127edo: Difference between revisions

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

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

~~: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 02:11:10 UTC</tt>.<br>~~

~~: The original revision id was <tt>288887301</tt>.<br>~~

~~: 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>~~

<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">**127edo**, which divides the [[octave]] into 127 parts of 9.45 [[cents]] each, is another equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]. In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence supports [[Würschmidt family|würschmidt temperament]]. In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

127edo is the ~~31st~~ [[~~prime numbers~~|~~prime~~]] ~~edo~~.

== Theory ==

127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]:

* In the [[5-limit]], it tempers out 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[würschmidt]] temperament.

* In the [[7-limit]], it also tempers out [[225/224]], and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.

* In the [[11-limit]], it tempers out [[99/98]], [[176/175]] and [[243/242]], and is an excellent tuning for the 11-limit version of würschmidt, as well as [[minerva]], the [[rank-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val.

~~[[MOS Scales of 127edo]]</pre></div>~~

=== Odd harmonics ===

~~<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>127edo</title></head><body><strong>127edo</strong>, which divides the <a class~~=~~"wiki_link" href~~=~~"/octave">octave</a> into 127 parts of 9.45 <a class~~=~~"wiki_link" href~~=~~"/cents">cents</a> each, is another~~ equal ~~division interesting because of its approximations, defined by the <a class~~=~~"wiki_link" href~~=~~"/comma">comma</a>s it <a class~~=~~"wiki_link" href~~=~~"/tempering%20out">tempers out</a>. In the <a class~~=~~"wiki_link" href~~=~~"/5-limit">5-limit</a>, it tempers out~~ the ~~würschmidt comma~~, ~~393216/390625~~ and ~~hence supports <a class~~=~~"wiki_link" href~~=~~"/W%C3%BCrschmidt%20family">würschmidt temperament</a>. In the <a class~~=~~"wiki_link" href~~=~~"/7-limit">7-limit</a>, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the <a class~~=~~"wiki_link" href~~="/11-limit">11-limit</a>, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the <a class=~~"wiki_link" href~~=~~"/optimal%20patent%20val">optimal patent val</a> and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val~~.~~<br />~~

~~<br />~~

=== Subsets and supersets ===

~~127edo is the 31st <a class~~=~~"wiki_link" href~~=~~"/prime%20numbers">prime</a> edo.<br />~~

127edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]].

~~<br />~~

~~<a class~~=~~"wiki_link" href~~=~~"/MOS%20Scales%20of%20127edo">MOS Scales of~~ 127edo~~</a></body></html></pre></div>~~

== Scales ==

=== MOS scales ===

See [[List of MOS scales in 127edo]].

== Instruments ==

* [[Lumatone mapping for 127edo]]

[[Category:Würschmidt]]

[[Category:Hemiwürschmidt]]

[[Category:Minerva]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+{{ED intro}}
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 02:11:10 UTC</tt>.<br>
-: The original revision id was <tt>288887301</tt>.<br>
-: 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>
-<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">**127edo**, which divides the [[octave]] into 127 parts of 9.45 [[cents]] each, is another equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]. In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence supports [[Würschmidt family|würschmidt temperament]]. In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
-edo is the 31st [[prime numbers|prime]] edo.
+== Theory ==
+edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out|tempers out]]:
+* In the [[5-limit]], it tempers out 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[würschmidt]] temperament.
+* In the [[7-limit]], it also tempers out [[225/224]], and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
+* In the [[11-limit]], it tempers out [[99/98]], [[176/175]] and [[243/242]], and is an excellent tuning for the 11-limit version of würschmidt, as well as [[minerva]], the [[rank-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val.
-[[MOS Scales of 127edo]]</pre></div>
+=== Odd harmonics ===
-<h4>Original HTML content:</h4>
+{{Harmonics in equal|127}}
-<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;127edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;127edo&lt;/strong&gt;, which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 127 parts of 9.45 &lt;a class="wiki_link" href="/cents"&gt;cents&lt;/a&gt; each, is another equal division interesting because of its approximations, defined by the &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s it &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt;. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out the würschmidt comma, 393216/390625 and hence supports &lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family"&gt;würschmidt temperament&lt;/a&gt;. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.&lt;br /&gt;
-&lt;br /&gt;
+=== Subsets and supersets ===
-edo is the 31st &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo.&lt;br /&gt;
+edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]].
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/MOS%20Scales%20of%20127edo"&gt;MOS Scales of 127edo&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+== Scales ==
+=== MOS scales ===
+See [[List of MOS scales in 127edo]].
+== Instruments ==
+* [[Lumatone mapping for 127edo]]
+[[Category:Würschmidt]]
+[[Category:Hemiwürschmidt]]
+[[Category:Minerva]]