Boogiewoogiescale: Difference between revisions
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In [http://launch.groups.yahoo.com/group/tuning/message/65608 this posting] of the Yahoo tuning list, Paul G. Hjelmstad wrote: | In [http://launch.groups.yahoo.com/group/tuning/message/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 | ||
C E G Bb | |||
Bb D F Ab | |||
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) | |||
Taking all the ratios, we find that they are all superparticular | |||
(n/n-1) | |||
Taking all the ratios, we find that they are all superparticular (n/n- | 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) | |||
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 | You also get 8/7, 7/6, 6/5, 4/3, 3/2, 1/1, with multiple scale | ||
steps.. | steps.. | ||
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 | ||
| Line 42: | Line 31: | ||
8/7 and 7/6 are the only ratios which are not squared or triangular | 8/7 and 7/6 are the only ratios which are not squared or triangular | ||
superparticular ratios but they are still superparticular! | superparticular ratios but they are still superparticular! | ||
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 [http://launch.groups.yahoo.com/group/tuning/message/65610 this posting]): | ||
<pre> | |||
Here it is in Scala format: | Here it is in Scala format: | ||
! boogie.scl | ! boogie.scl | ||
Paul Hjelmstad's boogie woogie scale | Paul Hjelmstad's boogie woogie scale | ||
10 | 10 | ||
! | ! | ||
9/8 | 9/8 | ||
5/4 | 5/4 | ||
21/16 | 21/16 | ||
45/32 | 45/32 | ||
3/2 | 3/2 | ||
27/16 | 27/16 | ||
7/4 | 7/4 | ||
15/8 | 15/8 | ||
63/32 | 63/32 | ||
2/1 | 2/1 | ||
Three otonal tetrads, no utonal tetrads, not CS or epimorphic, | Three otonal tetrads, no utonal tetrads, not CS or epimorphic, | ||
superparticular ratios as noted. | superparticular ratios as noted. | ||
I found a number of ten-note seven limit epimorphic scales with four | I found a number of ten-note seven limit epimorphic scales with four | ||
tetrads; here's one Paul Erlich found first: | tetrads; here's one Paul Erlich found first: | ||
! cx1.scl | ! cx1.scl | ||
First 10/4 scale = erlich11 <10 16 23 28| epimorphic | |||
First 10/4 scale = erlich11 | |||
10 | 10 | ||
! | ! | ||
15/14 | 15/14 | ||
7/6 | 7/6 | ||
5/4 | 5/4 | ||
4/3 | 4/3 | ||
10/7 | 10/7 | ||
3/2 | 3/2 | ||
5/3 | 5/3 | ||
7/4 | 7/4 | ||
15/8 | 15/8 | ||
2 | 2 | ||
! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1] | ! [0, -1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1] | ||
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. | JI scales, I think. | ||
</pre> | |||