4375/4374: Difference between revisions
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{{Wikipedia|Ragisma}} | {{Wikipedia|Ragisma}} | ||
'''4375/4374''', the '''ragisma''', being the difference between a stack of two [[27/25|large limmas]] and [[7/6]], is | '''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 == | == Etymology == | ||
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== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Revision as of 11:26, 5 November 2024
| Interval information |
Zoquadyo comma
reduced
4375/4374, the ragisma, being the difference between a stack of two large limmas and 7/6, is an 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
This comma was allegedly named by Erv Wilson no later than 2001[1]. Interestingly, by 2004 people had already lost track of its origin and meaning[2]. Maybe it was named after Indian ragas? (Pure speculation.)