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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
=Boogie Woogie Scale=
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:guest|guest]] and made on <tt>2010-07-03 21:33:45 UTC</tt>.<br>
: The original revision id was <tt>151471511</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">=Boogie Woogie Scale=  


In [[http://launch.groups.yahoo.com/group/tuning/message/65608|this posting]] of the Yahoo tuning list, Paul G. Hjelmstad wrote:
In [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_65608.html#65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote:


<pre>
Take the standard 12-bar boogie-woogie. Let's use F major:
Take the standard 12-bar boogie-woogie. Let's use F major:
 
F A C Eb
F A C Eb
Bb D F Ab
Bb D F Ab
C E G Bb
C E G Bb


Tune to the seven-limit and keep fifths. You get
Tune to the seven-limit and keep fifths. You get
12 15 18 21
12 15 18 21
4 5 6 7
4 5 6 7
36 45 54 63
36 45 54 63


Fit into one octave (F, G, Ab,A,Bb,C,D,Eb,E)
Fit into one octave (F,G,Ab,A,Bb,C,D,Eb,E)
24, 27,28,30,32,36,40,42,45 and 63 (extra Bb)
24,27,28,30,32,36,40,42,45 and 63 (extra Bb)


Taking all the ratios, we find that they are all superparticular (n/n-
Taking all the ratios, we find that they are all superparticular
1)
(n/n-1)
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (and the
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15
schisma for Bb/Bb 64/63)
(and the schisma for Bb/Bb 64/63)


You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale
You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale
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The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,
The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,
15/14, 21/20, 28/27
15/14, 21/20, 28/27
Five of the squares are used: 1/1, 4/3, 9/8, 16/15 and 64/63
Five of the squares are used: 1/1, 4/3, 9/8, 16/15 and 64/63


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All from the simple boogie woogie!
All from the simple boogie woogie!
----
</pre>
Gene Ward Smith described some additional properties (in [[http://launch.groups.yahoo.com/group/tuning/message/65610|this posting]]):
 
-----
 
Gene Ward Smith described some additional properties (in [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_65608.html#65610 this posting]):


<pre>
Here it is in Scala format:
Here it is in Scala format:


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! cx1.scl
! cx1.scl
First 10/4 scale = erlich11 &lt;10 16 23 28| epimorphic
First 10/4 scale = erlich11 <10 16 23 28| epimorphic
10
10
!
!
Line 84: Line 81:


Quite a lot of musical possibilities in these relatively small 7-limit
Quite a lot of musical possibilities in these relatively small 7-limit
JI scales, I think.</pre></div>
JI scales, I think.
<h4>Original HTML content:</h4>
</pre>
<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;boogiewoogiescale&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="Boogie Woogie Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Boogie Woogie Scale&lt;/h1&gt;
[[Category:10-tone scales]]
&lt;br /&gt;
[[Category:Just intonation scales]]
In &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65608" rel="nofollow"&gt;this posting&lt;/a&gt; of the Yahoo tuning list, Paul G. Hjelmstad wrote:&lt;br /&gt;
[[Category:Pages with mostly numerical content]]
&lt;br /&gt;
[[Category:7-limit]]
Take the standard 12-bar boogie-woogie. Let's use F major:&lt;br /&gt;
[[Category:Pages with Scala files]]
&lt;br /&gt;
[[Category:Archive]]
F A C Eb&lt;br /&gt;
Bb D F Ab&lt;br /&gt;
C E G Bb&lt;br /&gt;
&lt;br /&gt;
Tune to the seven-limit and keep fifths. You get&lt;br /&gt;
&lt;br /&gt;
12 15 18 21&lt;br /&gt;
4 5 6 7&lt;br /&gt;
36 45 54 63&lt;br /&gt;
&lt;br /&gt;
Fit into one octave (F, G, Ab,A,Bb,C,D,Eb,E)&lt;br /&gt;
24, 27,28,30,32,36,40,42,45 and 63 (extra Bb)&lt;br /&gt;
&lt;br /&gt;
Taking all the ratios, we find that they are all superparticular (n/n-&lt;br /&gt;
1)&lt;br /&gt;
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (and the&lt;br /&gt;
schisma for Bb/Bb 64/63)&lt;br /&gt;
&lt;br /&gt;
You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale&lt;br /&gt;
steps..&lt;br /&gt;
&lt;br /&gt;
The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,&lt;br /&gt;
15/14, 21/20, 28/27&lt;br /&gt;
Five of the squares are used: 1/1, 4/3, 9/8, 16/15 and 64/63&lt;br /&gt;
&lt;br /&gt;
8/7 and 7/6 are the only ratios which are not squared or triangular&lt;br /&gt;
superparticular ratios but they are still superparticular!&lt;br /&gt;
&lt;br /&gt;
All from the simple boogie woogie!&lt;br /&gt;
&lt;hr /&gt;
Gene Ward Smith described some additional properties (in &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65610" rel="nofollow"&gt;this posting&lt;/a&gt;):&lt;br /&gt;
&lt;br /&gt;
Here it is in Scala format:&lt;br /&gt;
&lt;br /&gt;
! boogie.scl&lt;br /&gt;
Paul Hjelmstad's boogie woogie scale&lt;br /&gt;
10&lt;br /&gt;
!&lt;br /&gt;
9/8&lt;br /&gt;
5/4&lt;br /&gt;
21/16&lt;br /&gt;
45/32&lt;br /&gt;
3/2&lt;br /&gt;
27/16&lt;br /&gt;
7/4&lt;br /&gt;
15/8&lt;br /&gt;
63/32&lt;br /&gt;
2/1&lt;br /&gt;
&lt;br /&gt;
Three otonal tetrads, no utonal tetrads, not CS or epimorphic,&lt;br /&gt;
superparticular ratios as noted.&lt;br /&gt;
&lt;br /&gt;
I found a number of ten-note seven limit epimorphic scales with four&lt;br /&gt;
tetrads; here's one Paul Erlich found first:&lt;br /&gt;
&lt;br /&gt;
! cx1.scl&lt;br /&gt;
First 10/4 scale = erlich11 &amp;lt;10 16 23 28| epimorphic&lt;br /&gt;
10&lt;br /&gt;
!&lt;br /&gt;
15/14&lt;br /&gt;
7/6&lt;br /&gt;
5/4&lt;br /&gt;
4/3&lt;br /&gt;
10/7&lt;br /&gt;
3/2&lt;br /&gt;
5/3&lt;br /&gt;
7/4&lt;br /&gt;
15/8&lt;br /&gt;
2&lt;br /&gt;
! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1]&lt;br /&gt;
&lt;br /&gt;
Quite a lot of musical possibilities in these relatively small 7-limit&lt;br /&gt;
JI scales, I think.&lt;/body&gt;&lt;/html&gt;</pre></div>
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