1395edo: 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>2015-08-15 17:11:19 UTC</tt>.<br>
 
: The original revision id was <tt>556739689</tt>.<br>
1395edo is a strong higher-limit system, being a [[zeta edo|zeta peak, peak integer, integral and gap edo]]. The [[patent val]] is the first one after [[311edo|311]] with a lower 37-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], though it is only [[consistent]] through the [[21-odd-limit]], due to [[harmonic]] [[23/1|23]] being all of 0.3 cents flat. A [[comma basis]] for the 19-limit is {[[2058/2057]], [[2401/2400]], [[4914/4913]], 5929/5928, 10985/10982, 12636/12635, 14875/14872}.
: 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>
Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.
<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 1395 division divides the octave into 1395 steps of 0.8602 cents each. It is a strong higher-limit system, being a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak, integral and gap edo]]. The patent val is the first one after 311 with a lower 37-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]], though it is only consistent through the 21 limit, due to 23 being all of 0.3 cents flat. A comma basis for the 19 limit is 2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635 and 14875/14872.</pre></div>
=== Prime harmonics ===
<h4>Original HTML content:</h4>
{{Harmonics in equal|1395|columns=15}}
<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;1395edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 1395 division divides the octave into 1395 steps of 0.8602 cents each. It is a strong higher-limit system, being a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta peak, integral and gap edo&lt;/a&gt;. The patent val is the first one after 311 with a lower 37-limit &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness"&gt;relative error&lt;/a&gt;, though it is only consistent through the 21 limit, due to 23 being all of 0.3 cents flat. A comma basis for the 19 limit is 2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635 and 14875/14872.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== Subsets and supersets ===
Since 1395 factors into {{factorization|1395}}, 1395edo has subset edos {{EDOs|3, 5, 9, 15, 31, 45, 93, 155, 279, and 465}}.

Latest revision as of 17:01, 18 February 2025

← 1394edo 1395edo 1396edo →
Prime factorization 32 × 5 × 31
Step size 0.860215 ¢ 
Fifth 816\1395 (701.935 ¢) (→ 272\465)
Semitones (A1:m2) 132:105 (113.5 ¢ : 90.32 ¢)
Consistency limit 21
Distinct consistency limit 21

1395 equal divisions of the octave (abbreviated 1395edo or 1395ed2), also called 1395-tone equal temperament (1395tet) or 1395 equal temperament (1395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1395 equal parts of about 0.86 ¢ each. Each step represents a frequency ratio of 21/1395, or the 1395th root of 2.

1395edo is a strong higher-limit system, being a zeta peak, peak integer, integral and gap edo. The patent val is the first one after 311 with a lower 37-limit relative error, though it is only consistent through the 21-odd-limit, due to harmonic 23 being all of 0.3 cents flat. A comma basis for the 19-limit is {2058/2057, 2401/2400, 4914/4913, 5929/5928, 10985/10982, 12636/12635, 14875/14872}.

Some no-23 37-limit commas it tempers out are 3367/3366, 7696/7695, 9425/9424, 11781/11780, 13300/13299, 13950/13949, 16576/16575, 20350/20349, 40300/40293, 55056/55055.

Prime harmonics

Approximation of prime harmonics in 1395edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.000 -0.020 -0.077 -0.224 +0.080 -0.098 -0.009 +0.121 -0.317 +0.100 -0.089 -0.161 +0.185 +0.310 +0.300
Relative (%) +0.0 -2.3 -9.0 -26.0 +9.3 -11.3 -1.1 +14.1 -36.9 +11.7 -10.4 -18.7 +21.5 +36.1 +34.9
Steps
(reduced) 		1395
(0) 		2211
(816) 		3239
(449) 		3916
(1126) 		4826
(641) 		5162
(977) 		5702
(122) 		5926
(346) 		6310
(730) 		6777
(1197) 		6911
(1331) 		7267
(292) 		7474
(499) 		7570
(595) 		7749
(774)

Subsets and supersets

Since 1395 factors into 32 × 5 × 31, 1395edo has subset edos 3, 5, 9, 15, 31, 45, 93, 155, 279, and 465.

Retrieved from "https://en.xen.wiki/index.php?title=1395edo&oldid=181343"