Boogiewoogiescale: Difference between revisions

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=Boogie Woogie Scale= 

In [[http://launch.groups.yahoo.com/group/tuning/message/65608|this posting]] of the Yahoo tuning list, Paul G. Hjelmstad wrote:

Take the standard 12-bar boogie-woogie. Let's use F major:

F A C Eb
Bb D F Ab
C E G Bb

Tune to the seven-limit and keep fifths. You get

12 15 18 21
4 5 6 7
36 45 54 63

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)

Taking all the ratios, we find that they are all superparticular (n/n-
1)
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (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
steps..

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

8/7 and 7/6 are the only ratios which are not squared or triangular
superparticular ratios but they are still superparticular!

All from the simple boogie woogie!
----
Gene Ward Smith described some additional properties (in [[http://launch.groups.yahoo.com/group/tuning/message/65610|this posting]]):

Here it is in Scala format:

! boogie.scl
Paul Hjelmstad's boogie woogie scale
10
!
9/8
5/4
21/16
45/32
3/2
27/16
7/4
15/8
63/32
2/1

Three otonal tetrads, no utonal tetrads, not CS or epimorphic,
superparticular ratios as noted.

I found a number of ten-note seven limit epimorphic scales with four
tetrads; here's one Paul Erlich found first:

! cx1.scl
First 10/4 scale = erlich11 <10 16 23 28| epimorphic
10
!
15/14
7/6
5/4
4/3
10/7
3/2
5/3
7/4
15/8
2
! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1]

Quite a lot of musical possibilities in these relatively small 7-limit
JI scales, I think.

Original HTML content:

<html><head><title>boogiewoogiescale</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Boogie Woogie Scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Boogie Woogie Scale</h1>
 <br />
In <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65608" rel="nofollow">this posting</a> of the Yahoo tuning list, Paul G. Hjelmstad wrote:<br />
<br />
Take the standard 12-bar boogie-woogie. Let's use F major:<br />
<br />
F A C Eb<br />
Bb D F Ab<br />
C E G Bb<br />
<br />
Tune to the seven-limit and keep fifths. You get<br />
<br />
12 15 18 21<br />
4 5 6 7<br />
36 45 54 63<br />
<br />
Fit into one octave (F, G, Ab,A,Bb,C,D,Eb,E)<br />
24, 27,28,30,32,36,40,42,45 and 63 (extra Bb)<br />
<br />
Taking all the ratios, we find that they are all superparticular (n/n-<br />
1)<br />
9/8, 28/27, 15/14, 16/15, 9/8, 10/9, 21/20, 15/14, 16/15 (and the<br />
schisma for Bb/Bb 64/63)<br />
<br />
You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale<br />
steps..<br />
<br />
The first seven triangular numbers are used; 1/1, 3/2, 6/5, 10/9,<br />
15/14, 21/20, 28/27<br />
Five of the squares are used: 1/1, 4/3, 9/8, 16/15 and 64/63<br />
<br />
8/7 and 7/6 are the only ratios which are not squared or triangular<br />
superparticular ratios but they are still superparticular!<br />
<br />
All from the simple boogie woogie!<br />
<hr />
Gene Ward Smith described some additional properties (in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/65610" rel="nofollow">this posting</a>):<br />
<br />
Here it is in Scala format:<br />
<br />
! boogie.scl<br />
Paul Hjelmstad's boogie woogie scale<br />
10<br />
!<br />
9/8<br />
5/4<br />
21/16<br />
45/32<br />
3/2<br />
27/16<br />
7/4<br />
15/8<br />
63/32<br />
2/1<br />
<br />
Three otonal tetrads, no utonal tetrads, not CS or epimorphic,<br />
superparticular ratios as noted.<br />
<br />
I found a number of ten-note seven limit epimorphic scales with four<br />
tetrads; here's one Paul Erlich found first:<br />
<br />
! cx1.scl<br />
First 10/4 scale = erlich11 &lt;10 16 23 28| epimorphic<br />
10<br />
!<br />
15/14<br />
7/6<br />
5/4<br />
4/3<br />
10/7<br />
3/2<br />
5/3<br />
7/4<br />
15/8<br />
2<br />
! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1]<br />
<br />
Quite a lot of musical possibilities in these relatively small 7-limit<br />
JI scales, I think.</body></html>

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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:hstraub|hstraub]] and made on <tt>2006-09-07 09:03:18 UTC</tt>.<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>1150522</tt>.<br>
+: The original revision id was <tt>151471511</tt>.<br>
-: The revision comment was: <tt>Paul G. Hjelmstad's boogie woogie scale</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:
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 Three otonal tetrads, no utonal tetrads, not CS or epimorphic,
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-&lt;br /&gt;
+ &lt;br /&gt;
 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;
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 Three otonal tetrads, no utonal tetrads, not CS or epimorphic,&lt;br /&gt;

Boogiewoogiescale: Difference between revisions

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