Septachord Map

Not mapping in the usual sense of commas or vals but in terms of some other symmetries:

2,2,6
9,12,7
12,9,7

Based on

M1,M7,* (Symmetrical)
M1,M7,* (Asymmetrical)
M1,M7,* (Asymmetrical)

Where * maps to self under M7. Location of Z's and W's (Z-related
and Weakly-related septachords:

0,0,(W,Z&Z,ZW)
0,0,(&ZW,Z&Z)
0,0,(&ZW,Z&Z)

Z-related: Two septachords have different type but same interval vector.

W-related: septachord/pentachord complex which must pass through a Z-related hexachord.

Location of nine septachords that are not MODMOS or MOS:

1,0,0
4,0,0
4,0,0

Location of septachords that map to Inverse under M7: (I've put
them diagonally just to be schematic about it):

0,0,0
0,3,0
3,0,0

This leaves these sets which do not map to the same type under
M7:

2,2,0
9,9,0
9,9,0

Here are the Z's

0,0,3
0,0,3
0,0,3

Here are the W's

0,0,2
0,0,1
0,0,1

One Z-related pair is Symmetrical. Two Z-related pairs are assymetical
(two types and their mirror images). One Z-related trio is S-A-A., with two types (S and A,A)

PGH

--- In tuning-math@yahoogroups.com, "Paul" <phjelmstad@...> wrote:
>
> Not mapping in the usual sense of commas or vals but in terms of some other symmetries:
>
> 2,2,6
> 9,12,7
> 12,9,7
>
> Based on
>
> M1,M7,* (Symmetrical)
> M1,M7,* (Asymmetrical)
> M1,M7,* (Asymmetrical)
>
> Where * maps to self under M7. Location of Z's and W's (Z-related
> and Weakly-related septachords:
>
> 0,0,(W,Z&Z,ZW)
> 0,0,(&ZW,Z&Z)
> 0,0,(&ZW,Z&Z)
>
> Z-related: Two septachords have different type but same interval vector.
>
> W-related: septachord/pentachord complex which must pass through a Z-related hexachord.
>
> Location of nine septachords that are not MODMOS or MOS:
>
> 1,0,0
> 4,0,0
> 4,0,0
>
> Location of septachords that map to Inverse under M7: (I've put
> them diagonally just to be schematic about it):
>
> 0,0,0
> 0,3,0
> 3,0,0
>
> This leaves these sets which do not map to the same type under
> M7:
>
> 2,2,0
> 9,9,0
> 9,9,0
>
> Here are the Z's
>
> 0,0,3
> 0,0,3
> 0,0,3
>
> Here are the W's
>
> 0,0,2
> 0,0,1
> 0,0,1
>
> One Z-related pair is Symmetrical. Two Z-related pairs are assymetical
> (two types and their mirror images). One Z-related trio is S-A-A., with two types (S and A,A)
>
> PGH

One more table: Tritone count (of complementary pentad)

A=0,B=1,C=2 (Just add 1 for septads A=1, B=2, C=3)

A1,B1,C0;A1,B1,C0;A2,B2,C2
A1,B8,C0;A3,B9,C0;A0,B3,C4
A3,B9,C0;A1,B8,C0;A0,B3,C4

Location of Z's:

*;*;A2,B1,C0
*;*;A0,B3,C0
*;*;A0,B3,C0

Location of W's

*;*;A0,B2,C0
*;*;A0,B1,C0
*;*;A0,B1,C0

Location of M7I's

*;A2,B1,C0;*
A2,B1,C0;*,*

PGH