Re: Arabic Maqamat

In (infinite) ordered set of gammiers, number 4 is close related to arabic
music. Its harmonic generator is (1 9 5 11 3). The following like-Partch
matrix gives not only the set of tones but all internal composition law.

1 9/8 5/4 11/8 3/2

11/9 1 10/9 11/9 4/3

8/5 9/5 1 11/10 6/5

16/11 18/11 20/11 1 12/11

4/3 3/2 5/3 11/6 1

There are 48 combinations of 7 degrees modes well intricated in this
structure. We can explicit them in the factorization lattice that we can
read directly on the matrix. Each diagonal corresponds to distinct degree.
The following diagram is to be completed with pencil for instant reading of
modes.

9/8 11/6
5/4 5/3
10/9 11/8 3/2 20/11
1 11/9 / 18/11 2
11/10 4/3 16/11 9/5
6/5 8/5
12/11 16/9

- the most major mode is near lydian with 11/8-triton and 11/6-sensible :

1 9/8 5/4 11/8 3/2 5/3 11/6 2

- the rast mode (4 3 3 4 4 3 3) corresponds to :

1 10/9 11/9 4/3 3/2 5/3 11/6 2

If someone is interested, I can give much more details and graphics.

Pierre Lamothe

I don't understand why I have always an error in my posts. I try to check
well but... I don't know : maybe I desire secretly be known for my errors
and not my theories.

11/9 was wrong on first column - changed for 16/9

1 9/8 5/4 11/8 3/2

16/9 1 10/9 11/9 4/3

8/5 9/5 1 11/10 6/5

16/11 18/11 20/11 1 12/11

4/3 3/2 5/3 11/6 1

Pierre,

Hello.

Please do send me the "much more details and graphics" if convenient.

Thanks,

Jacky

--- In tuning@egroups.com, Pierre Lamothe <plamothe@a...> wrote:
>
> In (infinite) ordered set of gammiers, number 4 is close related to
arabic
> music. Its harmonic generator is (1 9 5 11 3). The following like-
Partch
> matrix gives not only the set of tones but all internal composition
law.
>
>
> 1 9/8 5/4 11/8 3/2
>
> 11/9 1 10/9 11/9 4/3
>
> 8/5 9/5 1 11/10 6/5
>
> 16/11 18/11 20/11 1 12/11
>
> 4/3 3/2 5/3 11/6 1
>
>
> There are 48 combinations of 7 degrees modes well intricated in this
> structure. We can explicit them in the factorization lattice that
we can
> read directly on the matrix. Each diagonal corresponds to distinct
degree.
> The following diagram is to be completed with pencil for instant
reading of
> modes.
>
>
> 9/8 11/6
> 5/4 5/3
> 10/9 11/8 3/2 20/11
> 1 11/9 / 18/11 2
> 11/10 4/3 16/11 9/5
> 6/5 8/5
> 12/11 16/9
>
>
> - the most major mode is near lydian with 11/8-triton and 11/6-
sensible :
>
> 1 9/8 5/4 11/8 3/2 5/3 11/6 2
>
> - the rast mode (4 3 3 4 4 3 3) corresponds to :
>
> 1 10/9 11/9 4/3 3/2 5/3 11/6 2
>
>
> If someone is interested, I can give much more details and graphics.
>
>
> Pierre Lamothe

Jacky

I will give you in few hours graphical elements that are on my old computer.

For the moment it's a simple information on the only Zalzal scale I had on
my notes :

1 9/8 27/22 4/3 3/2 18/11 16/11 2

I can construct minimum coherent set of tones where that scale is a proper
mode as chain on prime tones. Well-ordered generator that construct this
set is
(9 81 11 3 27) and matrix is :

1 9/8 11/9 4/3 3/2

16/9 1 88/81 32/27 4/3

18/11 81/44 1 12/11 27/22

3/2 27/16 11/6 1 9/8

4/3 3/2 44/27 16/9 1

There are 36 modes embedded here. The nodes of factorization lattice in
symetrical representation are :

12/11 27/22 18/11 81/44

1 9/8 32/27 4/3 3/2 27/16 16/11 2

88/81 11/9 44/27 11/6

The tones of this gammier are very near of those in gammier 4. If we
compare generators, they differ only by a syntonic comma 81/80 :

(81)-(5) and (27)-(5/3)

The arabic t-gammier approximating this Zalzal one in T41 is gived by :

0 7 12 17 24
34 0 5 10 17
29 36 0 5 12
24 31 35 0 7
17 24 29 34 0

Only 9 well distinct modes are embedded here :

5 10 29 34
0 \ 17 24 \ 41
7 12 31 36

I project to write eventually a text which compares different manners (as
Safi al-Din 17 tones) to generate similar modes.

I think that ideal reference is gammier 4. But other systems can, maybe,
solve concrete problems of musician with which I'm not familiar.

I will communicate later.

Pierre

Jacky

I had put some graphical elements on my pages about Zalzal scale and
gammier 4. The file is temporary. But the link will not be breaked later. I
project to write a text on arabic topic (at the same URL).

http://www.aei.ca/~plamothe/arabic.htm

I wait specific questions before comments.

Pierre