50/49: Difference between revisions
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Cmloegcmluin (talk | contribs) direct triangular number link to definition within the xen wiki, to provide justifiably relevant xen-related information |
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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, 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 two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]] and [[54edo]]. | '''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 two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]] and [[54edo]]. | ||
== See also == | == See also == | ||
Revision as of 22:10, 19 January 2022
| Interval information |
septimal sixth-tone,
tritonic diesis
reduced
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, 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 two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include 12edo, 22edo, 26edo, 38edo, 48edo and 54edo.