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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>2015-08-18 00:27:11 UTC</tt>.<br>
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| : The original revision id was <tt>556855283</tt>.<br>
| | 2513edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until we reach the cosmically excellent [[4296edo]]. 2513 = {{factorization|2513}}, and it shares its [[harmonic]] [[3/1|3]] with [[359edo]]. A basis for its 5-limit commas consists of senior, {{monzo| -17 62 -35 }}, and fortune, {{monzo| -107 47 14 }}; it also [[tempering out|tempers out]] pirate, {{monzo| -90 -15 49 }}. It is uniquely [[consistent]] through to the [[11-odd-limit]], and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit. |
| : 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>
| | === Prime harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|2513|prec=4}} |
| <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 2513 division divides the octave into 2513 equal parts of 0.4775 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any edo until we reach the cosmically excellent [[4296edo]]. A basis for its 5-limit commas is senior, |-17 62 -35> and fortune, |-107 47 14>; it also tempers out pirate, |-90 -15 49>. It is uniquely consistent through to the 11-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.</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>2513edo</title></head><body>The 2513 division divides the octave into 2513 equal parts of 0.4775 cents each. It is a very strong 5-limit system, with a lower 5-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any edo until we reach the cosmically excellent <a class="wiki_link" href="/4296edo">4296edo</a>. A basis for its 5-limit commas is senior, |-17 62 -35&gt; and fortune, |-107 47 14&gt;; it also tempers out pirate, |-90 -15 49&gt;. It is uniquely consistent through to the 11-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.</body></html></pre></div>
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Latest revision as of 07:02, 20 February 2025
| Prime factorization
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7 × 359
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| Step size
|
0.477517 ¢
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| Fifth
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1470\2513 (701.95 ¢) (→ 210\359)
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| Semitones (A1:m2)
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238:189 (113.6 ¢ : 90.25 ¢)
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| Consistency limit
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11
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| Distinct consistency limit
|
11
|
2513 equal divisions of the octave (abbreviated 2513edo or 2513ed2), also called 2513-tone equal temperament (2513tet) or 2513 equal temperament (2513et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2513 equal parts of about 0.478 ¢ each. Each step represents a frequency ratio of 21/2513, or the 2513th root of 2.
2513edo is a very strong 5-limit system, with a lower 5-limit relative error than any edo until we reach the cosmically excellent 4296edo. 2513 = 7 × 359, and it shares its harmonic 3 with 359edo. A basis for its 5-limit commas consists of senior, [-17 62 -35⟩, and fortune, [-107 47 14⟩; it also tempers out pirate, [-90 -15 49⟩. It is uniquely consistent through to the 11-odd-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.
Prime harmonics
Approximation of prime harmonics in 2513edo
| Harmonic
|
2
|
3
|
5
|
7
|
11
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13
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17
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19
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23
|
29
|
31
|
| Error
|
Absolute (¢)
|
+0.0000
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-0.0051
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-0.0025
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+0.0559
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+0.2141
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-0.0979
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+0.0983
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-0.0200
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+0.1379
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-0.0507
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+0.0500
|
| Relative (%)
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+0.0
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-1.1
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-0.5
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+11.7
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+44.8
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-20.5
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+20.6
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-4.2
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+28.9
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-10.6
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+10.5
|
Steps
(reduced)
|
2513
(0)
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3983
(1470)
|
5835
(809)
|
7055
(2029)
|
8694
(1155)
|
9299
(1760)
|
10272
(220)
|
10675
(623)
|
11368
(1316)
|
12208
(2156)
|
12450
(2398)
|