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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>2011-07-06 00:10:54 UTC</tt>.<br>
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| : The original revision id was <tt>240149061</tt>.<br>
| | 215et [[tempering out|tempers out]] [[4000/3969]] and [[65625/65536]], and the [[patent val]] provides the [[optimal patent val]] for the 53 & 162 temperament ([[ditonic|ditonic extension]]) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out [[2401/2400]], [[5120/5103]], and [[support]]s [[hemififths]]. |
| : 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>
| | === Odd harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|215}} |
| <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 //215 equal temperament// divides the octave into 215 equal parts of 5.581 cents each. It tempers out 4000/3969 and 65625/65536, and the patent val provides the [[optimal patent val]] for the 3&53 temperament tempering them both out, and the rank three temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports [[Breedsmic temperaments#Hemififths|hemififths]] temperament.</pre></div>
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| <h4>Original HTML content:</h4>
| | === Subsets and supersets === |
| <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>215edo</title></head><body>The <em>215 equal temperament</em> divides the octave into 215 equal parts of 5.581 cents each. It tempers out 4000/3969 and 65625/65536, and the patent val provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the 3&amp;53 temperament tempering them both out, and the rank three temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports <a class="wiki_link" href="/Breedsmic%20temperaments#Hemififths">hemififths</a> temperament.</body></html></pre></div>
| | Since 215 factors into 5 × 43, 215edo contains [[5edo]] and [[43edo]] as its subsets. |
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| | [[Category:Ditonic]] |
| | [[Category:Octagar]] |
Latest revision as of 14:16, 20 February 2025
| Prime factorization
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5 × 43
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| Step size
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5.5814 ¢
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| Fifth
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126\215 (703.256 ¢)
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| Semitones (A1:m2)
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22:15 (122.8 ¢ : 83.72 ¢)
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| Consistency limit
|
5
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| Distinct consistency limit
|
5
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215 equal divisions of the octave (abbreviated 215edo or 215ed2), also called 215-tone equal temperament (215tet) or 215 equal temperament (215et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 215 equal parts of about 5.58 ¢ each. Each step represents a frequency ratio of 21/215, or the 215th root of 2.
215et tempers out 4000/3969 and 65625/65536, and the patent val provides the optimal patent val for the 53 & 162 temperament (ditonic extension) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports hemififths.
Odd harmonics
Approximation of odd harmonics in 215edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
|
13
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15
|
17
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19
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21
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23
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| Error
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Absolute (¢)
|
+1.30
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-1.20
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+2.34
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+2.60
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+1.24
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+2.26
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+0.10
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+1.09
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-1.70
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-1.94
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+2.42
|
| Relative (%)
|
+23.3
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-21.5
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+41.9
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+46.6
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+22.2
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+40.5
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+1.9
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+19.5
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-30.4
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-34.8
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+43.4
|
Steps
(reduced)
|
341
(126)
|
499
(69)
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604
(174)
|
682
(37)
|
744
(99)
|
796
(151)
|
840
(195)
|
879
(19)
|
913
(53)
|
944
(84)
|
973
(113)
|
Subsets and supersets
Since 215 factors into 5 × 43, 215edo contains 5edo and 43edo as its subsets.