305edo: 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>2012-05-23 22:54:41 UTC</tt>.<br>
 
: The original revision id was <tt>338987540</tt>.<br>
305edo has a flat tendency, with the [[3/1|3]], [[5/1|5]], [[7/1|7]] and [[11/1|11]] of the [[patent val]] all flat, and the equal temperament [[tempering out|tempers out]] 2109375/2097152, the [[semicomma|semicomma (orson comma)]] in the 5-limit, [[2401/2400]] in the 7-limit, and [[243/242]], [[441/440]], and [[540/539]] in the 11-limit. It provides the [[optimal patent val]] for 7- and 11-limit [[breedsmic temperaments #Neominor|neominor temperament]].  
: 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|305}}
<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 305 equal temperament divides the octave into 305 equal parts of 3.934 cents each. It has a flat tndency, with the 3, 5, 7 and 11 of the patent val all flat, and it tempers out 2109375/2097152, the semicomma (orson co0mma) in the 5-limit. 2401/2400 in the 7-limit, and 243/242, 441/440, and 540/539 in the 11-limit. It provides the optimal patent val for 11-limit [[Breedsmic temperaments#Neominor|neominor temperament]]. It factors as 305 = 5*61.</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;305edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 305 equal temperament divides the octave into 305 equal parts of 3.934 cents each. It has a flat tndency, with the 3, 5, 7 and 11 of the patent val all flat, and it tempers out 2109375/2097152, the semicomma (orson co0mma) in the 5-limit. 2401/2400 in the 7-limit, and 243/242, 441/440, and 540/539 in the 11-limit. It provides the optimal patent val for 11-limit &lt;a class="wiki_link" href="/Breedsmic%20temperaments#Neominor"&gt;neominor temperament&lt;/a&gt;. It factors as 305 = 5*61.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 305 factors into 5 × 61, 305edo has [[5edo]] and [[61edo]] as its subsets.
 
[[Category:Neominor]]

Latest revision as of 14:33, 20 February 2025

← 304edo 305edo 306edo →
Prime factorization 5 × 61
Step size 3.93443 ¢ 
Fifth 178\305 (700.328 ¢)
Semitones (A1:m2) 26:25 (102.3 ¢ : 98.36 ¢)
Dual sharp fifth 179\305 (704.262 ¢)
Dual flat fifth 178\305 (700.328 ¢)
Dual major 2nd 52\305 (204.59 ¢)
Consistency limit 7
Distinct consistency limit 7

305 equal divisions of the octave (abbreviated 305edo or 305ed2), also called 305-tone equal temperament (305tet) or 305 equal temperament (305et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 305 equal parts of about 3.93 ¢ each. Each step represents a frequency ratio of 21/305, or the 305th root of 2.

305edo has a flat tendency, with the 3, 5, 7 and 11 of the patent val all flat, and the equal temperament tempers out 2109375/2097152, the semicomma (orson comma) in the 5-limit, 2401/2400 in the 7-limit, and 243/242, 441/440, and 540/539 in the 11-limit. It provides the optimal patent val for 7- and 11-limit neominor temperament.

Odd harmonics

Approximation of odd harmonics in 305edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.63 -0.74 -0.96 +0.68 -0.50 +1.44 +1.57 +1.27 +1.50 +1.35 +1.23
Relative (%) -41.4 -18.8 -24.3 +17.3 -12.7 +36.6 +39.8 +32.4 +38.2 +34.3 +31.4
Steps
(reduced) 		483
(178) 		708
(98) 		856
(246) 		967
(52) 		1055
(140) 		1129
(214) 		1192
(277) 		1247
(27) 		1296
(76) 		1340
(120) 		1380
(160)

Subsets and supersets

Since 305 factors into 5 × 61, 305edo has 5edo and 61edo as its subsets.

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