Optimal patent val: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 201493456 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 201602598 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-02-14 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-14 11:40:28 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>201602598</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> | ||
<h4>Original Wikitext content:</h4> | <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">Given any collection of p-limit commas, there is a finite list of p-limit [[Patent val|patent vals]] tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest [[Tenney-Euclidean temperament measures|TE error]]; this is the //optimal (TE) patent val// for the temperament defined by the commas. Below are tabulated some values. | <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">Given any collection of p-limit commas, there is a finite list of p-limit [[Patent val|patent vals]] tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest [[Tenney-Euclidean temperament measures|TE error]]; this is the //optimal (TE) patent val// for the temperament defined by the commas. Note that other defintions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results. Below are tabulated some values. | ||
==5-limit rank two== | ==5-limit rank two== | ||
27/25: [[14edo]] | |||
16/15: [[8edo]] | 16/15: [[8edo]] | ||
135/128: [[23edo]] | |||
25/24: [[17edo]] | 25/24: [[17edo]] | ||
648/625: [[12edo]] | 648/625: [[12edo]] | ||
| Line 17: | Line 19: | ||
81/80: [[81edo]] | 81/80: [[81edo]] | ||
2048/2025: [[80edo]] | 2048/2025: [[80edo]] | ||
78732/78125: [[539edo]] | |||
393216/390625: [[164edo]] | |||
2109375/2097152: [[296edo]] | |||
15625/15552: [[458edo]] | |||
1600000/1594323: [[873edo]] | |||
1224440064/1220703125: [[1496edo]] | |||
6115295232/6103515625: [1400edo]] | |||
32805/32768: [[749edo]] | |||
274877906944/274658203125: [[1559edo]] | |||
7629394531250/7625597484987: [[3501edo]] | |||
</pre></div> | </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"><html><head><title>Optimal patent val</title></head><body>Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the <em>optimal (TE) patent val</em> for the temperament defined by the commas. Below are tabulated some values.<br /> | <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>Optimal patent val</title></head><body>Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the <em>optimal (TE) patent val</em> for the temperament defined by the commas. Note that other defintions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results. Below are tabulated some values.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-5-limit rank two"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit rank two</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-5-limit rank two"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit rank two</h2> | ||
27/25: <a class="wiki_link" href="/14edo">14edo</a><br /> | |||
16/15: <a class="wiki_link" href="/8edo">8edo</a><br /> | 16/15: <a class="wiki_link" href="/8edo">8edo</a><br /> | ||
135/128: <a class="wiki_link" href="/23edo">23edo</a><br /> | |||
25/24: <a class="wiki_link" href="/17edo">17edo</a><br /> | 25/24: <a class="wiki_link" href="/17edo">17edo</a><br /> | ||
648/625: <a class="wiki_link" href="/12edo">12edo</a><br /> | 648/625: <a class="wiki_link" href="/12edo">12edo</a><br /> | ||
| Line 29: | Line 44: | ||
3125/3072: <a class="wiki_link" href="/60edo">60edo</a><br /> | 3125/3072: <a class="wiki_link" href="/60edo">60edo</a><br /> | ||
81/80: <a class="wiki_link" href="/81edo">81edo</a><br /> | 81/80: <a class="wiki_link" href="/81edo">81edo</a><br /> | ||
2048/2025: <a class="wiki_link" href="/80edo">80edo</a></body></html></pre></div> | 2048/2025: <a class="wiki_link" href="/80edo">80edo</a><br /> | ||
78732/78125: <a class="wiki_link" href="/539edo">539edo</a><br /> | |||
393216/390625: <a class="wiki_link" href="/164edo">164edo</a><br /> | |||
2109375/2097152: <a class="wiki_link" href="/296edo">296edo</a><br /> | |||
15625/15552: <a class="wiki_link" href="/458edo">458edo</a><br /> | |||
1600000/1594323: <a class="wiki_link" href="/873edo">873edo</a><br /> | |||
1224440064/1220703125: <a class="wiki_link" href="/1496edo">1496edo</a><br /> | |||
6115295232/6103515625: [1400edo]]<br /> | |||
32805/32768: <a class="wiki_link" href="/749edo">749edo</a><br /> | |||
274877906944/274658203125: <a class="wiki_link" href="/1559edo">1559edo</a><br /> | |||
7629394531250/7625597484987: <a class="wiki_link" href="/3501edo">3501edo</a></body></html></pre></div> | |||
Revision as of 11:40, 14 February 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-02-14 11:40:28 UTC.
- The original revision id was 201602598.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
Given any collection of p-limit commas, there is a finite list of p-limit [[Patent val|patent vals]] tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest [[Tenney-Euclidean temperament measures|TE error]]; this is the //optimal (TE) patent val// for the temperament defined by the commas. Note that other defintions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results. Below are tabulated some values. ==5-limit rank two== 27/25: [[14edo]] 16/15: [[8edo]] 135/128: [[23edo]] 25/24: [[17edo]] 648/625: [[12edo]] 250/243: [[22edo]] 128/125: [[39edo]] 3125/3072: [[60edo]] 81/80: [[81edo]] 2048/2025: [[80edo]] 78732/78125: [[539edo]] 393216/390625: [[164edo]] 2109375/2097152: [[296edo]] 15625/15552: [[458edo]] 1600000/1594323: [[873edo]] 1224440064/1220703125: [[1496edo]] 6115295232/6103515625: [1400edo]] 32805/32768: [[749edo]] 274877906944/274658203125: [[1559edo]] 7629394531250/7625597484987: [[3501edo]]
Original HTML content:
<html><head><title>Optimal patent val</title></head><body>Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the <em>optimal (TE) patent val</em> for the temperament defined by the commas. Note that other defintions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results. Below are tabulated some values.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-5-limit rank two"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit rank two</h2> 27/25: <a class="wiki_link" href="/14edo">14edo</a><br /> 16/15: <a class="wiki_link" href="/8edo">8edo</a><br /> 135/128: <a class="wiki_link" href="/23edo">23edo</a><br /> 25/24: <a class="wiki_link" href="/17edo">17edo</a><br /> 648/625: <a class="wiki_link" href="/12edo">12edo</a><br /> 250/243: <a class="wiki_link" href="/22edo">22edo</a><br /> 128/125: <a class="wiki_link" href="/39edo">39edo</a><br /> 3125/3072: <a class="wiki_link" href="/60edo">60edo</a><br /> 81/80: <a class="wiki_link" href="/81edo">81edo</a><br /> 2048/2025: <a class="wiki_link" href="/80edo">80edo</a><br /> 78732/78125: <a class="wiki_link" href="/539edo">539edo</a><br /> 393216/390625: <a class="wiki_link" href="/164edo">164edo</a><br /> 2109375/2097152: <a class="wiki_link" href="/296edo">296edo</a><br /> 15625/15552: <a class="wiki_link" href="/458edo">458edo</a><br /> 1600000/1594323: <a class="wiki_link" href="/873edo">873edo</a><br /> 1224440064/1220703125: <a class="wiki_link" href="/1496edo">1496edo</a><br /> 6115295232/6103515625: [1400edo]]<br /> 32805/32768: <a class="wiki_link" href="/749edo">749edo</a><br /> 274877906944/274658203125: <a class="wiki_link" href="/1559edo">1559edo</a><br /> 7629394531250/7625597484987: <a class="wiki_link" href="/3501edo">3501edo</a></body></html>