] and [[1331/1024]]. It is of further note that this interval is only just slightly more than half of [[256/243]]- the Pythagorean limma- being separated from the nearby [[4096/3993]], the interval forming the other part of the Pythagorean limma, by the [[nexus comma]].


[[Category:11-limit]]
[[Category:Quartertone]]
[[Category:Quartertone]]
[[Category:Alpharabian]]
[[Category:Alpharabian]]
[[Category:Commas named after polymaths]]

Latest revision as of 05:15, 24 December 2024

Interval information
Ratio 1331/1296
Factorization 2-4 × 3-4 × 113
Monzo [-4 -4 0 0 3
Size in cents 46.13382¢
Names Alpharabian parachromatic semilimma,
Alpharabian semilimmic ultraprime
Color name 1o31, trilo 1sn, Trilo comma
FJS name [math]\displaystyle{ \text{d1}^{11,11,11} }[/math]
Special properties reduced
Tenney height (log2 nd) 20.7181
Weil height (log2 max(n, d)) 20.7566
Wilson height (sopfr(nd)) 53
Open this interval in xen-calc

1331/1296, the Alpharabian parachromatic semilimma or Alpharabian semilimmic ultraprime, is a quartertone in the 11-limit, specifically the 2.3.11 subgroup, that differs from the simpler 33/32 by the rastma, and is also the interval separating 81/64 and 1331/1024. It is of further note that this interval is only just slightly more than half of 256/243- the Pythagorean limma- being separated from the nearby 4096/3993, the interval forming the other part of the Pythagorean limma, by the nexus comma.