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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>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-09 10:46:17 UTC</tt>.<br>
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| : The original revision id was <tt>601788218</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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"><span style="font-size: 19.5px;">Division of a ninth (e. g. 9/4) into n equal parts</span>
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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 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.
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| 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.
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| The branches of the Napoli family are named thus:
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| Bipentachordal:
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| * 4&4: Macrodiminshed
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| * 6&2: Macroshrutis
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| 5&3: Grandfather</pre></div>
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| <h4>Original HTML content:</h4>
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| <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"><html><head><title>edIX</title></head><body><span style="font-size: 19.5px;">Division of a ninth (e. g. 9/4) into n equal parts</span><br />
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| <br />
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| <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 <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 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.<br />
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| <br />
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| 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.<br />
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| <br />
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| The branches of the Napoli family are named thus:<br />
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| Bipentachordal:<br />
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| <ul><li>4&amp;4: Macrodiminshed</li><li>6&amp;2: Macroshrutis</li></ul>5&amp;3: Grandfather</body></html></pre></div>
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