7L 3s: Difference between revisions
Wikispaces>genewardsmith **Imported revision 209500500 - Original comment: ** |
Wikispaces>Kosmo **Imported revision 216954838 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Kosmo|Kosmo]] and made on <tt>2011-04-04 13:20:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>216954838</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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=A continuum of compatible edos= | =A continuum of compatible edos= | ||
The generator range reflects two extremes: one where L=s (3\10), and another where s=0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 -- five degrees of [[17edo]]: | The generator range reflects two extremes: one where L=s (3\10), and another where s=0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 -- five degrees of [[17edo]]: | ||
m If, instead of an octave, the period is a ratio of 8:3 (octave + p.4th) then the same MOS can be constructed using 4:3 as a generating interval. Dividing this 8:3 into 17 equal tones is practically identical to 12-EDO. The scale thus formed is essentially common Dorian mode and a couple of notes above the octave. This is yet another "xenharmonic" use of the 12-EDO scale. | |||
C D Eb F G A Bb C' D' Eb' | |||
F' G' Ab' Bb' C" D" Eb" F" G" Ab" etc. | |||
|| || || generator || | || || || generator || | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="A continuum of compatible edos"></a><!-- ws:end:WikiTextHeadingRule:4 -->A continuum of compatible edos</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="A continuum of compatible edos"></a><!-- ws:end:WikiTextHeadingRule:4 -->A continuum of compatible edos</h1> | ||
The generator range reflects two extremes: one where L=s (3\10), and another where s=0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 -- five degrees of <a class="wiki_link" href="/17edo">17edo</a>:<br /> | The generator range reflects two extremes: one where L=s (3\10), and another where s=0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edo would be (3+2)\(10+7) = 5\17 -- five degrees of <a class="wiki_link" href="/17edo">17edo</a>:<br /> | ||
<br /> | |||
m If, instead of an octave, the period is a ratio of 8:3 (octave + p.4th) then the same MOS can be constructed using 4:3 as a generating interval. Dividing this 8:3 into 17 equal tones is practically identical to 12-EDO. The scale thus formed is essentially common Dorian mode and a couple of notes above the octave. This is yet another &quot;xenharmonic&quot; use of the 12-EDO scale.<br /> | |||
C D Eb F G A Bb C' D' Eb'<br /> | |||
F' G' Ab' Bb' C&quot; D&quot; Eb&quot; F&quot; G&quot; Ab&quot; etc.<br /> | |||
<br /> | <br /> | ||