7L 3s: 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:Kosmo|Kosmo]] and made on <tt>2011-04-04 13:20:14 UTC</tt>.<br>

: This revision was by author [[User:Kosmo|Kosmo]] and made on <tt>2011-04-04 13:22:07 UTC</tt>.<br>

: The original revision id was <tt>~~216954838~~</tt>.<br>

: The original revision id was <tt>216955580</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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=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]]:

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 ||

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t q a

q a t

q t a</pre></div>

q t a

Other repeating ntervals

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.</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"><html><head><title>7L 3s</title></head><body><h1 id="toc0"><a name="x7+3 - &quot;unfair mosh&quot; - &quot;neutral third scales&quot;"></a>7+3 - &quot;unfair mosh&quot; - &quot;neutral third scales&quot;</h1>

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<h1 id="toc2"><a name="A continuum of compatible edos"></a>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 />

~~<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 />

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t q a<br />

q a t<br />

q t a</body></html></pre></div>

q t a<br />

<br />

Other repeating ntervals<br />

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.</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:Kosmo|Kosmo]] and made on <tt>2011-04-04 13:20:14 UTC</tt>.<br>
+: This revision was by author [[User:Kosmo|Kosmo]] and made on <tt>2011-04-04 13:22:07 UTC</tt>.<br>
-: The original revision id was <tt>216954838</tt>.<br>
+: The original revision id was <tt>216955580</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 26: / Line 26: @@
 =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]]:
-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 ||
@@ Line 72: / Line 68: @@
 t q a
 q a t
-q t a</pre></div>
+q t a
+Other repeating ntervals
+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.</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;7L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x7+3 - &amp;quot;unfair mosh&amp;quot; - &amp;quot;neutral third scales&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;7+3 - &amp;quot;unfair mosh&amp;quot; - &amp;quot;neutral third scales&amp;quot;&lt;/h1&gt;
@@ Line 94: / Line 95: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="A continuum of compatible edos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;A continuum of compatible edos&lt;/h1&gt;
   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 &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;:&lt;br /&gt;
-&lt;br /&gt;
-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 &amp;quot;xenharmonic&amp;quot; use of the 12-EDO scale.&lt;br /&gt;
-C D Eb F G A Bb C' D' Eb'&lt;br /&gt;
-F' G' Ab' Bb' C&amp;quot; D&amp;quot; Eb&amp;quot; F&amp;quot; G&amp;quot; Ab&amp;quot; etc.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 173: / Line 170: @@
 t q a&lt;br /&gt;
 q a t&lt;br /&gt;
-q t a&lt;/body&gt;&lt;/html&gt;</pre></div>
+q t a&lt;br /&gt;
+&lt;br /&gt;
+Other repeating ntervals&lt;br /&gt;
+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 &amp;quot;xenharmonic&amp;quot; use of the 12-EDO scale.&lt;br /&gt;
+C D Eb F G A Bb C' D' Eb'&lt;br /&gt;
+F' G' Ab' Bb' C&amp;quot; D&amp;quot; Eb&amp;quot; F&amp;quot; G&amp;quot; Ab&amp;quot; etc.&lt;/body&gt;&lt;/html&gt;</pre></div>