88/63: Difference between revisions

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diminished -> augmented
Consolidate interval name
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| Monzo = 3 -2 0 -1 1
| Monzo = 3 -2 0 -1 1
| Cents = 578.582034
| Cents = 578.582034
| Name = werckismic augmented fourth
| Name = pentacircle diminished fifth
| Color name =  
| Color name =  
| FJS name =  
| FJS name = P4<sup>11</sup><sub>7</sub>
| Sound =  
| Sound =  
}}
}}


'''88/63''', the werckismic augmented fourth, is 441/440 (3.9 cents) below [[7/5]]. It is 0.01 cent sharp of the [[56edo]] augmented fourth of 27\56. It can arise in 11-limit scales as the interval from [[9/8]] to [[11/7]], or [[14/11]] to [[16/9]].
'''88/63''', the '''pentacircle diminished fifth''', is [[896/891]] below [[1024/729]], the Pythagorean diminished fifth. It is also 441/440 (3.9 cents) below [[7/5]]. It is 0.01 cent sharp of the [[56edo]] augmented fourth of 27\56. It arises in 11-limit scales as the interval from [[9/8]] to [[11/7]], or [[14/11]] to [[16/9]].
 
== Terminology ==
It could also be called ''werckismic augmented fourth'' if viewed as [[fudging]] from [[7/5]] instead.  


[[Category:11-limit]]
[[Category:11-limit]]
 
[[Category:Pentacircle]]
{{todo|review interval name}}
[[Category:Tritone]]

Revision as of 00:27, 23 January 2022

Interval information
Ratio 88/63
Factorization 23 × 3-2 × 7-1 × 11
Monzo [3 -2 0 -1 1
Size in cents 578.582¢
Name pentacircle diminished fifth
FJS name [math]\displaystyle{ \text{P4}^{11}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.4367
Weil norm (log2 max(n, d)) 12.9189
Wilson norm (sopfr(nd)) 30
Open this interval in xen-calc

88/63, the pentacircle diminished fifth, is 896/891 below 1024/729, the Pythagorean diminished fifth. It is also 441/440 (3.9 cents) below 7/5. It is 0.01 cent sharp of the 56edo augmented fourth of 27\56. It arises in 11-limit scales as the interval from 9/8 to 11/7, or 14/11 to 16/9.

Terminology

It could also be called werckismic augmented fourth if viewed as fudging from 7/5 instead.