Boogiewoogiescale

Boogie Woogie Scale

In 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 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.