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49/48: 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>
| de = 49/48
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 12:49:54 UTC</tt>.<br>
| en = 49/48
: The original revision id was <tt>602874810</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 large septimal or slendro diesis, 49/48 (35.6968 [[cent|cents]]), is a [[superparticular]] ratio spanning the small distance between a subminor third of [[7_6|7/6]] and a supermajor second of [[8_7|8/7]]. It is tempered out in [[15edo]] and [[19edo]], where the two intervals are equated. It cannot be tempered out if all of the consonances of the 7-limit are distinct, but it can be equated with other commas; for example (49/48)/(81/80) = 245/243, (49/48)/(64/63) = 1029/1024, (49/48)/(3125/3072) = 3136/3125, (49/48)/(50/49) = 2401/2400, (128/125)/(49/48) = 6144/6125, (36/35)/(49/48) = 1728/1715.
| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma
| Color name = zz2, zozo 2nd,<br>zzM, zozoma
| Sound = Ji-49-48-csound-foscil-220hz.mp3
| Comma = yes
}}
{{Wikipedia|Septimal diesis}}
'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[superparticular]] ratio spanning the small distance between a subminor third ([[7/6]]) and a supermajor second ([[8/7]]) or between the supermajor sixth ([[12/7]]) and the harmonic seventh ([[7/4]]). Measuring about 35.7{{cent}}, it is a [[medium comma]]; however, in classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo|12tet]].


This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1|1]], [[3/1|3]], and [[7/1|7]] [[octave reduced]] to span the [[4/3|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15|1/(6:5:4)]].


[[http://en.wikipedia.org/wiki/Septimal_diesis]]</pre></div>
== Temperaments ==
<h4>Original HTML content:</h4>
49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where 7/6 and 8/7 are equated, and the fourth is split in a perfect half. 3/1 is also split into two [[7/4]]~[[12/7]]'s. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''.  
<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;49_48&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The large septimal or slendro diesis, 49/48 (35.6968 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt;), is a &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; ratio spanning the small distance between a subminor third of &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; and a supermajor second of &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;. It is tempered out in &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; and &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, where the two intervals are equated. It cannot be tempered out if all of the consonances of the 7-limit are distinct, but it can be equated with other commas; for example (49/48)/(81/80) = 245/243, (49/48)/(64/63) = 1029/1024, (49/48)/(3125/3072) = 3136/3125, (49/48)/(50/49) = 2401/2400, (128/125)/(49/48) = 6144/6125, (36/35)/(49/48) = 1728/1715.&lt;br /&gt;
 
&lt;br /&gt;
''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:
&lt;br /&gt;
* (49/48)/([[81/80]]) = [[245/243]]
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_diesis" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_diesis&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* (49/48)/([[64/63]]) = [[1029/1024]]
* (49/48)/([[3125/3072]]) = [[3136/3125]]
* (49/48)/([[50/49]]) = [[2401/2400]]
* ([[128/125]])/(49/48) = [[6144/6125]]
* ([[36/35]])/(49/48) = [[1728/1715]]
 
See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out.
 
== Approximations ==
{{interval edo approximation|min_edo=5}}
 
== See also ==
* [[Medium comma]]
* [[List of superparticular intervals]]
* [[Gallery of just intervals]]
 
[[Category:Semaphore]]
[[Category:Semaphoresmic]]
[[Category:Commas named for how they divide the fourth]]
[[Category:Commas named after musical traditions]]
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