458edo: 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>2011-07-13 16:58:08 UTC</tt>.<br>
 
: The original revision id was <tt>241226327</tt>.<br>
458edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[5/1|5]] is about halfway between its steps. It is most notable for [[tempering out]] the kleisma, [[15625/15552]], in the 5-limit and provides the [[optimal patent val]] for the 5-limit [[kleismic]] 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|458}}
<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 //458 equal division// divides the octave into 458 equal parts of 2.620 cents each. It tempers out the kleisma, 15625/15552, in the 5-limit and provides the [[optimal patent val]] for the 5-limit planar kleismic 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;458edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;458 equal division&lt;/em&gt; divides the octave into 458 equal parts of 2.620 cents each. It tempers out the kleisma, 15625/15552, in the 5-limit and provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the 5-limit planar kleismic temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 458 factors into {{factorization|458}}, 458edo contains [[2edo]] and [[229edo]] as subsets.  
 
[[Category:Kleismic]]

Latest revision as of 14:58, 20 February 2025

← 457edo 458edo 459edo →
Prime factorization 2 × 229
Step size 2.62009 ¢ 
Fifth 268\458 (702.183 ¢) (→ 134\229)
Semitones (A1:m2) 44:34 (115.3 ¢ : 89.08 ¢)
Consistency limit 3
Distinct consistency limit 3

458 equal divisions of the octave (abbreviated 458edo or 458ed2), also called 458-tone equal temperament (458tet) or 458 equal temperament (458et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 458 equal parts of about 2.62 ¢ each. Each step represents a frequency ratio of 21/458, or the 458th root of 2.

458edo is inconsistent to the 5-odd-limit and harmonic 5 is about halfway between its steps. It is most notable for tempering out the kleisma, 15625/15552, in the 5-limit and provides the optimal patent val for the 5-limit kleismic temperament.

Odd harmonics

Approximation of prime harmonics in 458edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.23 -1.16 +0.61 -1.10 +0.52 -0.15 +1.18 +0.55 +0.12 -0.06
Relative (%) +0.0 +8.7 -44.3 +23.1 -42.0 +19.9 -5.8 +44.9 +20.9 +4.5 -2.2
Steps
(reduced) 		458
(0) 		726
(268) 		1063
(147) 		1286
(370) 		1584
(210) 		1695
(321) 		1872
(40) 		1946
(114) 		2072
(240) 		2225
(393) 		2269
(437)

Subsets and supersets

Since 458 factors into 2 × 229, 458edo contains 2edo and 229edo as subsets.

Retrieved from "https://en.xen.wiki/index.php?title=458edo&oldid=181783"