Proper Scale Search

I have now quite a backlog of stuff I was supposed to do. Some time
ago I proposed that we find a way to index the near-MOS's of a
temperament, because we might be missing out on some really beautiful
scales. Furthermore, I think if we had some way to do that, we'd see
all (or at least a lot) of these commonly used maqam scales emerging
from any temperament that has a half a fifth generator, whether you
believe it's 11/9 or not.

In fact, I guess this isn't even related to regular mapping, as it'd
be more related to MOS's: how does one index these scales in which
"most" intervals fall into 2 sizes, but some fall into 3?

Anyway, it was suggested that I do an exhaustive proper scale search.
I'm not sure exactly what to search for, but I guess here's a start.
Here are all of the proper scales in 12-tet. These scales are all
magical, especially the 8 and 9 note ones that I've never messed
around with before. The 8-note ones are near-MOS's of diminished[8]
and the 9-note ones are near-MOS's of augmented[9]. They are magical.
I'm serious

1 note:
12

2 notes:
1 11
2 10
3 9
4 8
5 7
6 6

3 notes:
1 1 10
2 1 9
1 2 9
3 1 8
2 2 8
1 3 8
4 1 7
3 2 7
2 3 7
1 4 7
5 1 6
4 2 6
3 3 6
2 4 6
1 5 6
5 2 5
4 3 5
3 4 5
4 4 4

4 notes:
2 4 1 5
2 3 2 5
1 5 1 5
1 4 2 5
4 3 1 4
4 2 2 4
4 1 3 4
3 4 1 4
3 3 2 4
3 2 3 4
2 4 2 4
2 3 3 4
3 3 3 3

5 notes:
3 1 3 1 4
2 2 3 1 4
2 2 2 2 4
1 3 3 1 4
1 3 2 2 4
1 3 1 3 4
3 3 2 1 3
3 3 1 2 3
3 2 3 1 3
3 2 2 2 3
3 1 3 2 3
2 3 2 2 3

6 notes:
2 2 2 2 1 3
2 2 2 1 2 3
2 2 1 3 1 3
2 2 1 2 2 3
2 1 3 2 1 3
2 1 3 1 2 3
2 1 2 3 1 3
2 1 2 2 2 3
1 3 1 3 1 3
1 3 1 2 2 3
1 2 3 1 2 3
1 2 2 2 2 3
2 2 2 2 2 2

7 notes:
1 2 2 1 2 1 3
1 2 1 2 2 1 3
2 2 2 2 1 1 2
2 2 2 1 2 1 2
2 2 1 2 2 1 2

8 notes:
2 1 2 1 2 1 1 2
2 1 2 1 1 2 1 2
2 1 1 2 2 1 1 2
2 1 1 2 1 2 1 2
1 2 1 2 1 2 1 2

9 notes:
1 2 1 1 2 1 1 1 2
1 2 1 1 1 2 1 1 2
1 1 2 1 1 2 1 1 2

10 notes:
1 1 1 2 1 1 1 1 1 2
1 1 1 1 2 1 1 1 1 2

11 notes:
1 1 1 1 1 1 1 1 1 1 2

12 notes:
1 1 1 1 1 1 1 1 1 1 1 1

-Mike

Algorithm has now crapped out at 22-tet. Looks like there was a bug in
it. I'll update it and finish up here tomorrow. I tried to fix it, now
it's completely wrecked, and it's 7:40 AM and I'm still awake. God
damn it.

-Mike

Good work!

At 04:26 AM 3/13/2011, you wrote:
>I have now quite a backlog of stuff I was supposed to do. Some time
>ago I proposed that we find a way to index the near-MOS's of a
>temperament, because we might be missing out on some really beautiful
>scales. Furthermore, I think if we had some way to do that, we'd see
>all (or at least a lot) of these commonly used maqam scales emerging
>from any temperament that has a half a fifth generator, whether you
>believe it's 11/9 or not.
>
>In fact, I guess this isn't even related to regular mapping, as it'd
>be more related to MOS's: how does one index these scales in which
>"most" intervals fall into 2 sizes, but some fall into 3?
>
>Anyway, it was suggested that I do an exhaustive proper scale search.
>I'm not sure exactly what to search for, but I guess here's a start.
>Here are all of the proper scales in 12-tet. These scales are all
>magical, especially the 8 and 9 note ones that I've never messed
>around with before. The 8-note ones are near-MOS's of diminished[8]
>and the 9-note ones are near-MOS's of augmented[9]. They are magical.
>I'm serious
>
>1 note:
> 12
>
>2 notes:
> 1 11
> 2 10
> 3 9
> 4 8
> 5 7
> 6 6
>
>3 notes:
> 1 1 10
> 2 1 9
> 1 2 9
> 3 1 8
> 2 2 8
> 1 3 8
> 4 1 7
> 3 2 7
> 2 3 7
> 1 4 7
> 5 1 6
> 4 2 6
> 3 3 6
> 2 4 6
> 1 5 6
> 5 2 5
> 4 3 5
> 3 4 5
> 4 4 4
>
>4 notes:
> 2 4 1 5
> 2 3 2 5
> 1 5 1 5
> 1 4 2 5
> 4 3 1 4
> 4 2 2 4
> 4 1 3 4
> 3 4 1 4
> 3 3 2 4
> 3 2 3 4
> 2 4 2 4
> 2 3 3 4
> 3 3 3 3
>
>5 notes:
> 3 1 3 1 4
> 2 2 3 1 4
> 2 2 2 2 4
> 1 3 3 1 4
> 1 3 2 2 4
> 1 3 1 3 4
> 3 3 2 1 3
> 3 3 1 2 3
> 3 2 3 1 3
> 3 2 2 2 3
> 3 1 3 2 3
> 2 3 2 2 3
>
>6 notes:
> 2 2 2 2 1 3
> 2 2 2 1 2 3
> 2 2 1 3 1 3
> 2 2 1 2 2 3
> 2 1 3 2 1 3
> 2 1 3 1 2 3
> 2 1 2 3 1 3
> 2 1 2 2 2 3
> 1 3 1 3 1 3
> 1 3 1 2 2 3
> 1 2 3 1 2 3
> 1 2 2 2 2 3
> 2 2 2 2 2 2
>
>7 notes:
> 1 2 2 1 2 1 3
> 1 2 1 2 2 1 3
> 2 2 2 2 1 1 2
> 2 2 2 1 2 1 2
> 2 2 1 2 2 1 2
>
>8 notes:
> 2 1 2 1 2 1 1 2
> 2 1 2 1 1 2 1 2
> 2 1 1 2 2 1 1 2
> 2 1 1 2 1 2 1 2
> 1 2 1 2 1 2 1 2
>
>9 notes:
> 1 2 1 1 2 1 1 1 2
> 1 2 1 1 1 2 1 1 2
> 1 1 2 1 1 2 1 1 2
>
>10 notes:
> 1 1 1 2 1 1 1 1 1 2
> 1 1 1 1 2 1 1 1 1 2
>
>11 notes:
> 1 1 1 1 1 1 1 1 1 1 2
>
>12 notes:
> 1 1 1 1 1 1 1 1 1 1 1 1
>
>-Mike
>