Don't kill the pawn

I'm reading Graham Lock's entertaining biography/tour diary of Anthony
Braxton and his (Crispell, Dresser, and Hemingway) Quartet, _FORCES IN
MOTION_. This is a wonderful bit (well I like it anyway...) where Lock
is trying his very best to pry something substantial about that which
is "separate from its musical function" out of an admirably evasive
Braxton...

L: You're saying that each of the language types you've compiled, for
example, has a particular function separate from its musical function?
B: I'm saying that every force sets something in motion. If you say,
what? I'd say that's part of what I'm learning.
L: The question would be more how do you find out which forces you set
in motion?
B: I'll let you know by your book ten (laughs).
L: After twenty years of study, you must have *some* idea!
B: I can only talk about aspects of this. In terms of what I'm really
dealing with in this time period, I can't talk about that because I
would be disrespecting you and disrespecting me.
L: Well, tell me what you can tell me (laughs).
B: But I've just told you! (laughs.) OK, I don't want to play with you
in this area...play is not the right way of saying it, but I don't
want to disrespect you by talking about something that I have not
thought out, or that I have thought out but am not ready to talk
about. Remember the isolated pawn theory!
L: The *what*?
B: The isolated pawn theory. Is it justified to kill an innocent pawn
just because your opponent has made a mistake and left that pawn
unprotected? I was very concerned about this question as a young man
and later in Paris I met Bruce Carrington, who is a very special
friend of mine, and he talked to me about a woman who had told him
that she just destroyed a man, destroyed him vibrationally, and this
man was hurt. He asked her, why did you do it? And she said, well, he
came into my path. That's what she said; so we had to deal with that -
she destroyed him because he was there. OK, I can relate to that. Now,
on the chess board, if a person puts out a pawn that is not protected,
you have to destroy that pawn - like, how dare they do that! It's
*just* to kill a pawn that is not protected, as long as it doesn't
disturb your position on the board and if it further enhances your
objectives. To destroy that pawn would be part of the lesson that has
to be learned: destruction in that context becomes even respectable.
That was the isolated pawn theory.
L: This is a justice without mercy ...
B: No, wait, that's not the end of the story. I suddenly discovered
something - you don't *want* to destroy anybody! If you can help it.
Don't kill the pawn. Why? Because of *unlogic*. OK, back to the
question: I can't answer it because of the isolated pawn theory.

(a few more experiments) MAPPING TWENTY-TONE EQUAL TEMPERAMENT...

I just noticed that by taking a major scale (F to B) on a circle of
fifths in 20e with a fifth size of (log(3)-log(2))*(20/log(2)), you
get the same (5L 2s) four step-size scale:

L(3)L(4)s(1)L(4)L(3)L(3)s(2)

that I've posted about previously (TD 381.20). Rather than
illustrating this scale here as a:

A---E---B
/ \ / \ / \
F---C---G---D

i.e.,

15------7```````18
/ \ / \ ` \
/ \ / \ ` \
/ \ / \ ` \
8-------0------12```````3

I'll use a consistent 3rd, and 5th mapping derived from the ~11.7
fifth:

B
\
D---A---E
\ / \ / \
F---C---G

(or):

19
/ \
/ \
12-----4
/ \ / \
/ \ / \
5----17-----9
/ \ / \ / \
/ \ / \ / \
18----10-----2-----14
\ / \ / \ /
\ / \ / \ /
3----15-----7
\ / \ / \
\ / \ / \
8-----0-----12
\ / \ / \
\ / \ / \
13-----5-----17
/ \ / \ / \
/ \ / \ / \
6----18-----10----2
\ / \ / \ /
\ / \ / \ /
11-----3-----15
\ / \ /
\ / \ /
16-----8
\ /
\ /
1

This would give a 20e spelled C, Ebbb, C#=Db, D=Ebb, Cx, Eb=D#, Fb, E,
F=Gbb, E#, F#=Gb, Abb, G=Fx, Ab, G#, A=Bbb, Cbb, Bb=A#, B=Cb, Ax, C:

Ax
/|\
/ | \
/ | \
Fx--|---Cx
/|\ | /|\
/ | \ | / | \
/ | \|/ | \
D#--|---A#--|---E#
/|\ | /|\ | /|\
/ | \ | / | \ | / | \
/ | \|/ | \|/ | \
B---|---F#--|---C#--|---G#
\ | /|\ | /|\ | /|
\ | / | \ | / | \ | / |
\|/ | \|/ | \|/ |
D---|---A---|---E |
\ | /|\ | /|\ |
\ | / | \ | / | \ |
\|/ | \|/ | \|
F---|---C---|---G
|\ | /|\ | /|\
| \ | / | \ | / | \
| \|/ | \|/ | \
| Ab--|---Eb--|---Bb
| /|\ | /|\ | /|\
| / | \ | / | \ | / | \
|/ | \|/ | \|/ | \
Fb--|---Cb--|---Gb--|--Db
\ | /|\ | /|\ | /
\ | / | \ | / | \ | /
\|/ | \|/ | \|/
Abb-|---Ebb-|---Bbb
\ | /|\ | /
\ | / | \ | /
\|/ | \|/
Cbb-|---Gbb
\ | /
\ | /
\|/
Ebbb

Dan

PS - Converting the fifth size of 20e to a QCM like sequence of fifths
and fourths, (log(5)-log(1))*(20/log(2^4)):

19-----11
/ \ \
/ \ \
1-----13 4----16
/ \ \ / / \
/ \ \ / / \
3-----15 6-----18-----10 1
/ \ \ / / \ \ /
/ \ \ / / \ \ /
5-----17 8-----0-----12 3----15
/ \ \ / / \ \ /
/ \ \ / / \ \ /
19 10------2-----14 5-----17
\ / / \ \ /
\ / / \ \ /
4-----16 7-----19
\ \ /
\ \ /
9------1

would give only one enharmonic equivalency, the F#=Gb 10/20
half-octave, but you would also have four cases of single intervals
with dueling spellings:

B#----Fx
/|\ |\
/ | \ | \
C#----G# | D#----A#
/|\ |\ | /| | /|
/ | \ | \|/ | |/ |
D-----A | E-----B-----F# |
/|\ |\ | /| | /|\ | \ |
/ | \ | \|/ | |/ | \| \|
Eb---Bb | F-----C-----G | D-----A
|\ |\ | /| | /|\ | \ | /
| \ | \|/ | |/ | \| \|/
| Gb-----Db----Ab | Eb----Bb
| /| | /|\ | \ | /
|/ | |/ | \| \|/
Ebb--Bbb | Fb----Cb
\ | \ | /
\| \|/
Gbb----Dbb

1/20=C#&Dbb, 4/20=D#&Ebb, 16/20=A#&Bbb, and 19/20=Cb&B#.