749edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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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>2011-07-14 01:18:48 UTC</tt>.<br>
 
: The original revision id was <tt>241285917</tt>.<br>
The equal temperament is most notable for [[tempering out]] the [[schisma]], 32805/32768, and provides the [[optimal patent val]] for the 5-limit [[schismatic|schismatic (helmholtz)]] 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|749}}
<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 //749 equal division// divides the octave into 749 equal parts of 1.602 cents each. It tempers out the schisma, 32805/32768, and provides the [[optimal patent val]] for the 5-limit schismatic (helmholtz) 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;749edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;749 equal division&lt;/em&gt; divides the octave into 749 equal parts of 1.602 cents each. It tempers out the schisma, 32805/32768, and provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the 5-limit schismatic (helmholtz) temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
Since 749 factors into {{factorization|749}}, 749edo contains [[7edo]] and [[107edo]] as subsets.  
 
[[Category:Schismic]]

Latest revision as of 09:11, 7 January 2026

← 748edo 749edo 750edo →
Prime factorization 7 × 107
Step size 1.60214 ¢ 
Fifth 438\749 (701.736 ¢)
Semitones (A1:m2) 70:57 (112.1 ¢ : 91.32 ¢)
Consistency limit 7
Distinct consistency limit 7

749 equal divisions of the octave (abbreviated 749edo or 749ed2), also called 749-tone equal temperament (749tet) or 749 equal temperament (749et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 749 equal parts of about 1.6 ¢ each. Each step represents a frequency ratio of 21/749, or the 749th root of 2.

The equal temperament is most notable for tempering out the schisma, 32805/32768, and provides the optimal patent val for the 5-limit schismatic (helmholtz) temperament.

Prime harmonics

Approximation of prime harmonics in 749edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.219 -0.199 +0.466 -0.183 +0.594 +0.786 +0.484 -0.237 +0.596 +0.492
Relative (%) +0.0 -13.7 -12.4 +29.1 -11.4 +37.1 +49.0 +30.2 -14.8 +37.2 +30.7
Steps
(reduced) 		749
(0) 		1187
(438) 		1739
(241) 		2103
(605) 		2591
(344) 		2772
(525) 		3062
(66) 		3182
(186) 		3388
(392) 		3639
(643) 		3711
(715)

Subsets and supersets

Since 749 factors into 7 × 107, 749edo contains 7edo and 107edo as subsets.

Retrieved from "https://en.xen.wiki/index.php?title=749edo&oldid=221051"