50/49: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = 50/49

| de = 50/49

~~| en = 50/49~~

| es =

| ja =

}}

{{Infobox Interval

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

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

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

| Comma = yes

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'''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]]) }}.

'''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]]) }}.

== 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:

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

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

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

* (50/49)/([[55/54]]) = [[540/539]]

* (50/49)/([[56/55]]) = [[1375/1372]]

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

== Approximations ==

== Etymology ==

The name ''jubilisma'' is likely a reference to the 50-year biblical jubilee cycle.

== See also ==

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[[Category:Jubilismic]]

[[Category:Commas ~~with unknown etymology~~]]

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

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-{{interwiki
+{{Interwiki
+| en = 50/49
 | de = 50/49
-| en = 50/49
 | es =
 | ja =
 }}
 {{Infobox Interval
-| Name = small septimal sixth-tone, (septimal) tritonic diesis, jubilisma
+| Name = small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma
 | Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma
 | Comma = yes
@@ Line 12: / Line 12: @@
 {{Wikipedia|Septimal third tone #Septimal sixth tone}}
-'''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]]) }}.
+'''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]]) }}.
 == 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:
 * ([[36/35]])/(50/49) = [[126/125]]
 * ([[45/44]])/(50/49) = [[441/440]]
+* ([[49/48]])/(50/49) = [[2401/2400]]
 * (50/49)/([[55/54]]) = [[540/539]]
 * (50/49)/([[56/55]]) = [[1375/1372]]
@@ Line 31: / Line 32: @@
 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 ==
@@ Line 37: / Line 44: @@
 [[Category:Jubilismic]]
-[[Category:Commas with unknown etymology]]
+[[Category:Commas referencing a famous use of a number]]