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Cv scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
From [http://tech.groups.yahoo.com/group/tuning-math/message/11451 http://tech.groups.yahoo.com/group/tuning-math/message/11451] {{dead link}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-02 12:50:37 UTC</tt>.<br>
: The original revision id was <tt>206540752</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">From [[http://tech.groups.yahoo.com/group/tuning-math/message/11451]]


It turns out there are a lot of five tetrad scales involving only 11 notes (I've got a list of 132 of them) but none I've found are
"''It turns out there are a lot of five tetrad scales involving only 11 notes (I've got a list of 132 of them) but none I've found are strictly [[Periodic_scale|epimorphic]]. Checking for permutation epimorphic scales may be a good plan.''
strictly epimorphic. Checking for permutation epimorphic scales may be a good plan.


Of course, there are even more five tetrad scales with 12 notes, but here I give only ones which are epimorphic--all, as it turns out, with the [[Patent vals|standard val]]. I cataloged these in pairs, where the odd numbers have three major and two minor tetrads, and the even pairs the reverse. Marvel tempering removes this distinction, and I only list the odd, with the three major tetrads.
''Of course, there are even more five tetrad scales with 12 notes, but here I give only ones which are epimorphic--all, as it turns out, with the [[Patent_val|standard val]]. I cataloged these in pairs, where the odd numbers have three major and two minor tetrads, and the even pairs the reverse. Marvel tempering removes this distinction, and I only list the odd, with the three major tetrads.''


I found two scales I've found before, "pris" and "hen12". The latter is an adjusted version of the Hahn reduction of a chain of fifths.
''I found two scales I've found before, "pris" and "hen12". The latter is an adjusted version of the Hahn reduction of a chain of fifths.''"


<pre>
! cv1.scl
! cv1.scl
First 12/5 &lt;12 19 28 34| epimorphic
First 12/5 &lt;12 19 28 34| epimorphic
Line 30: Line 23:
7/4
7/4
28/15
28/15
2
2/1
</pre>


<pre>
! cv3.scl
! cv3.scl
Third 12/5 scale &lt;12 19 28 34| epimorphic = pris
Third 12/5 scale &lt;12 19 28 34| epimorphic = pris
Line 47: Line 42:
7/4
7/4
28/15
28/15
2
2/1
</pre>


<pre>
! cv5.scl
! cv5.scl
Fifth 12/5 scale &lt;12 19 28 34| epimorphic = inverse hen12
Fifth 12/5 scale &lt;12 19 28 34| epimorphic = inverse hen12
Line 65: Line 62:
15/8
15/8
2
2
</pre>


<pre>
! cv7.scl
! cv7.scl
Seventh 12/5 scale &lt;12 19 28 34| epimorphic
Seventh 12/5 scale &lt;12 19 28 34| epimorphic
Line 81: Line 80:
9/5
9/5
15/8
15/8
2
2/1
</pre>


<pre>
! cv9.scl
! cv9.scl
Ninth 12/5 scale &lt;12 19 28 34| epimorphic
Ninth 12/5 scale &lt;12 19 28 34| epimorphic
Line 98: Line 99:
25/14
25/14
40/21
40/21
2
2/1
</pre>


<pre>
! cv11.scl
! cv11.scl
Eleventh 12/5 scale &lt;12 19 28 34| epimorphic
Eleventh 12/5 scale &lt;12 19 28 34| epimorphic
Line 115: Line 118:
9/5
9/5
15/8
15/8
2
2/1
</pre>


<pre>
! cv13.scl
! cv13.scl
Thirteenth 12/5 scale &lt;12 19 28 34| epimorphic
Thirteenth 12/5 scale &lt;12 19 28 34| epimorphic
Line 132: Line 137:
7/4
7/4
28/15
28/15
2
2/1
</pre></div>
</pre>
<h4>Original HTML content:</h4>
[[Category:Lists of scales]]
<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;cv scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;From &lt;a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11451" rel="nofollow"&gt;http://tech.groups.yahoo.com/group/tuning-math/message/11451&lt;/a&gt;&lt;br /&gt;
[[Category:Pages with Scala files]]
&lt;br /&gt;
[[Category:Todo:cleanup]]
It turns out there are a lot of five tetrad scales involving only 11 notes (I've got a list of 132 of them) but none I've found are&lt;br /&gt;
strictly epimorphic. Checking for permutation epimorphic scales may be a good plan.&lt;br /&gt;
&lt;br /&gt;
Of course, there are even more five tetrad scales with 12 notes, but here I give only ones which are epimorphic--all, as it turns out, with the &lt;a class="wiki_link" href="/Patent%20vals"&gt;standard val&lt;/a&gt;. I cataloged these in pairs, where the odd numbers have three major and two minor tetrads, and the even pairs the reverse. Marvel tempering removes this distinction, and I only list the odd, with the three major tetrads.&lt;br /&gt;
&lt;br /&gt;
I found two scales I've found before, &amp;quot;pris&amp;quot; and &amp;quot;hen12&amp;quot;. The latter is an adjusted version of the Hahn reduction of a chain of fifths.&lt;br /&gt;
&lt;br /&gt;
! cv1.scl&lt;br /&gt;
First 12/5 &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
16/15&lt;br /&gt;
8/7&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
5/3&lt;br /&gt;
7/4&lt;br /&gt;
28/15&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv3.scl&lt;br /&gt;
Third 12/5 scale &amp;lt;12 19 28 34| epimorphic = pris&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
16/15&lt;br /&gt;
28/25&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
5/3&lt;br /&gt;
7/4&lt;br /&gt;
28/15&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv5.scl&lt;br /&gt;
Fifth 12/5 scale &amp;lt;12 19 28 34| epimorphic = inverse hen12&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
9/8&lt;br /&gt;
6/5&lt;br /&gt;
5/4&lt;br /&gt;
21/16&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
7/4&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv7.scl&lt;br /&gt;
Seventh 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
21/20&lt;br /&gt;
9/8&lt;br /&gt;
6/5&lt;br /&gt;
9/7&lt;br /&gt;
21/16&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
9/5&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv9.scl&lt;br /&gt;
Ninth 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
8/7&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
10/7&lt;br /&gt;
32/21&lt;br /&gt;
8/5&lt;br /&gt;
5/3&lt;br /&gt;
25/14&lt;br /&gt;
40/21&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv11.scl&lt;br /&gt;
Eleventh 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
9/8&lt;br /&gt;
6/5&lt;br /&gt;
9/7&lt;br /&gt;
21/16&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
9/5&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
&lt;br /&gt;
! cv13.scl&lt;br /&gt;
Thirteenth 12/5 scale &amp;lt;12 19 28 34| epimorphic&lt;br /&gt;
12&lt;br /&gt;
!&lt;br /&gt;
16/15&lt;br /&gt;
28/25&lt;br /&gt;
6/5&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
7/5&lt;br /&gt;
3/2&lt;br /&gt;
8/5&lt;br /&gt;
12/7&lt;br /&gt;
7/4&lt;br /&gt;
28/15&lt;br /&gt;
2&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Cv_scales"