50/49: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = 50/49

| de = 50/49

~~| en = 50/49~~

| es =

| ja =

}}

{{Infobox Interval

~~| JI glyph =~~

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

~~| Ratio = 50/49~~

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

~~| Monzo = 1 0 2 -2~~

| Comma = yes

~~| Cents = 34.97561~~

| Name = ~~jubilisma~~, ~~<br>~~septimal sixth-tone, ~~<br>~~tritonic diesis

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''50/49''' , the '''~~jubilisma~~''' (~~also~~ '''septimal sixth-tone''' or '''tritonic diesis''') is the only [[superparticular]] [[comma]] aside from [[126/125]] which has a numerator which is neither square nor 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 '''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'''. 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]]

* (50/49)/([[64/63]]) = [[225/224]]

* (50/49)/([[65/64]]) = [[640/637]]

* (50/49)/([[66/65]]) = [[1625/1617]]

* (50/49)/([[78/77]]) = [[275/273]]

* (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]].

== Approximations ==

== Etymology ==

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

== See also ==

* [[List of superparticular intervals]]

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

* [[Jubilismic family]]

[[Category:Jubilismic]]

* [https://en.wikipedia.org/wiki/Septimal_sixth-tone Septimal sixth-tone - Wikipedia]

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

[[Category:~~Medium comma]]~~

~~[[Category:Definition]]~~

~~[[Category:Interval]]~~

~~[[Category:Jubilisma]]~~

~~[[Category:Ratio~~]]

[[Category:~~Superparticular~~]]

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-{{interwiki
+{{Interwiki
+| en = 50/49
 | de = 50/49
-| en = 50/49
 | es =
 | ja =
 }}
 {{Infobox Interval
-| JI glyph =
+| Name = small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma
-| Ratio = 50/49
+| Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma
-| Monzo = 1 0 2 -2
+| Comma = yes
-| Cents = 34.97561
-| Name = jubilisma, <br>septimal sixth-tone, <br>tritonic diesis
-| Color name =
-| FJS name =
-| Sound =
 }}
+{{Wikipedia|Septimal third tone #Septimal sixth tone}}
-'''50/49''' , the '''jubilisma''' (also '''septimal sixth-tone''' or '''tritonic diesis''') is the only [[superparticular]] [[comma]] aside from [[126/125]] which has a numerator which is neither square nor 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 '''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'''. 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]]
+* (50/49)/([[64/63]]) = [[225/224]]
+* (50/49)/([[65/64]]) = [[640/637]]
+* (50/49)/([[66/65]]) = [[1625/1617]]
+* (50/49)/([[78/77]]) = [[275/273]]
+* (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]].
+== Approximations ==
+{{Interval edo approximation|min_edo=12}}
+== Etymology ==
+The name ''jubilisma'' is likely a reference to the 50-year biblical jubilee cycle.
 == See also ==
+* [[List of superparticular intervals]]
+* [[49/48]] – the large septimal sixth-tone
-* [[Jubilismic family]]
+[[Category:Jubilismic]]
-* [https://en.wikipedia.org/wiki/Septimal_sixth-tone Septimal sixth-tone - Wikipedia]
+[[Category:Commas referencing a famous use of a number]]
-[[Category:Medium comma]]
-[[Category:Definition]]
-[[Category:Interval]]
-[[Category:Jubilisma]]
-[[Category:Ratio]]
-[[Category:Superparticular]]