50/49: Difference between revisions

| en = 50/49

| de = 50/49

| Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma

'''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]]) }}.  

[[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:

* ([[49/48]])/(50/49) = [[2401/2400]]

* (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]].

 

 

 

* [[List of superparticular intervals]]

* [[49/48]] – the large septimal sixth-tone

 

[[Category:Jubilismic]]

[[Category:Commas referencing a famous use of a number]]