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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | For any [[equal temperament]], there are technically an unlimited number of different [[abstract regular temperaments]] that it "[[support]]s" 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. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-17 21:22:25 UTC</tt>.<br>
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| : The original revision id was <tt>514265010</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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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.<br>
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| <h4>Original Wikitext content:</h4>
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| <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">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.
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| 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. | | 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. |
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| 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. | | 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. |
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| =Rank-2 lists= | | == Rank-2 lists == |
| || [[List of edo-distinct 12et rank two temperaments|12]] || [[List of edo-distinct 12f rank two temperaments|12f]] || | | {| class="wikitable" |
| || [[List of edo-distinct 15et rank two temperaments|15]] || || | | |- |
| || [[List of edo-distinct 16et rank two temperaments|16]] || || | | | | [[List_of_edo-distinct_12et_rank_two_temperaments|12]] |
| || [[List of edo-distinct 17et rank two temperaments|17]] || [[List of edo-distinct 17c rank two temperaments|17c]] || | | | | [[List_of_edo-distinct_12f_rank_two_temperaments|12f]] |
| || [[List of edo-distinct 19et rank two temperaments|19]] || || | | |- |
| || [[List of edo-distinct 22et rank two temperaments|22]] || || | | | | [[List_of_edo-distinct_15et_rank_two_temperaments|15]] |
| || [[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_16et_rank_two_temperaments|16]] |
| || [[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_17et_rank_two_temperaments|17]] |
| || [[List of edo-distinct 41et rank two temperaments|41]] || || | | | | [[List_of_edo-distinct_17c_rank_two_temperaments|17c]] |
| || [[List of edo-distinct 43et rank two temperaments|43]] || || | | |- |
| || [[List of edo-distinct 46et rank two temperaments|46]] || || | | | | [[List_of_edo-distinct_19et_rank_two_temperaments|19]] |
| || [[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_22et_rank_two_temperaments|22]] |
| || [[List of edo-distinct 72et rank two temperaments|72]] || || | | | | |
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| | | | [[List_of_edo-distinct_24et_rank_two_temperaments|24]] |
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| | | | [[List_of_edo-distinct_26et_rank_two_temperaments|26]] |
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| | | | [[List_of_edo-distinct_27et_rank_two_temperaments|27]] |
| | | | [[List_of_edo-distinct_27e_rank_two_temperaments|27e]] |
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| | | | [[List_of_edo-distinct_29et_rank_two_temperaments|29]] |
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| | | | [[List_of_edo-distinct_31et_rank_two_temperaments|31]] |
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| | | | [[List_of_edo-distinct_34et_rank_two_temperaments|34]] |
| | | | [[List_of_edo-distinct_34d_rank_two_temperaments|34d]] |
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| | | | [[List_of_edo-distinct_41et_rank_two_temperaments|41]] |
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| | | | [[List_of_edo-distinct_43et_rank_two_temperaments|43]] |
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| | | | [[List_of_edo-distinct_46et_rank_two_temperaments|46]] |
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| | | | [[List_of_edo-distinct_50et_rank_two_temperaments|50]] |
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| | | | [[List_of_edo-distinct_53et_rank_two_temperaments|53]] |
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| | | | [[List_of_edo-distinct_58et_rank_two_temperaments|58]] |
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| | | | [[List_of_edo-distinct_72et_rank_two_temperaments|72]] |
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| | |} |
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| ==No fives== | | === No-fives === |
| || [[List of edo-distinct 17et no-fives rank two temperaments|17]] || ||</pre></div> | | {| class="wikitable" |
| <h4>Original HTML content:</h4>
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| <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>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 />
| | | | [[List_of_edo-distinct_17et_no-fives_rank_two_temperaments|17]] |
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| 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 />
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| 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 />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Rank-2 lists"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank-2 lists</h1>
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| <table class="wiki_table">
| | [[Category:Lists of edo-distinct temperaments| ]] <!-- main article --> |
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2012et%20rank%20two%20temperaments">12</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2012f%20rank%20two%20temperaments">12f</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2015et%20rank%20two%20temperaments">15</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2016et%20rank%20two%20temperaments">16</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2017et%20rank%20two%20temperaments">17</a><br />
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| </td>
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2017c%20rank%20two%20temperaments">17c</a><br />
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| </td>
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2019et%20rank%20two%20temperaments">19</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2022et%20rank%20two%20temperaments">22</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2024et%20rank%20two%20temperaments">24</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2026et%20rank%20two%20temperaments">26</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2027et%20rank%20two%20temperaments">27</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2027e%20rank%20two%20temperaments">27e</a><br />
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| </td>
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2029et%20rank%20two%20temperaments">29</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2031et%20rank%20two%20temperaments">31</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2034et%20rank%20two%20temperaments">34</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2034d%20rank%20two%20temperaments">34d</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments">41</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2043et%20rank%20two%20temperaments">43</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2046et%20rank%20two%20temperaments">46</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2050et%20rank%20two%20temperaments">50</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">53</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2058et%20rank%20two%20temperaments">58</a><br />
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2072et%20rank%20two%20temperaments">72</a><br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Rank-2 lists-No fives"></a><!-- ws:end:WikiTextHeadingRule:2 -->No fives</h2>
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| <td><a class="wiki_link" href="/List%20of%20edo-distinct%2017et%20no-fives%20rank%20two%20temperaments">17</a><br />
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| </body></html></pre></div>
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For any equal temperament, there are technically an unlimited number of different 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
No-fives