539edo: Difference between revisions

← 538edo 539edo 540edo →
Prime factorization	72 × 11
Step size	2.22635 ¢
Fifth	315\539 (701.299 ¢) (→ 45\77)
Semitones (A1:m2)	49:42 (109.1 ¢ : 93.51 ¢)
Consistency limit	3
Distinct consistency limit	3

VisualWikitext

Latest revision as of 15:19, 20 February 2025

539 equal divisions of the octave (abbreviated 539edo or 539ed2), also called 539-tone equal temperament (539tet) or 539 equal temperament (539et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 539 equal parts of about 2.23 ¢ each. Each step represents a frequency ratio of 2^1/539, or the 539th root of 2.

539edo is inconsistent to the 5-odd-limit. If harmonic 5 is used at all, the 539c val has better overall accuracy than the patent val. Meanwhile, the patent val tempers out the sensipent comma, 78732/78125, and provides the optimal patent val for the 5-limit sensipent temperament, tuning it more accurate than 65et by a tiny margin.

Odd harmonics

Approximation of odd harmonics in 539edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.656	+1.070	-0.366	+0.914	+0.816	+1.031	+0.414	-0.317	+0.817	-1.022	-0.445
Error	Relative (%)	-29.5	+48.1	-16.4	+41.0	+36.6	+46.3	+18.6	-14.2	+36.7	-45.9	-20.0
Steps (reduced)		854 (315)	1252 (174)	1513 (435)	1709 (92)	1865 (248)	1995 (378)	2106 (489)	2203 (47)	2290 (134)	2367 (211)	2438 (282)

Subsets and supersets

Since 539 factors into 7² × 11, 539edo has subset edos 7, 11, 49, and 77.

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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>2011-07-13 19:40:59 UTC</tt>.<br>
-: The original revision id was <tt>241247835</tt>.<br>
+edo is in[[consistent]] to the [[5-odd-limit]]. If [[harmonic]] [[5/1|5]] is used at all, the 539c [[val]] has better overall accuracy than the [[patent val]]. Meanwhile, the patent val [[tempering out|tempers out]] the [[sensipent comma]], 78732/78125, and provides the [[optimal patent val]] for the 5-limit [[sensipent]] temperament, tuning it more accurate than 65et by a tiny margin.
-: 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|539}}
-<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 //539 equal division// divides the octave into 539 equal parts of 2.227 cents each. It tempers out the sensipent comma, 78732/78125, and provides the [[optimal patent val]] for the 5-limit sensipent 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;539edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;539 equal division&lt;/em&gt; divides the octave into 539 equal parts of 2.227 cents each. It tempers out the sensipent comma, 78732/78125, and provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the 5-limit sensipent temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
+Since 539 factors into {{factorization|539}}, 539edo has subset edos {{EDOs| 7, 11, 49, and 77 }}.
+[[Category:Sensipent]]

539edo: Difference between revisions

Latest revision as of 15:19, 20 February 2025

Odd harmonics

Subsets and supersets

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