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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>2011-06-27 12:33:32 UTC</tt>.<br>
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| : The original revision id was <tt>238967493</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 3600 equal division divides the octave into 3600 equal parts of exactly 1/3 of a cent each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps. It also has the advantage of expressing the steps of [[72edo]] in whole numbers. Aside from its relationship to cents, it is of interest as a system supporting [[Ragismic microtemperaments#Ennealimmal|ennealimmal temperament]], tempering out the ennealimma, |1 -27 18>, in the [[5-limit]] and (with the patent val) 2401/2400 and 4375/4374 in the [[7-limit]]. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.
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| The divisors of 3600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, and 1800.
| | == Theory == |
| </pre></div>
| | [[Category:Equal divisions of the octave|####]] |
| <h4>Original HTML content:</h4>
| | 3600edo is consistent in the 5-limit and it is a good 2.3.5.11.17.23.31.37.41 subgroup tuning. |
| <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>3600edo</title></head><body>The 3600 equal division divides the octave into 3600 equal parts of exactly 1/3 of a cent each. A cent is therefore three steps; also, the Dröbisch Angle which is 1/360 octave is ten steps. It also has the advantage of expressing the steps of <a class="wiki_link" href="/72edo">72edo</a> in whole numbers. Aside from its relationship to cents, it is of interest as a system supporting <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">ennealimmal temperament</a>, tempering out the ennealimma, |1 -27 18&gt;, in the <a class="wiki_link" href="/5-limit">5-limit</a> and (with the patent val) 2401/2400 and 4375/4374 in the <a class="wiki_link" href="/7-limit">7-limit</a>. An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex.<br />
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| | In the 5-limit, 3600edo [[support|supports]] the [[ennealimmal temperament]], tempering out the ennealimma, {{monzo| 1 -27 18 }}, and (with the [[patent val]]) 2401/2400 and 4375/4374 in the [[7-limit]]. Via the 3600e [[val]] {{val| 3600 5706 8359 10106 12453}}, 3600edo also supports the [[hemiennealimmal temperament]] in the 11-limit. |
| The divisors of 3600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, and 1800.</body></html></pre></div>
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| | An alternative 7-limit mapping is 3600d, with the 7 slightly sharp rather than slightly flat; this no longer supports ennealimmal, but it does temper out 52734375/52706752; together with the ennealimma that leads to a sort of strange sibling to ennealimmal temperament, more accurate but also more complex. |
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| | One step of 3600edo is close to the [[landscape comma]]. |
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| | === Prime harmonics === |
| | {{Harmonics in equal|3600}} |
| | === Subsets and supersets === |
| | [[Category:Equal divisions of the octave|####]] |
| | 3600edo factors as {{Factorization|3600}}, and has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800}}. |
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| | A cent is therefore represented by three steps; and the Dröbisch angle, which is [[360edo|logarithmically 1/360 of the octave]], is ten steps. EDOs corresponding to other notable divisors include [[72edo]], which has found a dissemination in practice and one step of which is represented by 50 steps, and [[200edo]], which holds the continued fraction expansion record for the best perfect fifth and its step is represented by 18 steps. |
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| | [[Category:Equal divisions of the octave|####]]<!-- 4-digit number --> |
| | [[Category:Ennealimmal]] |