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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 an extremely strong 7-limit system, with a lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until [[84814edo|84814]], and a lower [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any besides [[171edo|171]] and [[3125edo|3125]]. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-23 12:07:13 UTC</tt>.<br>
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| : The original revision id was <tt>557206015</tt>.<br>
| | === Prime harmonics === |
| : The revision comment was: <tt></tt><br>
| | {{Harmonics in equal|18355|prec=4}} |
| 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 18355 division divides the octave into 18355 equal parts of 0.065377 cents each. It is a very strong 7-limit division, with a lower [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any division until [[84814edo|84814]], and a lower [[Tenney-Euclidean metrics#Logflat TE badness| TE loglfat badness]] than any besides [[171edo|171]] and [[3125edo|3125]].</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>18355edo</title></head><body>The 18355 division divides the octave into 18355 equal parts of 0.065377 cents each. It is a very strong 7-limit division, with a lower <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any division until <a class="wiki_link" href="/84814edo">84814</a>, and a lower <a class="wiki_link" href="/Tenney-Euclidean%20metrics#Logflat TE badness"> TE loglfat badness</a> than any besides <a class="wiki_link" href="/171edo">171</a> and <a class="wiki_link" href="/3125edo">3125</a>.</body></html></pre></div>
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Latest revision as of 14:08, 20 February 2025
| Prime factorization
|
5 × 3671
|
| Step size
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0.0653773 ¢
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| Fifth
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10737\18355 (701.956 ¢)
|
| Semitones (A1:m2)
|
1739:1380 (113.7 ¢ : 90.22 ¢)
|
| Consistency limit
|
15
|
| Distinct consistency limit
|
15
|
18355 equal divisions of the octave (abbreviated 18355edo or 18355ed2), also called 18355-tone equal temperament (18355tet) or 18355 equal temperament (18355et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 18355 equal parts of about 0.0654 ¢ each. Each step represents a frequency ratio of 21/18355, or the 18355th root of 2. It is an extremely strong 7-limit system, with a lower relative error than any division until 84814, and a lower TE logflat badness than any besides 171 and 3125.
Prime harmonics
Approximation of prime harmonics in 18355edo
| Harmonic
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
19
|
23
|
29
|
31
|
| Error
|
Absolute (¢)
|
+0.0000
|
+0.0009
|
+0.0006
|
+0.0000
|
+0.0087
|
+0.0280
|
-0.0249
|
+0.0190
|
+0.0013
|
-0.0158
|
-0.0179
|
| Relative (%)
|
+0.0
|
+1.3
|
+1.0
|
+0.0
|
+13.3
|
+42.9
|
-38.0
|
+29.0
|
+2.0
|
-24.1
|
-27.3
|
Steps
(reduced)
|
18355
(0)
|
29092
(10737)
|
42619
(5909)
|
51529
(14819)
|
63498
(8433)
|
67922
(12857)
|
75025
(1605)
|
77971
(4551)
|
83030
(9610)
|
89168
(15748)
|
90934
(17514)
|