Lists of edo-distinct temperaments: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 514264974 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 514265010 - 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>2014-06-17 21: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-17 21:22:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>514265010</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> | ||
| Line 30: | Line 30: | ||
|| [[List of edo-distinct 50et rank two temperaments|50]] || || | || [[List of edo-distinct 50et rank two temperaments|50]] || || | ||
|| [[List of edo-distinct 53et rank two temperaments|53]] || || | || [[List of edo-distinct 53et rank two temperaments|53]] || || | ||
|| [[List of edo-distinct 58et rank two temperaments| | || [[List of edo-distinct 58et rank two temperaments|58]] || || | ||
|| [[List of edo-distinct 72et rank two temperaments|72]] || || | || [[List of edo-distinct 72et rank two temperaments|72]] || || | ||
| Line 149: | Line 149: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments"> | <td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments">58</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Revision as of 21:22, 17 June 2014
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 2014-06-17 21:22:25 UTC.
- The original revision id was 514265010.
- 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:
For any [[equal]] temperament, there are technically an unlimited number of different [[abstract regular temperament|abstract regular temperaments]] that it "supports" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament. However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in [[12edo]], [[pajara]] and [[injera]] become the same, even though in anything other than 12 they are distinct temperaments. Two temperaments are called "edo-distinct" if they remain distinct even when tuned to the same equal temperament. For rank-2, it turns out that the number of edo-distinct rank-2 temperaments in N-edo is floor(N/2); that is, N/2 if N is even and (N-1)/2 if N is odd. =Rank-2 lists= || [[List of edo-distinct 12et rank two temperaments|12]] || [[List of edo-distinct 12f rank two temperaments|12f]] || || [[List of edo-distinct 15et rank two temperaments|15]] || || || [[List of edo-distinct 16et rank two temperaments|16]] || || || [[List of edo-distinct 17et rank two temperaments|17]] || [[List of edo-distinct 17c rank two temperaments|17c]] || || [[List of edo-distinct 19et rank two temperaments|19]] || || || [[List of edo-distinct 22et rank two temperaments|22]] || || || [[List of edo-distinct 24et rank two temperaments|24]] || || || [[List of edo-distinct 26et rank two temperaments|26]] || || || [[List of edo-distinct 27et rank two temperaments|27]] || [[List of edo-distinct 27e rank two temperaments|27e]] || || [[List of edo-distinct 29et rank two temperaments|29]] || || || [[List of edo-distinct 31et rank two temperaments|31]] || || || [[List of edo-distinct 34et rank two temperaments|34]] || [[List of edo-distinct 34d rank two temperaments|34d]] || || [[List of edo-distinct 41et rank two temperaments|41]] || || || [[List of edo-distinct 43et rank two temperaments|43]] || || || [[List of edo-distinct 46et rank two temperaments|46]] || || || [[List of edo-distinct 50et rank two temperaments|50]] || || || [[List of edo-distinct 53et rank two temperaments|53]] || || || [[List of edo-distinct 58et rank two temperaments|58]] || || || [[List of edo-distinct 72et rank two temperaments|72]] || || ==No fives== || [[List of edo-distinct 17et no-fives rank two temperaments|17]] || ||
Original HTML content:
<html><head><title>Lists of edo-distinct temperaments</title></head><body>For any <a class="wiki_link" href="/equal">equal</a> temperament, there are technically an unlimited number of different <a class="wiki_link" href="/abstract%20regular%20temperament">abstract regular temperaments</a> that it "supports" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.<br />
<br />
However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/pajara">pajara</a> and <a class="wiki_link" href="/injera">injera</a> become the same, even though in anything other than 12 they are distinct temperaments.<br />
<br />
Two temperaments are called "edo-distinct" if they remain distinct even when tuned to the same equal temperament. For rank-2, it turns out that the number of edo-distinct rank-2 temperaments in N-edo is floor(N/2); that is, N/2 if N is even and (N-1)/2 if N is odd.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Rank-2 lists"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank-2 lists</h1>
<table class="wiki_table">
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2012et%20rank%20two%20temperaments">12</a><br />
</td>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2012f%20rank%20two%20temperaments">12f</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2015et%20rank%20two%20temperaments">15</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2016et%20rank%20two%20temperaments">16</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2017et%20rank%20two%20temperaments">17</a><br />
</td>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2017c%20rank%20two%20temperaments">17c</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2019et%20rank%20two%20temperaments">19</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2022et%20rank%20two%20temperaments">22</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments">24</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2026et%20rank%20two%20temperaments">26</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2027et%20rank%20two%20temperaments">27</a><br />
</td>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2027e%20rank%20two%20temperaments">27e</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2029et%20rank%20two%20temperaments">29</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2031et%20rank%20two%20temperaments">31</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2034et%20rank%20two%20temperaments">34</a><br />
</td>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2034d%20rank%20two%20temperaments">34d</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments">41</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2043et%20rank%20two%20temperaments">43</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2046et%20rank%20two%20temperaments">46</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2050et%20rank%20two%20temperaments">50</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">53</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments">58</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2072et%20rank%20two%20temperaments">72</a><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Rank-2 lists-No fives"></a><!-- ws:end:WikiTextHeadingRule:2 -->No fives</h2>
<table class="wiki_table">
<tr>
<td><a class="wiki_link" href="/List%20of%20edo-distinct%2017et%20no-fives%20rank%20two%20temperaments">17</a><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>