50/49: Difference between revisions
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Added Wikipedia box, added color name, misc. edits, categories |
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 50/49 | | Ratio = 50/49 | ||
| Monzo = 1 0 2 -2 | | Monzo = 1 0 2 -2 | ||
| Cents = 34.97561 | | Cents = 34.97561 | ||
| Name = jubilisma, <br>septimal sixth-tone, <br>tritonic diesis | | Name = jubilisma, <br>septimal sixth-tone, <br>tritonic diesis | ||
| Color name = | | Color name = rryy-2, biruyo negative 2nd | ||
| FJS name = d-2<sup>25</sup><sub>49</sub> | | FJS name = d-2<sup>25</sup><sub>49</sub> | ||
| Sound = | | Sound = | ||
}} | }} | ||
{{Wikipedia|Septimal third tone#Septimal sixth tone}} | |||
'''50/49''', the '''jubilisma''' (also '''septimal sixth-tone''' or '''tritonic diesis''') 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, 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 == | ||
* [[Jubilismic family]] | * [[Jubilismic family]] | ||
* [[Jubilismic clan]] | * [[Jubilismic clan]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Medium comma]] | [[Category:Medium comma]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Jubilismic]] | [[Category:Jubilismic]] | ||
{{todo|clarify}} <!-- only superparticular comma... in the 7-limit only, maybe? --> | |||
Revision as of 03:54, 20 December 2021
| 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.