User:Moremajorthanmajor/Ed9/4: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
#redirect [[Ed9/4]]
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-02 22:25:17 UTC</tt>.<br>
: The original revision id was <tt>601266748</tt>.<br>
: 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>
<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">&lt;span style="font-size: 19.5px;"&gt;Division of a ninth (e. g. 9/4) into n equal parts&lt;/span&gt;
 
 
Division of e. g. the 9:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 9:4 or another ninth as a base though, is apparent by being the standard replacement for the root in jazz piano voicings. Also, as a ninth is the double of a fifth, normal triads will not contain other factors of an octatonic scale than the root, third and fifth when inverted. However, thirds and sixths are no longer inverses, and thus an octatonic scale (especially those of the Napoli temperament families proper which are generated by a third or a fourth optionally with a period of a [wolf] fifth at least ~636.95 cents wide). Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.
 
Incidentally, one way to treat 9/4 as an equivalence is the use of the 4:5:6:7:[8]:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes three 5/4 backwards or eight forwards to get to 7/6 (tempering out the comma 875/864 or [[tel:390625/372072|390625/372072]] or |-16 -6 11&gt;) or three 7/6 to get between 6/5 and the period of 3/2 (tempering out the comma 1728/1715). So, doing this yields 8 or 10, 12 or 14, and 22 note 2MOS. While the notes are rather farther apart, the scheme is uncannily similar to the "equally" tempered shrutis. "Macroshrutis" might be a practically perfect term for it if it hasn't been named yet.</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;edIX&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 19.5px;"&gt;Division of a ninth (e. g. 9/4) into n equal parts&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Division of e. g. the 9:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of &lt;a class="wiki_link" href="/equivalence"&gt;equivalence&lt;/a&gt; has not even been posed yet. The utility of 9:4 or another ninth as a base though, is apparent by being the standard replacement for the root in jazz piano voicings. Also, as a ninth is the double of a fifth, normal triads will not contain other factors of an octatonic scale than the root, third and fifth when inverted. However, thirds and sixths are no longer inverses, and thus an octatonic scale (especially those of the Napoli temperament families proper which are generated by a third or a fourth optionally with a period of a [wolf] fifth at least ~636.95 cents wide). Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.&lt;br /&gt;
&lt;br /&gt;
Incidentally, one way to treat 9/4 as an equivalence is the use of the 4:5:6:7:[8]:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes three 5/4 backwards or eight forwards to get to 7/6 (tempering out the comma 875/864 or [[tel:390625/372072|390625/372072]] or |-16 -6 11&amp;gt;) or three 7/6 to get between 6/5 and the period of 3/2 (tempering out the comma 1728/1715). So, doing this yields 8 or 10, 12 or 14, and 22 note 2MOS. While the notes are rather farther apart, the scheme is uncannily similar to the &amp;quot;equally&amp;quot; tempered shrutis. &amp;quot;Macroshrutis&amp;quot; might be a practically perfect term for it if it hasn't been named yet.&lt;/body&gt;&lt;/html&gt;</pre></div>

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