User:Moremajorthanmajor/Ed9/4: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>diagonalia
**Imported revision 603046128 - Original comment: **
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
m Redirected page to Ed9/4
Tag: New redirect
 
(54 intermediate revisions by 9 users not shown)
Line 1: Line 1:
<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:diagonalia|diagonalia]] and made on <tt>2017-01-03 16:51:33 UTC</tt>.<br>
: The original revision id was <tt>603046128</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 (5-4 or 5-6) of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an [[Pseudo-traditional harmonic functions of octatonic scale degrees|octatonic scale]] (i. e. any of those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period equivalent to six macrotones, in particular ones at least as wide as 4 degrees of [[45edo|4]][[45edo|5edo]]) 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.
 
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 certain versions of the regularly tempered approximate ("full-status") [[A shruti list|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.)
 
The temperament family in the Neapolitan temperament area which has an interlaced enneatonic scale is named Fujiyama (i. e. the volcano viewable from practically anywhere in Japan due to the Japanese archipelago consisting of such flat islands).
 
[[8edIX]]
[[9edIX]]
[[13edIX]]
[[14edIX]]
[[17edIX]]
 
Surprisingly, though sort of obviously, the golden tunings of edIXs must be forced to turn out to divide a (nearly) pure 9:4.</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 (5-4 or 5-6) of a ninth-based system. However, thirds and sixths are no longer inverses, and thus an &lt;a class="wiki_link" href="/Pseudo-traditional%20harmonic%20functions%20of%20octatonic%20scale%20degrees"&gt;octatonic scale&lt;/a&gt; (i. e. any of those of the proper Napoli temperament family which are generated by a third or a fourth optionally with a period equivalent to six macrotones, in particular ones at least as wide as 4 degrees of &lt;a class="wiki_link" href="/45edo"&gt;4&lt;/a&gt;&lt;a class="wiki_link" href="/45edo"&gt;5edo&lt;/a&gt;) 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.&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 certain versions of the regularly tempered approximate (&amp;quot;full-status&amp;quot;) &lt;a class="wiki_link" href="/A%20shruti%20list"&gt;shrutis&lt;/a&gt;. &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;br /&gt;
&lt;br /&gt;
The temperament family in the Neapolitan temperament area which has an interlaced enneatonic scale is named Fujiyama (i. e. the volcano viewable from practically anywhere in Japan due to the Japanese archipelago consisting of such flat islands).&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/8edIX"&gt;8edIX&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/9edIX"&gt;9edIX&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/13edIX"&gt;13edIX&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/14edIX"&gt;14edIX&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/17edIX"&gt;17edIX&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Surprisingly, though sort of obviously, the golden tunings of edIXs must be forced to turn out to divide a (nearly) pure 9:4.&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 03:23, 22 May 2025

Redirect to:

Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/Ed9/4&oldid=197369"