4375/4374: Difference between revisions

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'''4375/4374''', the '''ragisma''', being the difference between a stack of two [[27/25|large limmas]] and [[7/6]], is a [[7-limit]] [[~~unnoticeable~~ comma]]. It is the smallest 7-limit [[superparticular]] ratio~~. It is tempered out in [[ragismic microtemperaments]]~~. 4375/4374 is also equal to ([[25/18]])2/([[27/14]]) and the difference between a [[kleisma]] (S252 × S26) and a [[marvel comma]] (S15 = S25 × S26 × S27), hence its expression as S25 / S27 which directly implies it can be expressed as (28/24 = [[7/6]])/([[27/25]])2.

'''4375/4374''', the '''ragisma''', being the difference between a stack of two [[27/25|large limmas]] and [[7/6]], is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]]. It is the smallest 7-limit [[superparticular]] ratio. 4375/4374 is also equal to ([[25/18]])2/([[27/14]]) and the difference between a [[kleisma]] (S252 × S26) and a [[marvel comma]] (S15 = S25 × S26 × S27), hence its expression as S25 / S27 which directly implies it can be expressed as (28/24 = [[7/6]])/([[27/25]])2.

== Temperaments ==

[[Tempering out]] this comma leads to the [[ragismic]] temperament, enabling [[ragismic chords]] in the [[27-odd-limit]]. See [[Ragismic family]] for the rank-3 family where it is tempered out. See [[Ragismic microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.

== Etymology ==

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== See also ==

* [[Ragismic chords]]

* [[Ragismic family]] – the rank-3 family where it is tempered out

* [[Ragismic microtemperaments]] – a collection of rank-2 temperaments where it is tempered out

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

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 {{Wikipedia|Ragisma}}
-'''4375/4374''', the '''ragisma''', being the difference between a stack of two [[27/25|large limmas]] and [[7/6]], is a [[7-limit]] [[unnoticeable comma]]. It is the smallest 7-limit [[superparticular]] ratio. It is tempered out in [[ragismic microtemperaments]]. 4375/4374 is also equal to ([[25/18]])<sup>2</sup>/([[27/14]]) and the difference between a [[kleisma]] (S25<sup>2</sup> × S26) and a [[marvel comma]] (S15 = S25 × S26 × S27), hence its expression as S25 / S27 which directly implies it can be expressed as (28/24 = [[7/6]])/([[27/25]])<sup>2</sup>.
+'''4375/4374''', the '''ragisma''', being the difference between a stack of two [[27/25|large limmas]] and [[7/6]], is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]]. It is the smallest 7-limit [[superparticular]] ratio. 4375/4374 is also equal to ([[25/18]])<sup>2</sup>/([[27/14]]) and the difference between a [[kleisma]] (S25<sup>2</sup> × S26) and a [[marvel comma]] (S15 = S25 × S26 × S27), hence its expression as S25 / S27 which directly implies it can be expressed as (28/24 = [[7/6]])/([[27/25]])<sup>2</sup>.
+== Temperaments ==
+[[Tempering out]] this comma leads to the [[ragismic]] temperament, enabling [[ragismic chords]] in the [[27-odd-limit]]. See [[Ragismic family]] for the rank-3 family where it is tempered out. See [[Ragismic microtemperaments]] for a collection of rank-2 temperaments where it is tempered out.
 == Etymology ==
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 == See also ==
-* [[Ragismic chords]]
-* [[Ragismic family]] – the rank-3 family where it is tempered out
-* [[Ragismic microtemperaments]] – a collection of rank-2 temperaments where it is tempered out
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]