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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:xenwolf|xenwolf]] and made on <tt>2011-08-09 03:11:33 UTC</tt>.<br>
| | | de = 50/49 |
| : The original revision id was <tt>244988225</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">The **septimal sixth-tone** or **jubilisma**, 50/49, is the only superparticular [[comma]] aside from [[126_125|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|10/7]])/([[7_5|7/5]]). [[tempering out|Tempering it 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|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]] and [[54edo]].
| | | Name = small septimal diesis, 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}} |
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| [[http://en.wikipedia.org/wiki/Septimal_sixth-tone]]</pre></div>
| | '''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]]) }}. |
| <h4>Original HTML content:</h4>
| | |
| <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>The <strong>septimal sixth-tone</strong> or <strong>jubilisma</strong>, 50/49, is the only superparticular <a class="wiki_link" href="/comma">comma</a> aside from <a class="wiki_link" href="/126_125">126/125</a> 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 = (<a class="wiki_link" href="/10_7">10/7</a>)/(<a class="wiki_link" href="/7_5">7/5</a>). <a class="wiki_link" href="/tempering%20out">Tempering it out</a> equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/38edo">38</a>, <a class="wiki_link" href="/48edo">48</a> and <a class="wiki_link" href="/54edo">54edo</a>.<br />
| | == Temperaments == |
| <br />
| | [[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]]. |
| <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>
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| | ''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]] |