50/49: Difference between revisions
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{{Wikipedia|Septimal third tone#Septimal sixth tone}} | {{Wikipedia|Septimal third tone#Septimal sixth tone}} | ||
'''50/49''', the '''jubilisma''' (also '''septimal sixth-tone''' or '''tritonic diesis''') is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] aside from [[126/125]] which has a numerator which is neither square nor [[triangular number|triangular]], meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = ([[10/7]])/([[7/5]]). [[Tempering out]] equates the | '''50/49''', the '''jubilisma''' (also '''septimal sixth-tone''' or '''tritonic diesis''') is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit aside from [[126/125]] which has a numerator which is neither square nor [[triangular number|triangular]], meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = ([[10/7]])/([[7/5]]). | ||
== Temperaments == | |||
[[Tempering out]] this comma equates the 7/5 with 10/7, its octave complement, leading to temperaments where the square root of two does service for both. See [[Jubilismic family]] for the rank-3 family where it is tempered out. See [[Jubilismic clan]] for the rank-2 clan where it is tempered out. | |||
Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]] and [[54edo]]. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Jubilismic]] | [[Category:Jubilismic]] | ||
Revision as of 08:27, 13 March 2023
| Interval information |
septimal sixth-tone,
tritonic diesis
Biruyo comma
reduced
50/49, the jubilisma (also septimal sixth-tone or tritonic diesis) is a 7-limit medium comma. It is the only superparticular comma in the 7-limit aside from 126/125 which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = (10/7)/(7/5).
Temperaments
Tempering out this comma equates the 7/5 with 10/7, its octave complement, leading to temperaments where the square root of two does service for both. See Jubilismic family for the rank-3 family where it is tempered out. See Jubilismic clan for the rank-2 clan where it is tempered out.
Equal temperaments tempering out 50/49 include 12edo, 22edo, 26edo, 38edo, 48edo and 54edo.