225/224: Difference between revisions
m Moving from Category:Small comma to Category:Small commas using Cat-a-lot |
Merge some see-also links to the temperament section; make a separate approximation section |
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| Monzo = -5 2 2 -1 | | Monzo = -5 2 2 -1 | ||
| Cents = 7.71152 | | Cents = 7.71152 | ||
| Name = septimal kleisma, <br | | Name = septimal kleisma, <br>marvel comma | ||
| Color name = ryy-2, ruyoyo negative 2nd,<br> Ruyoyo comma | | Color name = ryy-2, ruyoyo negative 2nd,<br> Ruyoyo comma | ||
| FJS name = d-2<sup>25</sup><sub>7</sub> | | FJS name = d-2<sup>25</sup><sub>7</sub> | ||
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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]]). | 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]]). | ||
It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[ | |||
It is also the difference between [[81/80]] and [[126/125]] and is tempered out alongside these two commas in [[septimal meantone]]. In the 11-limit, it factors neatly into ([[385/384]])([[540/539]]). | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]]. | Tempering out this comma leads to the [[marvel family]] of temperaments, which enables [[marvel chords]]. See [[marvel temperaments]] for a collection of rank-2 temperaments where it is tempered out. | ||
== Approximation == | |||
If we do not temper out this interval and instead repeatedly stack (and octave-reduce) it, we get [[311edo]], where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo. | |||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
Revision as of 12:48, 22 October 2022
| Interval information |
marvel comma
Ruyoyo comma
reduced
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).
It is also the difference between 81/80 and 126/125 and is tempered out alongside these two commas in septimal meantone. In the 11-limit, it factors neatly into (385/384)(540/539).
Temperaments
Tempering out this comma leads to the marvel family of temperaments, which enables marvel chords. See marvel temperaments for a collection of rank-2 temperaments where it is tempered out.
Approximation
If we do not temper out this interval and instead repeatedly stack (and octave-reduce) it, we get 311edo, where it is equal to 2 steps, meaning 311edo is a circle of 225/224's. Note that this is not true for 226/225 or 224/223, the adjacent superparticulars, as they accumulate too much error to close into a circle in 311edo.