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Kite's thoughts on pergens: Difference between revisions

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**Imported revision 625629867 - Original comment: **
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**Imported revision 625630605 - 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:TallKite|TallKite]] and made on <tt>2018-01-30 20:53:15 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-30 21:11:53 UTC</tt>.<br>
: The original revision id was <tt>625629867</tt>.<br>
: The original revision id was <tt>625630605</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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==Supplemental materials==  
==Supplemental materials==  


This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block.
This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block. It includes alternate enharmonics for many pergens.
http://www.tallkite.com/misc_files/pergens.pdf
http://www.tallkite.com/misc_files/pergens.pdf


Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.
Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. Alternate enharmonics are not listed, but single-pair notation for false-double pergens is. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.
http://www.tallkite.com/misc_files/alt-pergenLister.zip
http://www.tallkite.com/misc_files/alt-pergenLister.zip


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Simplify by dividing by b to get (P8/m, (q - ap, -m) / qm) = (P8/m, (a',b')/n')
Simplify by dividing by b to get (P8/m, (q - ap, -m) / qm) = (P8/m, (a',b')/n')
[//unfinished proof//]
[//unfinished proof//]
Although not rigorously proven, these last two tests have been empirically verified by alt-pergenlister.




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  &lt;br /&gt;
  &lt;br /&gt;
This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block.&lt;br /&gt;
This PDF is a rank-2 notation guide that shows the full lattice for the first 15 pergens, up through the third-splits block. It includes alternate enharmonics for many pergens.&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:4939:http://www.tallkite.com/misc_files/pergens.pdf --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/pergens.pdf" rel="nofollow"&gt;http://www.tallkite.com/misc_files/pergens.pdf&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4939 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:4941:http://www.tallkite.com/misc_files/pergens.pdf --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/pergens.pdf" rel="nofollow"&gt;http://www.tallkite.com/misc_files/pergens.pdf&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4941 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.&lt;br /&gt;
Alt-pergenLister lists out thousands of pergens, and suggests periods, generators and enharmonics for each one. Alternate enharmonics are not listed, but single-pair notation for false-double pergens is. It can also list only those pergens supported by a specific edo. Written in Jesusonic, runs inside Reaper.&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:4940:http://www.tallkite.com/misc_files/alt-pergenLister.zip --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergenLister.zip" rel="nofollow"&gt;http://www.tallkite.com/misc_files/alt-pergenLister.zip&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4940 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:4942:http://www.tallkite.com/misc_files/alt-pergenLister.zip --&gt;&lt;a class="wiki_link_ext" href="http://www.tallkite.com/misc_files/alt-pergenLister.zip" rel="nofollow"&gt;http://www.tallkite.com/misc_files/alt-pergenLister.zip&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:4942 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Screenshot of the first 38 pergens:&lt;br /&gt;
Screenshot of the first 38 pergens:&lt;br /&gt;
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Simplify by dividing by b to get (P8/m, (q - ap, -m) / qm) = (P8/m, (a',b')/n')&lt;br /&gt;
Simplify by dividing by b to get (P8/m, (q - ap, -m) / qm) = (P8/m, (a',b')/n')&lt;br /&gt;
[&lt;em&gt;unfinished proof&lt;/em&gt;]&lt;br /&gt;
[&lt;em&gt;unfinished proof&lt;/em&gt;]&lt;br /&gt;
&lt;br /&gt;
Although not rigorously proven, these last two tests have been empirically verified by alt-pergenlister.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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