50/49: Difference between revisions

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<h2>~~IMPORTED REVISION FROM WIKISPACES<~~/~~h2>~~

{{Interwiki

~~This~~ is ~~an imported revision~~ from ~~Wikispaces. The revision metadata~~ is ~~included below for reference:<br>~~

| en = 50/49

~~: This revision was~~ by ~~author~~ [[~~User:genewardsmith|genewardsmith~~]] ~~and made on <tt>2011-08-08 14:29:18 UTC<~~/~~tt>~~.~~<br>~~

| de = 50/49

~~: The original revision id was <tt>244873375<~~/~~tt>.<br>~~

| es =

~~: The revision comment was: <tt><~~/~~tt><br>~~

| ja =

~~The revision contents are below~~, ~~presented~~ both in the ~~original Wikispaces Wikitext format~~, and ~~in HTML exactly~~ as ~~Wikispaces rendered it~~.~~<br>~~

}}

~~<h4>Original Wikitext content:</h4>~~

{{Infobox Interval

~~<div style="width:100%; max~~-~~height:400pt; overflow:auto; background~~-~~color:#f8f9fa~~; ~~border~~: ~~1px solid #eaecf0; padding:0em"><pre style~~=~~"margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class~~=~~"old-revision-html">~~[[~~http:~~//~~en.wikipedia.org~~/~~wiki~~/~~Septimal_sixth-tone~~]]</~~pre><~~/~~div>~~

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

~~<h4>Original HTML content:<~~/~~h4>~~

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

~~<div style~~=~~"width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style~~=~~"margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class~~=~~"old-revision-html"><html><head><title>50_49<~~/~~title><~~/~~head><body><a class~~=~~"wiki_link_ext" href="http:~~//~~en.wikipedia.org~~/~~wiki~~/~~Septimal_sixth-tone" rel~~=~~"nofollow">http:~~//en.~~wikipedia~~.~~org~~/~~wiki/Septimal_sixth~~-tone~~</~~a~~></body></html></pre></div>~~

| Comma = yes

}}

'''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

[[Category:Jubilismic]]

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

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Interwiki
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| en = 50/49
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-08 14:29:18 UTC</tt>.<br>
+| de = 50/49
-: The original revision id was <tt>244873375</tt>.<br>
+| es =
-: The revision comment was: <tt></tt><br>
+| ja =
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+}}
-<h4>Original Wikitext content:</h4>
+{{Infobox Interval
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[http://en.wikipedia.org/wiki/Septimal_sixth-tone]]</pre></div>
+| Name = small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma
-<h4>Original HTML content:</h4>
+| Color name = rryy-2, biruyo negative 2nd,<br>Biruyo comma
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;50_49&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_sixth-tone" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_sixth-tone&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+| Comma = yes
+}}
+{{Wikipedia|Septimal third tone #Septimal sixth tone}}
+'''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
+[[Category:Jubilismic]]
+[[Category:Commas referencing a famous use of a number]]