50/49: Difference between revisions
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{{ | {{Interwiki | ||
| en = 50/49 | |||
| de = 50/49 | | de = 50/49 | ||
| es = | | es = | ||
| ja = | | ja = | ||
}} | }} | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma | ||
| Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma | | Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
{{Wikipedia|Septimal third tone#Septimal sixth tone}} | {{Wikipedia|Septimal third tone #Septimal sixth tone}} | ||
'''50/49''', the '''small septimal diesis''' (a.k.a. '''small septimal sixth-tone''' or '''septimal tritonic diesis'''), is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit aside from [[126/125]] and [[4375/4374]] 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, {{nowrap| 50/49 = ([[10/7]])/([[7/5]]) }}. | |||
== Temperaments == | |||
[[Tempering out]] this comma equates the two septimal tritones (i.e. [[7/5]] and [[10/7]]) with each other, leading to temperaments where [[sqrt(2/1)]] approximates both. In the [[2.5.7 subgroup]], this is known as the jubilic temperament, and the comma is thus known as the '''jubilisma'''. In the full 7-limit, this comma further equates [[15/14]] and [[21/20]] and enables all the [[jubilismic chords]]. | |||
''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', | ''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', but it ''can'' be equated with other commas; for example: | ||
* ([[36/35]])/(50/49) = [[126/125]] | * ([[36/35]])/(50/49) = [[126/125]] | ||
* ([[45/44]])/(50/49) = [[441/440]] | * ([[45/44]])/(50/49) = [[441/440]] | ||
* ([[49/48]])/(50/49) = [[2401/2400]] | |||
* (50/49)/([[55/54]]) = [[540/539]] | * (50/49)/([[55/54]]) = [[540/539]] | ||
* (50/49)/([[56/55]]) = [[1375/1372]] | * (50/49)/([[56/55]]) = [[1375/1372]] | ||
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* (50/49)/([[81/80]]) = [[4000/3969]] | * (50/49)/([[81/80]]) = [[4000/3969]] | ||
See [[Jubilismic family]] for the rank-3 family where it is tempered out, and [[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]]. | |||
== Approximations == | |||
{{Interval edo approximation|min_edo=12}} | |||
== Etymology == | |||
The name ''jubilisma'' is likely a reference to the 50-year biblical jubilee cycle. | |||
== See also == | == See also == | ||
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[[Category:Jubilismic]] | [[Category:Jubilismic]] | ||
[[Category:Commas | [[Category:Commas referencing a famous use of a number]] | ||