50/49: Difference between revisions

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'''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]].

'''50/49''', the '''jubilisma''' (also '''septimal sixth-tone''' or '''tritonic diesis''') is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit 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]]).

== Temperaments ==

[[Tempering out]] this comma equates the 7/5 with 10/7, its octave complement, leading to temperaments where the square root of two does service for both. See [[Jubilismic family]] for the rank-3 family where it is tempered out. See [[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]].

== See also ==

* [[Jubilismic family]]

* [[Jubilismic clan]]

* [[List of superparticular intervals]]

[[Category:Jubilismic]]

~~{{todo|clarify}} ~~

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 {{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 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]].
+'''50/49''', the '''jubilisma''' (also '''septimal sixth-tone''' or '''tritonic diesis''') is a [[7-limit]] [[medium comma]]. It is the only [[superparticular]] [[comma]] in the 7-limit 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]]).
+== Temperaments ==
+[[Tempering out]] this comma equates the 7/5 with 10/7, its octave complement, leading to temperaments where the square root of two does service for both. See [[Jubilismic family]] for the rank-3 family where it is tempered out. See [[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]].
 == See also ==
-* [[Jubilismic family]]
-* [[Jubilismic clan]]
 * [[List of superparticular intervals]]
 [[Category:Jubilismic]]
-{{todo|clarify}} <!-- only superparticular comma... in the 7-limit only, maybe? -->