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 '''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 = ( | '''50/49''', the '''small septimal diesis''' (a.k.a. '''small septimal sixth-tone''' or '''septimal tritonic diesis'''), is a [[7-limit]] [[medium comma]] equal to {{nowrap| 50/49 = ([[10/7]])/([[7/5]]) }}. 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 == | == 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'''. | [[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'', but it ''can'' be equated with other commas; for example: | ''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: | ||
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Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]], and [[54edo]]. | 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]] | ||