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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}} It is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], which has to do with the fact that it is a strong 13-limit division, with a lower 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo, though [[6079edo|6079]], only slightly larger, beats it. A basis for its 13-limit commas is {123201/123200, 151263/151250, 8858304/8857805, 8859375/8859136, 62752536/62748517}. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-18 18:45:54 UTC</tt>.<br>
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| : The original revision id was <tt>556913153</tt>.<br>
| | === Prime harmonics === |
| : The revision comment was: <tt></tt><br>
| | {{Harmonics in equal|5585}} |
| 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 5585 division divides the octave into 5585 equal parts of 0.21486 cents each. It is a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak edo]], which has to do with the fact that it is a strong 13-limit division, with a lower 13-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any smaller edo, though [[6079edo|6079]], only slightly larger, beats it. A basis for its 13-limit commas is {123201/123200, 151263/151250, 8858304/8857805, 8859375/8859136, 62752536/62748517}.</pre></div>
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| <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>5585edo</title></head><body>The 5585 division divides the octave into 5585 equal parts of 0.21486 cents each. It is a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak edo</a>, which has to do with the fact that it is a strong 13-limit division, with a lower 13-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any smaller edo, though <a class="wiki_link" href="/6079edo">6079</a>, only slightly larger, beats it. A basis for its 13-limit commas is {123201/123200, 151263/151250, 8858304/8857805, 8859375/8859136, 62752536/62748517}.</body></html></pre></div>
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| Prime factorization
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5 × 1117
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| Step size
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0.214861 ¢
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| Fifth
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3267\5585 (701.952 ¢)
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| Semitones (A1:m2)
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529:420 (113.7 ¢ : 90.24 ¢)
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| Consistency limit
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15
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| Distinct consistency limit
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15
|
5585 equal divisions of the octave (abbreviated 5585edo or 5585ed2), also called 5585-tone equal temperament (5585tet) or 5585 equal temperament (5585et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5585 equal parts of about 0.215 ¢ each. Each step represents a frequency ratio of 21/5585, or the 5585th root of 2. It is a zeta peak edo, which has to do with the fact that it is a strong 13-limit division, with a lower 13-limit relative error than any smaller edo, though 6079, only slightly larger, beats it. A basis for its 13-limit commas is {123201/123200, 151263/151250, 8858304/8857805, 8859375/8859136, 62752536/62748517}.
Prime harmonics
Approximation of prime harmonics in 5585edo
| Harmonic
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
19
|
23
|
29
|
31
|
| Error
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Absolute (¢)
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+0.0000
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-0.0033
|
+0.0068
|
-0.0166
|
+0.0160
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+0.0095
|
-0.1031
|
+0.0698
|
-0.0201
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+0.0378
|
-0.0400
|
| Relative (%)
|
+0.0
|
-1.6
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+3.2
|
-7.7
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+7.4
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+4.4
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-48.0
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+32.5
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-9.4
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+17.6
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-18.6
|
Steps
(reduced)
|
5585
(0)
|
8852
(3267)
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12968
(1798)
|
15679
(4509)
|
19321
(2566)
|
20667
(3912)
|
22828
(488)
|
23725
(1385)
|
25264
(2924)
|
27132
(4792)
|
27669
(5329)
|