Lists of edo-distinct temperaments: Difference between revisions

Revision as of 12:33, 9 February 2014

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2014-02-09 12:33:58 UTC.

The original revision id was 488278318.

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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]] ||   ||

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 &quot;supports&quot; 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 &quot;edo-distinct&quot; 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:&lt;h1&gt; --><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>
</table>

</body></html>

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-: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-05-17 19:34:59 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-09 12:33:58 UTC</tt>.<br>
-: The original revision id was <tt>336831210</tt>.<br>
+: The original revision id was <tt>488278318</tt>.<br>
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 =Rank-2 lists=
 || [[List of edo-distinct 12et rank two temperaments|12]] || [[List of edo-distinct 12f rank two temperaments|12f]] ||
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 || [[List of edo-distinct 15et rank two temperaments|15]] ||   ||
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Lists of edo-distinct temperaments: Difference between revisions

Revision as of 12:33, 9 February 2014

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