2197/2187: Difference between revisions

The threedie, 2197/2187, is a 3.13-subgroup analog of the 2.5-subgroup diesis. Measuring about 7.9 ¢, it is a small comma. Analogous to tempering out the diesis, which divides the octave into three sharp 5/4's, tempering out the threedie divides the tritave into three slightly flat 13/9's, since (13/9)³/3 = 2197/2187. Furthermore, tempering out the threedie divides 9/8 into three instances of 27/26. 596edo provides the optimal patent val for the corresponding rank-5 temperament.

It factors into simpler commas in the 2.3.5.13 subgroup as (325/324)(676/675), or can be expressed in the 2.3.7.13 subgroup as (169/168)/(729/728), i.e. S13/S27.

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox Interval
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| Name = threedie
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-09-12 17:10:23 UTC</tt>.<br>
+| Color name = s3o<sup>3</sup>2, satritho 2nd,<br>Satritho comma
-: The original revision id was <tt>450702378</tt>.<br>
+| Comma = yes
-: The revision comment was: <tt></tt><br>
+}}
-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>
+The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.
-<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">Threedie, the interval 13^3/3^7, is a 3.13 analog of the 2.5 [[128_125|diesis]], 2^7/5^3. Tempering by it, instead of chopping the octave into three sharp 5/4s, chops the tritave (3) into three slightly flat 13/9s, since (13/9)^3/3 = 2197/2187. 596 provides the optimal patent val for the corresponding rank five temperament.</pre></div>
-<h4>Original HTML content:</h4>
+It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. S13/S27.
-<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;threedie&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Threedie, the interval 13^3/3^7, is a 3.13 analog of the 2.5 &lt;a class="wiki_link" href="/128_125"&gt;diesis&lt;/a&gt;, 2^7/5^3. Tempering by it, instead of chopping the octave into three sharp 5/4s, chops the tritave (3) into three slightly flat 13/9s, since (13/9)^3/3 = 2197/2187. 596 provides the optimal patent val for the corresponding rank five temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
+[[Category:Commas with unknown etymology]]

2197/2187: Difference between revisions

Latest revision as of 23:57, 15 November 2024

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