225/224: Difference between revisions

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m gave another example and made it clear from the writing which of each pair of intervals is bigger
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The interval of '''225/224''', the '''septimal kleisma''' or '''marvel comma''' is a [[superparticular]] [[7-limit]] ratio. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]). It is tempered out in temperaments of the [[marvel family]].
The interval of '''225/224''', the '''septimal kleisma''' or '''marvel comma''' is a [[7-limit]] [[superparticular]] ratio. It pops up as the difference between pairs of 7-limit ratios, for example as ([[15/14]])/([[16/15]]) or ([[45/32]])/([[7/5]]).  
 
== Temperaments ==
Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]].


== See also ==
== See also ==
* [[Marvel family]]
* [[Marvel family]], the family of rank-3 temperaments where it is tempered out
* [[Marvel temperaments]]
* [[Marvel temperaments]], a collection of rank-2 temperaments where it is tempered out
* [[Marvel chords]]
* [[Marvel chords]]
* [[Small comma]]
* [[Small comma]]
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[[Category:Superparticular]]
[[Category:Superparticular]]
[[Category:Marvel]]
[[Category:Marvel]]
[[Category:Stub]]

Revision as of 14:24, 16 April 2021

Interval information
Ratio 225/224
Factorization 2-5 × 32 × 52 × 7-1
Monzo [-5 2 2 -1
Size in cents 7.711523¢
Names septimal kleisma,
marvel comma
Color name ryy-2, ruyoyo negative 2nd
FJS name [math]\displaystyle{ \text{d}{-2}^{25}_{7} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 15.6211
Weil height (log2 max(n, d)) 15.6276
Wilson height (sopfr(nd)) 33
Open this interval in xen-calc

The interval of 225/224, the septimal kleisma or marvel comma is a 7-limit superparticular ratio. It pops up as the difference between pairs of 7-limit ratios, for example as (15/14)/(16/15) or (45/32)/(7/5).

Temperaments

Tempering out this comma leads to the marvel family of temperaments, which enables marvel chords.

See also