Boogie Woogie Tuning

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!

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> All from the simple boogie woogie!

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

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.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
>
> > All from the simple boogie woogie!
>
> 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
>
> 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.
>
Thanks Gene. I think there is definitely a connection between
African tribal music that is in the 7-limit, and the roots
of jazz and blues, which is so definitely based on dominant seventh
chords. Your use of the <10 16 23 28| val is interesting - I take
it that epimorphic scales don't have to be equi-tempered?

> Thanks Gene. I think there is definitely a connection between
> African tribal music that is in the 7-limit, and the roots
> of jazz and blues, which is so definitely based on dominant seventh
> chords.

Hiya Paul- can you tell us what African music you're thinking of?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Thanks Gene. I think there is definitely a connection between
> > African tribal music that is in the 7-limit, and the roots
> > of jazz and blues, which is so definitely based on dominant
seventh
> > chords.
>
> Hiya Paul- can you tell us what African music you're thinking of?
>
> -Carl
>
It was actually just a few posts back, even though I have
studied African music which goes as high as the 11-limit
and other completely different African music that believe it or not,
uses 7-ET temperament.

Here it is -

Message 65494

I don't know if this is what you meant but I can highly recommend
listening to Tanzanian folk music, especially the way it was
performed by the "Master Musicians of Tanzania" with their lead
singer Hukwe Zawose. Almost everything they sang and played was in
the simple 5-tone scale of 6:7:8:9:10:12.

Notice also that (6/5)/(7/6)=(8/7)/(10/9)=(9/7)/(5/4)=36/35

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> Thanks Gene. I think there is definitely a connection between
> African tribal music that is in the 7-limit, and the roots
> of jazz and blues, which is so definitely based on dominant seventh
> chords. Your use of the <10 16 23 28| val is interesting - I take
> it that epimorphic scales don't have to be equi-tempered?

No, they simply have to map to something equi-tempered; it's closely
related to Constant Structure. If a scale has this property there is
more of an underlying logic in how the interval classes relate.

> > > Thanks Gene. I think there is definitely a connection between
> > > African tribal music that is in the 7-limit, and the roots
> > > of jazz and blues, which is so definitely based on dominant
> > > seventh chords.
> >
> > Hiya Paul- can you tell us what African music you're thinking of?
> >
> > -Carl
> >
> It was actually just a few posts back, even though I have
> studied African music which goes as high as the 11-limit
> and other completely different African music that believe it
> or not, uses 7-ET temperament.
>
> Here it is -
>
> Message 65494
>
> I don't know if this is what you meant but I can highly recommend
> listening to Tanzanian folk music, especially the way it was
> performed by the "Master Musicians of Tanzania" with their lead
> singer Hukwe Zawose. Almost everything they sang and played was
> in the simple 5-tone scale of 6:7:8:9:10:12.

Oh yes. But, and I could be wrong, I hardly think this is
tribal music. I think it's a 20th-century thing, with
practioners who live in a more-or-less Western way. Is that
wrong?

7-ET, yes, this is well established, and this is, if not tribal,
certainly pretty old.

11-limit? Which music is that!?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > Thanks Gene. I think there is definitely a connection between
> > > > African tribal music that is in the 7-limit, and the roots
> > > > of jazz and blues, which is so definitely based on dominant
> > > > seventh chords.
> > >
> > > Hiya Paul- can you tell us what African music you're thinking
of?
> > >
> > > -Carl
> > >
> > It was actually just a few posts back, even though I have
> > studied African music which goes as high as the 11-limit
> > and other completely different African music that believe it
> > or not, uses 7-ET temperament.
> >
> > Here it is -
> >
> > Message 65494
> >
> > I don't know if this is what you meant but I can highly recommend
> > listening to Tanzanian folk music, especially the way it was
> > performed by the "Master Musicians of Tanzania" with their lead
> > singer Hukwe Zawose. Almost everything they sang and played was
> > in the simple 5-tone scale of 6:7:8:9:10:12.
>
> Oh yes. But, and I could be wrong, I hardly think this is
> tribal music. I think it's a 20th-century thing, with
> practioners who live in a more-or-less Western way. Is that
> wrong?

I think one would have to ask an Ethnomusicologist about that.
It seems pretty tribal to me - think how flat 7 is to our ears.

>
> 7-ET, yes, this is well established, and this is, if not tribal,
> certainly pretty old.
>
> 11-limit? Which music is that!?
>
> -Carl
>

The 11-limit music is no longer is use. I read it in Encyclopedia
Britannica. I'll can look it up when I get home if you want.

> > > listening to Tanzanian folk music, especially the way it was
> > > performed by the "Master Musicians of Tanzania" with their lead
> > > singer Hukwe Zawose. Almost everything they sang and played was
> > > in the simple 5-tone scale of 6:7:8:9:10:12.
> >
> > Oh yes. But, and I could be wrong, I hardly think this is
> > tribal music. I think it's a 20th-century thing, with
> > practioners who live in a more-or-less Western way. Is that
> > wrong?
>
> I think one would have to ask an Ethnomusicologist about that.
> It seems pretty tribal to me - think how flat 7 is to our ears.

Maybe our very own Daniel Wolf has something to add....

> > 11-limit? Which music is that!?
>
> The 11-limit music is no longer is use. I read it in Encyclopedia
> Britannica. I'll can look it up when I get home if you want.

Thanks!

-Carl