534edo: Difference between revisions

← 533edo 534edo 535edo →
Prime factorization	2 × 3 × 89
Step size	2.24719 ¢
Fifth	312\534 (701.124 ¢) (→ 52\89)
Semitones (A1:m2)	48:42 (107.9 ¢ : 94.38 ¢)
Dual sharp fifth	313\534 (703.371 ¢)
Dual flat fifth	312\534 (701.124 ¢) (→ 52\89)
Dual major 2nd	91\534 (204.494 ¢)
Consistency limit	7
Distinct consistency limit	7

VisualWikitext

Latest revision as of 15:19, 20 February 2025

534 equal divisions of the octave (abbreviated 534edo or 534ed2), also called 534-tone equal temperament (534tet) or 534 equal temperament (534et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 534 equal parts of about 2.25 ¢ each. Each step represents a frequency ratio of 2^1/534, or the 534th root of 2.

534edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The patent val tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the optimal patent val for 7-limit harry temperament.

Odd harmonics

Approximation of odd harmonics in 534edo
Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.831	+0.203	-0.287	+0.584	-0.756	-0.078	-0.628	+0.663	-0.884	-1.118	+0.939
Error	Relative (%)	-37.0	+9.0	-12.8	+26.0	-33.6	-3.5	-28.0	+29.5	-39.3	-49.8	+41.8
Steps (reduced)		846 (312)	1240 (172)	1499 (431)	1693 (91)	1847 (245)	1976 (374)	2086 (484)	2183 (47)	2268 (132)	2345 (209)	2416 (280)

Subsets and supersets

Since 534 factors into 2 × 3 × 89, 534edo has subset edos 2, 3, 6, 89, 178, and 267.

@@ Line 1: / Line 1: @@
-<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 17:31:58 UTC</tt>.<br>
-: The original revision id was <tt>241231227</tt>.<br>
+edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. The [[patent val]] [[tempering out|tempers out]] [[2401/2400]] and [[19683/19600]] in the 7-limit and provides the [[optimal patent val]] for 7-limit [[harry]] 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|534}}
-<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 //534 equal division// divides the octave into 534 equal parts of 2.247 cents each. It tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the [[optimal patent val]] for 7-limit [[Breedsmic temperaments#Harry|harry 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;534edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;534 equal division&lt;/em&gt; divides the octave into 534 equal parts of 2.247 cents each. It tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-limit &lt;a class="wiki_link" href="/Breedsmic%20temperaments#Harry"&gt;harry temperament&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
+Since 534 factors into {{factorization|534}}, 534edo has subset edos {{EDOs| 2, 3, 6, 89, 178, and 267 }}.
+[[Category:Harry]]

534edo: Difference between revisions

Latest revision as of 15:19, 20 February 2025

Odd harmonics

Subsets and supersets

Navigation menu

Search