333edo: 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:genewardsmith|genewardsmith]] and made on <tt>2012-02-09 16:31:10 UTC</tt>.<br>
 
: The original revision id was <tt>300282248</tt>.<br>
The equal temperament tempers out [[15625/15552]] in the 5-limit and [[5120/5103]] in the 7-limit, so it [[support]]s [[countercata]]. In the 11-limit it tempers out 1375/1372 and [[4000/3993]], and in the 13-limit [[325/324]], [[364/363]], [[625/624]] and [[676/675]], and provides the [[optimal patent val]] for the rank-2 temperament [[novemkleismic]], for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.
: 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>
=== Prime harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|333}}
<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 //333 equal temperament// divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports [[Kleismic family#Countercata|countercata temperament]]. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the [[optimal patent val]] for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.</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;333edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;333 equal temperament&lt;/em&gt; divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports &lt;a class="wiki_link" href="/Kleismic%20family#Countercata"&gt;countercata temperament&lt;/a&gt;. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 333 factors into 3<sup>2</sup> × 37, 333edo has subset edos {{EDOs| 3, 9, 37, and 111 }}.  
 
[[Category:Countercata]]
[[Category:Marveltwin]]

Latest revision as of 14:42, 20 February 2025

← 332edo 333edo 334edo →
Prime factorization 32 × 37
Step size 3.6036 ¢ 
Fifth 195\333 (702.703 ¢) (→ 65\111)
Semitones (A1:m2) 33:24 (118.9 ¢ : 86.49 ¢)
Consistency limit 7
Distinct consistency limit 7

333 equal divisions of the octave (abbreviated 333edo or 333ed2), also called 333-tone equal temperament (333tet) or 333 equal temperament (333et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 333 equal parts of about 3.6 ¢ each. Each step represents a frequency ratio of 21/333, or the 333rd root of 2.

The equal temperament tempers out 15625/15552 in the 5-limit and 5120/5103 in the 7-limit, so it supports countercata. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the optimal patent val for the rank-2 temperament novemkleismic, for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.

Prime harmonics

Approximation of prime harmonics in 333edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.75 -0.73 +0.54 +0.03 -0.89 -0.45 +1.59 -1.25 +1.05 +0.91
Relative (%) +0.0 +20.7 -20.2 +15.1 +0.9 -24.6 -12.5 +44.0 -34.6 +29.2 +25.3
Steps
(reduced) 		333
(0) 		528
(195) 		773
(107) 		935
(269) 		1152
(153) 		1232
(233) 		1361
(29) 		1415
(83) 		1506
(174) 		1618
(286) 		1650
(318)

Subsets and supersets

Since 333 factors into 32 × 37, 333edo has subset edos 3, 9, 37, and 111.

Retrieved from "https://en.xen.wiki/index.php?title=333edo&oldid=181740"