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>2016-12-09 11:06:22 UTC</tt>.<br>
: The original revision id was <tt>601789986</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, the fifth of normal root position triads will become the common suspension of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an octatonic scale (especially those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period of a [wolf] fifth wider than equal to the 17edo tritone) takes 1-3-6 as the root position of its regular triad. 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 nine 5/4 to get to the same place as thirteen 7/6 (tempering out the comma |5 -13 9 -13&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.
 
The branches of the Napoli family are named thus:
Bipentachordal:
* 4&amp;4: Macrodiminshed
* 6&amp;2: Macroshrutis
5&amp;3: Grandfather
(Difficult to call these names colorful, no? Yet still they are something.)</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, the fifth of normal root position triads will become the common suspension of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an octatonic scale (especially those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period of a [wolf] fifth wider than equal to the 17edo tritone) takes 1-3-6 as the root position of its regular triad. 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 nine 5/4 to get to the same place as thirteen 7/6 (tempering out the comma |5 -13 9 -13&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;br /&gt;
&lt;br /&gt;
The branches of the Napoli family are named thus:&lt;br /&gt;
Bipentachordal:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;4&amp;amp;4: Macrodiminshed&lt;/li&gt;&lt;li&gt;6&amp;amp;2: Macroshrutis&lt;/li&gt;&lt;/ul&gt;5&amp;amp;3: Grandfather&lt;br /&gt;
(Difficult to call these names colorful, no? Yet still they are something.)&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 03:23, 22 May 2025

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