4375/4374: Difference between revisions
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{{Wikipedia|Ragisma}} | {{Wikipedia|Ragisma}} | ||
'''4375/4374''', the '''ragisma''', is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] which is the difference between a stack of two [[27/25|large limmas]] and [[7/6]], the difference between a stack of four [[10/9|classical whole tones (10/9)]] and [[32/21]], and the difference between a stack of four [[6/5|classical minor thirds (6/5)]] [[octave reduction|octave-reduced]] and [[28/27]]. It is the smallest 7-limit [[superparticular]] ratio. It is also equal to 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''', is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] which is the difference between a stack of two [[27/25|large limmas]] and [[7/6]], the difference between a stack of four [[10/9|classical whole tones (10/9)]] and [[32/21]], and the difference between a stack of four [[6/5|classical minor thirds (6/5)]] [[octave reduction|octave-reduced]] and [[28/27]]. It is the smallest 7-limit [[superparticular]] ratio. It is also equal to the difference between a [[15625/15552|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 == | == Temperaments == | ||
Latest revision as of 23:31, 12 July 2025
| Interval information |
Zoquadyo comma
reduced
4375/4374, the ragisma, is an unnoticeable 7-limit comma which is the difference between a stack of two large limmas and 7/6, the difference between a stack of four classical whole tones (10/9) and 32/21, and the difference between a stack of four classical minor thirds (6/5) octave-reduced and 28/27. It is the smallest 7-limit superparticular ratio. It is also equal to 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]. It is speculated that it could have been named after Indian ragas.