284edo: 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>2011-10-24 00:56:38 UTC</tt>.<br>
 
: The original revision id was <tt>267789856</tt>.<br>
The equal temperament [[tempering out|tempers out]] the kleisma, [[15625/15552]], and the breedsma, [[2401/2400]], and is a good tuning for [[quadritikleismic]] temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out [[385/384]], for which it provides the [[optimal patent val]]. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments [[agni]] and [[enlil]] and keenanismic, the 385/384 rank-4 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>
=== Prime harmonics ===
<h4>Original Wikitext content:</h4>
{{Harmonics in equal|284}}
<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 //284 equal division// divides the octave into 284 equal parts of size 4.225 cents each. It tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for [[Kleismic family|quadritikleismic temperament]] which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the [[optimal patent val]]. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for both quadritikleismic and keenanismic, the 385/384 rank four temperament.</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;284edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;284 equal division&lt;/em&gt; divides the octave into 284 equal parts of size 4.225 cents each. It tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for &lt;a class="wiki_link" href="/Kleismic%20family"&gt;quadritikleismic temperament&lt;/a&gt; which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for both quadritikleismic and keenanismic, the 385/384 rank four temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 284 factors into {{factorization|284}}, 284edo has subset edos {{EDOs| 2, 4, 71, and 142 }}.
 
[[Category:Keenanismic]]
[[Category:Agni]]
[[Category:Enlil]]
[[Category:Quadritikleismic]]

Latest revision as of 14:28, 20 February 2025

← 283edo 284edo 285edo →
Prime factorization 22 × 71
Step size 4.22535 ¢ 
Fifth 166\284 (701.408 ¢) (→ 83\142)
Semitones (A1:m2) 26:22 (109.9 ¢ : 92.96 ¢)
Consistency limit 11
Distinct consistency limit 11

284 equal divisions of the octave (abbreviated 284edo or 284ed2), also called 284-tone equal temperament (284tet) or 284 equal temperament (284et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 284 equal parts of about 4.23 ¢ each. Each step represents a frequency ratio of 21/284, or the 284th root of 2.

The equal temperament tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for quadritikleismic temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the optimal patent val. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments agni and enlil and keenanismic, the 385/384 rank-4 temperament.

Prime harmonics

Approximation of odd harmonics in 284edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.55 -1.81 -1.22 -1.09 -2.02 +0.32 +1.87 +0.68 -1.74 -1.77 +1.30
Relative (%) -12.9 -42.8 -28.9 -25.9 -47.9 +7.5 +44.3 +16.1 -41.1 -41.8 +30.8
Steps
(reduced) 		450
(166) 		659
(91) 		797
(229) 		900
(48) 		982
(130) 		1051
(199) 		1110
(258) 		1161
(25) 		1206
(70) 		1247
(111) 		1285
(149)

Subsets and supersets

Since 284 factors into 22 × 71, 284edo has subset edos 2, 4, 71, and 142.

Retrieved from "https://en.xen.wiki/index.php?title=284edo&oldid=181719"