50/49: Difference between revisions

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'''50/49''', the '''~~jubilisma~~''' ~~(also~~ '''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~~, 50/49 = ([[10/7]])/([[7/5]]).

'''50/49''', also known as the '''small septimal sixth-tone''', '''small septimal diesis''', '''septimal tritonic diesis''', or '''jubilisma''', 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, 50/49 = ([[10/7]])/([[7/5]]).

''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', however, 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, however, it ''can'' be equated with other commas; for example:

* ([[36/35]])/(50/49) = [[126/125]]

* ([[45/44]])/(50/49) = [[441/440]]

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== Temperaments ==

[[Tempering out]] this comma equates the ~~tritone~~ [[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.

[[Tempering out]] this comma equates the two septimal tritones (i.e. [[7/5]] and [[10/7]]) with each other, leading to temperaments where the square root of two approximates both. 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]].

Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]], and [[54edo]].

== See also ==

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 {{Wikipedia|Septimal third tone#Septimal sixth tone}}
-'''50/49''', the '''jubilisma''' (also '''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, 50/49 = ([[10/7]])/([[7/5]]).
+'''50/49''', also known as the '''small septimal sixth-tone''', '''small septimal diesis''', '''septimal tritonic diesis''', or '''jubilisma''', 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, 50/49&nbsp;=&nbsp;([[10/7]])/([[7/5]]).
-''It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct'', however, 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, however, it ''can'' be equated with other commas; for example:
 * ([[36/35]])/(50/49) = [[126/125]]
 * ([[45/44]])/(50/49) = [[441/440]]
@@ Line 26: / Line 26: @@
 == Temperaments ==
-[[Tempering out]] this comma equates the tritone [[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.
+[[Tempering out]] this comma equates the two septimal tritones (i.e. [[7/5]] and [[10/7]]) with each other, leading to temperaments where the square root of two approximates both. 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]].
+Equal temperaments tempering out 50/49 include [[12edo]], [[22edo]], [[26edo]], [[38edo]], [[48edo]], and [[54edo]].
 == See also ==