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The three tetrachordal modes of the blackjack scale

🔗paul@stretch-music.com

5/2/2001 2:03:29 PM

All 4:3 spans indicated contain identical "tetrachords" (actually
decachords):

Disjunction on bottom:

9:8 4:3 4:3
| |--------------------------||--------------------------|
0,5,7,12,14,19,21,26,28,33,35,40,42,44,49,51,56,58,63,65,70,72

Disjunction in middle:

4:3 9:8 4:3
|-----------------------| |---------------------------|
0,2,7,9,14,16,21,23,28,30,35,37,42,44,49,51,56,58,63,65,70,72

Disjunction on top:

4:3 4:3 9:8
|----------------------||--------------------------| |
0,2,7,9,14,16,21,23,28,30,32,37,39,44,46,51,53,58,60,65,67,72

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

5/3/2001 8:01:13 AM

--- In tuning@y..., paul@s... wrote:
> All 4:3 spans indicated contain identical "tetrachords" (actually
> decachords):
>
> Disjunction on bottom:
>
> 9:8 4:3 4:3
> | |--------------------------||--------------------------|
> 0,5,7,12,14,19,21,26,28,33,35,40,42,44,49,51,56,58,63,65,70,72

Step sizes for these would be nice.

🔗paul@stretch-music.com

5/3/2001 11:45:34 AM

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., paul@s... wrote:
> > All 4:3 spans indicated contain identical "tetrachords" (actually
> > decachords):
> >
> > Disjunction on bottom:
> >
> > 9:8 4:3 4:3
> > | |--------------------------||--------------------------|
> > 0,5,7,12,14,19,21,26,28,33,35,40,42,44,49,51,56,58,63,65,70,72
>
> Step sizes for these would be nice.

The 9:8 disjunction always goes 5-2-5.

The 4:3 "tetrachord" always goes 2-5-2-5-2-5-2-5-2.