269edo: Difference between revisions

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**Imported revision 240481181 - Original comment: **
 
m I think we can keep this one
Tag: Manual revert
 
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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>2011-07-08 03:33:04 UTC</tt>.<br>
 
: The original revision id was <tt>240481181</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>
 
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. It tempers out 225/224 and 4375/4374 in the 7-limit and 385/384 in the 7-limit, so that it supports and provides a good tuning for [[Kleismic family#Catakleismic|catakleismic]] and [[Marvel family|marvel]] temperament.</pre></div>
 
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;269edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;269 equal division&lt;/em&gt; divides the octave into 269 equal parts of 4.461 cents each. It tempers out 225/224 and 4375/4374 in the 7-limit and 385/384 in the 7-limit, so that it supports and provides a good tuning for &lt;a class="wiki_link" href="/Kleismic%20family#Catakleismic"&gt;catakleismic&lt;/a&gt; and &lt;a class="wiki_link" href="/Marvel%20family"&gt;marvel&lt;/a&gt; temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
269edo is the 57th [[prime edo]].

Latest revision as of 19:17, 8 June 2026

← 268edo 269edo 270edo →
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.

Retrieved from "https://en.xen.wiki/index.php?title=269edo&oldid=232040"