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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>2011-11-11 17:05:58 UTC</tt>.<br>
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| : The original revision id was <tt>274505592</tt>.<br>
| | 269edo is in[[consistent]] in the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large. The [[patent val]] [[tempering out|tempers out]] [[6144/6125]] in the 7-limit, [[540/539]] and [[5632/5625]] in the 11-limit and [[364/363]] and [[676/675]] in the 13-limit. The 269c val tempers out [[225/224]] and [[4375/4374]] in the 7-limit, and 269ce [[385/384]] in the 11-limit, so that it [[support]]s and provides an excellent tuning for [[catakleismic]] and [[marvel]] temperaments. |
| : 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|269}} |
| <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 //269 equal division// divides the octave into 269 equal parts of 4.461 cents each. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for [[Kleismic family#Catakleismic|catakleismic]] and [[Marvel family|marvel]] temperaments.</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>269edo</title></head><body>The <em>269 equal division</em> divides the octave into 269 equal parts of 4.461 cents each. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for <a class="wiki_link" href="/Kleismic%20family#Catakleismic">catakleismic</a> and <a class="wiki_link" href="/Marvel%20family">marvel</a> temperaments.</body></html></pre></div>
| | 269edo is the 57th [[prime edo]]. |
Latest revision as of 19:17, 8 June 2026
| Prime factorization
|
269 (prime)
|
| Step size
|
4.46097 ¢
|
| Fifth
|
157\269 (700.372 ¢)
|
| Semitones (A1:m2)
|
23:22 (102.6 ¢ : 98.14 ¢)
|
| Dual sharp fifth
|
158\269 (704.833 ¢)
|
| Dual flat fifth
|
157\269 (700.372 ¢)
|
| Dual major 2nd
|
46\269 (205.204 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
269 equal divisions of the octave (abbreviated 269edo or 269ed2), also called 269-tone equal temperament (269tet) or 269 equal temperament (269et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 269 equal parts of about 4.46 ¢ each. Each step represents a frequency ratio of 21/269, or the 269th root of 2.
269edo is inconsistent in the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for catakleismic and marvel temperaments.
Odd harmonics
Approximation of odd harmonics in 269edo
| Harmonic
|
3
|
5
|
7
|
9
|
11
|
13
|
15
|
17
|
19
|
21
|
23
|
| Error
|
Absolute (¢)
|
-1.58
|
+1.79
|
-0.80
|
+1.29
|
+1.84
|
-1.87
|
+0.21
|
+2.11
|
+1.37
|
+2.08
|
+0.72
|
| Relative (%)
|
-35.5
|
+40.1
|
-17.8
|
+29.0
|
+41.3
|
-41.8
|
+4.6
|
+47.2
|
+30.7
|
+46.7
|
+16.2
|
Steps
(reduced)
|
426
(157)
|
625
(87)
|
755
(217)
|
853
(46)
|
931
(124)
|
995
(188)
|
1051
(244)
|
1100
(24)
|
1143
(67)
|
1182
(106)
|
1217
(141)
|
Subsets and supersets
269edo is the 57th prime edo.