Projection pair: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 247755143 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 247765057 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 16:40:58 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 17:33:02 UTC</tt>.<br>
: The original revision id was <tt>247755143</tt>.<br>
: The original revision id was <tt>247765057</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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50421/50000: 3 50000/16807 to 2.5.7
50421/50000: 3 50000/16807 to 2.5.7
245/243: 5 243/49 to 2.3.7
245/243: 5 243/49 to 2.3.7
</pre></div>
126/125: 7 125/18
4000/3969: 5 3969/800 7 27783/4000 to 2.3.7/5
1728/1715: 5 1728/343 to 2.3.7
1029/1024: 3 1024/343 to 2.5.7
225/224: 7 225/32
19683/19600: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7
16875/16807: 5 84375/16807 7 16875/2401 to 2.3.7/5
10976/10935: 5 10976/2187 to 2.3.7
3136/3125: 5 3136/625 7 68841472/9765625 to 2.3.25/7
5120/5103: 7 5120/729
6144/6125: 3 6125/2048 to 2.5.7
33554432/33480743: 7 33554432/4782969
201768035/201326592: 5 201326592/40353607 to 2.3.7
65625/65536: 7 65536/9375
703125/702464: 5 702464/140625 7 3454189699072/494384765625 to 2.3.25/7
420175/419904: 5 882735153125/176319369216 7 419904/60025 to 2.3.245
2401/2400: 3 2401/800 to 2.5.7
4375/4374: 7 4374/625</pre></div>
<h4>Original HTML content:</h4>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Projection pair&lt;/title&gt;&lt;/head&gt;&lt;body&gt;By a &lt;em&gt;projection pair&lt;/em&gt; is meant a pair of two rational intervals which can be employed by the &lt;a class="wiki_link" href="/Scala"&gt;Scala&lt;/a&gt; &amp;quot;project&amp;quot; command to reduce a JI scale to a scale in a &lt;a class="wiki_link" href="/JI%20subgroup"&gt;JI subgroup&lt;/a&gt; of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing &lt;a class="wiki_link" href="/planar%20temperaments"&gt;planar temperaments&lt;/a&gt;, as the projection can then be viewed in lattice form by Scala's &amp;quot;lattice&amp;quot; or &amp;quot;lattice and player&amp;quot; command. &lt;br /&gt;
<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;Projection pair&lt;/title&gt;&lt;/head&gt;&lt;body&gt;By a &lt;em&gt;projection pair&lt;/em&gt; is meant a pair of two rational intervals which can be employed by the &lt;a class="wiki_link" href="/Scala"&gt;Scala&lt;/a&gt; &amp;quot;project&amp;quot; command to reduce a JI scale to a scale in a &lt;a class="wiki_link" href="/JI%20subgroup"&gt;JI subgroup&lt;/a&gt; of the group generated by the scale, in such a way that tempered versions of each are equivalent. This is particularly useful for analyzing &lt;a class="wiki_link" href="/planar%20temperaments"&gt;planar temperaments&lt;/a&gt;, as the projection can then be viewed in lattice form by Scala's &amp;quot;lattice&amp;quot; or &amp;quot;lattice and player&amp;quot; command. &lt;br /&gt;
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2430/2401: 5 2401/486 to 2.3.7&lt;br /&gt;
2430/2401: 5 2401/486 to 2.3.7&lt;br /&gt;
50421/50000: 3 50000/16807 to 2.5.7&lt;br /&gt;
50421/50000: 3 50000/16807 to 2.5.7&lt;br /&gt;
245/243: 5 243/49 to 2.3.7&lt;/body&gt;&lt;/html&gt;</pre></div>
245/243: 5 243/49 to 2.3.7&lt;br /&gt;
126/125: 7 125/18&lt;br /&gt;
4000/3969: 5 3969/800 7 27783/4000 to 2.3.7/5&lt;br /&gt;
1728/1715: 5 1728/343 to 2.3.7&lt;br /&gt;
1029/1024: 3 1024/343 to 2.5.7&lt;br /&gt;
225/224: 7 225/32&lt;br /&gt;
19683/19600: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7&lt;br /&gt;
16875/16807: 5 84375/16807 7 16875/2401 to 2.3.7/5&lt;br /&gt;
10976/10935: 5 10976/2187 to 2.3.7&lt;br /&gt;
3136/3125: 5 3136/625 7 68841472/9765625 to 2.3.25/7&lt;br /&gt;
5120/5103: 7 5120/729&lt;br /&gt;
6144/6125: 3 6125/2048 to 2.5.7&lt;br /&gt;
33554432/33480743: 7 33554432/4782969 &lt;br /&gt;
201768035/201326592: 5 201326592/40353607 to 2.3.7&lt;br /&gt;
65625/65536: 7 65536/9375&lt;br /&gt;
703125/702464: 5 702464/140625 7 3454189699072/494384765625 to 2.3.25/7&lt;br /&gt;
420175/419904: 5 882735153125/176319369216 7 419904/60025 to 2.3.245&lt;br /&gt;
2401/2400: 3 2401/800 to 2.5.7&lt;br /&gt;
4375/4374: 7 4374/625&lt;/body&gt;&lt;/html&gt;</pre></div>