Boogiewoogiescale
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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:<h1> --><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 <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>