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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-17 13:49:57 UTC</tt>.<br>
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| : The original revision id was <tt>556818047</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">The 2000 equal division divides the octave into 2000 equal parts of exactly 0.6 cents each. It is distinctly consistent through the 29 limit and a strong 29-limit system; the only smaller edo with a smaller 29-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] being [[1578edo|1578]]. The only ones to beat it in the 23-limit are 1578 and [[1889edo|1889]], and in the 19-limit, nothing smaller defeats it, the first edo to do so being [[2460edo|2460]].
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| 2000 = 2^4 * 5^3; some of its divisors are [[10edo|10]], [[16edo|16]], [[25edo|25]], [[50edo|50]], [[80edo|80]], [[100edo|100]], [[125edo|125]] and [[200edo|200]]. also there is the 1000 division of [[millioctave|millioctaves]], where it might be argued that cutting these in half makes for a better system.</pre></div>
| | == Theory == |
| <h4>Original HTML content:</h4>
| | 2000edo is [[consistency|distinctly consistent]] through the [[29-odd-limit]] and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are [[1578edo|1578-]] and [[1889edo]], and in the 19-limit, nothing smaller defeats it. |
| <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>2000edo</title></head><body>The 2000 equal division divides the octave into 2000 equal parts of exactly 0.6 cents each. It is distinctly consistent through the 29 limit and a strong 29-limit system; the only smaller edo with a smaller 29-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> being <a class="wiki_link" href="/1578edo">1578</a>. The only ones to beat it in the 23-limit are 1578 and <a class="wiki_link" href="/1889edo">1889</a>, and in the 19-limit, nothing smaller defeats it, the first edo to do so being <a class="wiki_link" href="/2460edo">2460</a>.<br />
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| | === Prime harmonics === |
| 2000 = 2^4 * 5^3; some of its divisors are <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/25edo">25</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/80edo">80</a>, <a class="wiki_link" href="/100edo">100</a>, <a class="wiki_link" href="/125edo">125</a> and <a class="wiki_link" href="/200edo">200</a>. also there is the 1000 division of <a class="wiki_link" href="/millioctave">millioctaves</a>, where it might be argued that cutting these in half makes for a better system.</body></html></pre></div>
| | {{Harmonics in equal|2000|columns=12}} |
| | {{Harmonics in equal|2000|start=13|columns=12|collapsed=1|title=Approximation of prime harmonics in 2000edo (continued)}} |
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| | === Subsets and supersets === |
| | 2000 = {{factorization|2000}}, and its nontrivial divisors are {{EDOs| 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000 }}. From these, [[1000edo]] is notable because it carries the interval size measure [[millioctave]]. It is argued that cutting millioctaves in half makes for a better interval measuring system, in light of 2000edo's high consistency limit, which introduces just interval approximations not present in 1000edo. In addition, 2000edo inherits its fifth from [[200edo]], where it is semiconvergent. |
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| | == Regular temperament properties == |
| | 2000edo has the smallest relative error than any previous equal temperaments in the 19-limit. It is only bettered by [[2460edo]]. |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br />per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br />ratio* |
| | ! Temperaments |
| | |- |
| | | 20 |
| | | 287\2000<br />(87\2000) |
| | | 172.2<br />(52.2) |
| | | 169/153<br />(?) |
| | | [[Calcium]] |
| | |- |
| | |25 |
| | |301\2000<br />(1\2000) |
| | |180.6<br />(0.6) |
| | |272/245<br />(?) |
| | |[[Hemimanganese]] |
| | |- |
| | | 80 |
| | | 619\2000<br />(19\2000) |
| | | 371.4<br />(11.4) |
| | | 2275/1836<br />(?) |
| | | [[Mercury]] |
| | |} |
| | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |
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| | == Music == |
| | ; [[Eliora]] |
| | * ''[https://www.youtube.com/watch?v=gM4dfrF5wPg Fugue, but Not (in A Mercury & Bidia)]'' (2024) |
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| | [[Category:Listen]] |