User:Moremajorthanmajor/Ed9/4: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2016-12-06 15:23~~:31~~ UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-06 15:27:23 UTC</tt>.<br>

: The original revision id was <tt>~~601553976~~</tt>.<br>

: The original revision id was <tt>601554400</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>

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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 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.

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 at least ~636.95 cents wide) 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>) 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>

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<br />

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 <a class="wiki_link" href="/equivalence">equivalence</a> 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 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.<br />

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 <a class="wiki_link" href="/equivalence">equivalence</a> 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 at least ~636.95 cents wide) 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.<br />

<br />

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 &quot;equally&quot; tempered shrutis. &quot;Macroshrutis&quot; might be a practically perfect term for it if it hasn't been named yet.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-12-06 15:23:31 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-06 15:27:23 UTC</tt>.<br>
-: The original revision id was <tt>601553976</tt>.<br>
+: The original revision id was <tt>601554400</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>
@@ Line 9: / Line 9: @@
-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 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.
+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 at least ~636.95 cents wide) 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.</pre></div>
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 &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 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;
+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 at least ~636.95 cents wide) 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;/body&gt;&lt;/html&gt;</pre></div>