50/49: Difference between revisions

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}}

{{Infobox Interval

| Name = ~~jubilisma,~~ small septimal sixth-tone, (septimal) tritonic diesis

| Name = small septimal sixth-tone, (septimal) tritonic diesis, jubilisma

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

| Comma = yes

}}

'''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, {{nowrap| 50/49 = ([[10/7]])/([[7/5]]) }}.

'''50/49''', the '''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]]) }}.

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:

== 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'''.

''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]]

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

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* (50/49)/([[81/80]]) = [[4000/3969]]

~~== Temperaments ==~~

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.

~~[[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]].

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 }}
 {{Infobox Interval
-| Name = jubilisma, small septimal sixth-tone, (septimal) tritonic diesis
+| Name = small septimal sixth-tone, (septimal) tritonic diesis, jubilisma
 | Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma
 | Comma = yes
 }}
-{{Wikipedia|Septimal third tone#Septimal sixth tone}}
+{{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, {{nowrap| 50/49 = ([[10/7]])/([[7/5]]) }}.
+'''50/49''', the '''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]]) }}.
-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:
+== 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'''.
+''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]]
 * ([[45/44]])/(50/49) = [[441/440]]
@@ Line 25: / Line 28: @@
 * (50/49)/([[81/80]]) = [[4000/3969]]
-== Temperaments ==
+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.
-[[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]].