4375/4374: Difference between revisions

'''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]] (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.

 

[[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.  

This comma was allegedly named by [[Erv Wilson]] no later than 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_22165.html#22220 Yahoo! Tuning Group | ''Re: What is a monzisma?'']</ref>. Interestingly, by 2004 people had already lost track of its origin and meaning<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10195.html#10202 Yahoo! Tuning Group | ''Comma names'']</ref>. It is speculated that it could have been named after [[Indian]] ragas.