350edo: 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>2011-07-05 22:59:44 UTC</tt>.<br>
: The original revision id was <tt>240142497</tt>.<br>
: 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>
<h4>Original Wikitext content:</h4>
<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 //350 equal division// divides the octave into 350 equal parts of 3.429 cents each. It tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the [[optimal patent val]] for [[Ragismic microtemperaments#Amity|amity temperament]]. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for hemiamity temperament.


350 is divisible by 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.</pre></div>
350edo has a sharp tendency, with [[harmonic]]s 3 to 11 all tuned sharp. The equal temperament [[tempering out|tempers out]] 1600000/1594323, the [[amity comma]], in the 5-limit, and [[4375/4374]], [[5120/5103]] and [[6144/6125]] in the 7-limit, and it provides the [[optimal patent val]] for the 7-limit [[amity]] temperament. In the 11-limit it tempers out [[3025/3024]] and [[9801/9800]], and provides the optimal patent val for 11-limit [[hemiamity]], whereas the 350f [[val]] is an excellent tuning for 13-limit hemiamity.  
<h4>Original HTML content:</h4>
 
<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;350edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;350 equal division&lt;/em&gt; divides the octave into 350 equal parts of 3.429 cents each. It tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="/Ragismic%20microtemperaments#Amity"&gt;amity temperament&lt;/a&gt;. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for hemiamity temperament.&lt;br /&gt;
=== Odd harmonics ===
&lt;br /&gt;
{{Harmonics in equal|350}}
350 is divisible by 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== Subsets and supersets ===
Since 350 factors into {{factorization|350}}, 350edo has subset edos {{EDOs| 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175 }}.
 
[[Category:Amity]]
[[Category:Hemiamity]]

Latest revision as of 14:45, 20 February 2025

← 349edo 350edo 351edo →
Prime factorization 2 × 52 × 7
Step size 3.42857 ¢ 
Fifth 205\350 (702.857 ¢) (→ 41\70)
Semitones (A1:m2) 35:25 (120 ¢ : 85.71 ¢)
Consistency limit 7
Distinct consistency limit 7

350 equal divisions of the octave (abbreviated 350edo or 350ed2), also called 350-tone equal temperament (350tet) or 350 equal temperament (350et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 350 equal parts of about 3.43 ¢ each. Each step represents a frequency ratio of 21/350, or the 350th root of 2.

350edo has a sharp tendency, with harmonics 3 to 11 all tuned sharp. The equal temperament tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the optimal patent val for the 7-limit amity temperament. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for 11-limit hemiamity, whereas the 350f val is an excellent tuning for 13-limit hemiamity.

Odd harmonics

Approximation of odd harmonics in 350edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.90 +1.11 +1.46 -1.62 +0.68 -0.53 -1.41 +1.33 +0.77 -1.07 -0.85
Relative (%) +26.3 +32.5 +42.6 -47.4 +19.9 -15.4 -41.2 +38.8 +22.5 -31.1 -24.7
Steps
(reduced) 		555
(205) 		813
(113) 		983
(283) 		1109
(59) 		1211
(161) 		1295
(245) 		1367
(317) 		1431
(31) 		1487
(87) 		1537
(137) 		1583
(183)

Subsets and supersets

Since 350 factors into 2 × 52 × 7, 350edo has subset edos 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.

Retrieved from "https://en.xen.wiki/index.php?title=350edo&oldid=181750"