3558edo: Difference between revisions

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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:hstraub|hstraub]] and made on <tt>2011-06-22 04:48:31 UTC</tt>.<br>
 
: The original revision id was <tt>238131865</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
3558edo is only [[consistent]] to the [[5-odd-limit]].  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
=== Odd harmonics ===
<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">Some MOS scales:
{{Harmonics in equal|3558}}
[[terrain9]]
 
[[terrain15]]</pre></div>
=== Subsets and supersets ===
<h4>Original HTML content:</h4>
Since 3558 factors into {{factorization|3558}}, 3558edo has subset edos 2, 3, 6, 593, 1186, and 1779.  
<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;3558edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Some MOS scales:&lt;br /&gt;
 
&lt;a class="wiki_link" href="/terrain9"&gt;terrain9&lt;/a&gt;&lt;br /&gt;
== Scales ==
&lt;a class="wiki_link" href="/terrain15"&gt;terrain15&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Some MOS scales:
* [[Terrain9|Terrain[9]]]
* [[Terrain15|Terrain[15]]]
 
[[Category:Terrain]]

Latest revision as of 14:46, 20 February 2025

← 3557edo 3558edo 3559edo →
Prime factorization 2 × 3 × 593
Step size 0.337268 ¢ 
Fifth 2081\3558 (701.855 ¢)
Semitones (A1:m2) 335:269 (113 ¢ : 90.73 ¢)
Consistency limit 5
Distinct consistency limit 5

3558 equal divisions of the octave (abbreviated 3558edo or 3558ed2), also called 3558-tone equal temperament (3558tet) or 3558 equal temperament (3558et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3558 equal parts of about 0.337 ¢ each. Each step represents a frequency ratio of 21/3558, or the 3558th root of 2.

Theory

3558edo is only consistent to the 5-odd-limit.

Odd harmonics

Approximation of odd harmonics in 3558edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.100 -0.142 +0.145 +0.137 +0.115 -0.055 +0.096 -0.065 -0.043 +0.045 +0.056
Relative (%) -29.7 -42.0 +43.1 +40.7 +34.2 -16.5 +28.3 -19.3 -12.6 +13.5 +16.7
Steps
(reduced) 		5639
(2081) 		8261
(1145) 		9989
(2873) 		11279
(605) 		12309
(1635) 		13166
(2492) 		13901
(3227) 		14543
(311) 		15114
(882) 		15628
(1396) 		16095
(1863)

Subsets and supersets

Since 3558 factors into 2 × 3 × 593, 3558edo has subset edos 2, 3, 6, 593, 1186, and 1779.

Scales

Some MOS scales:

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