Help needed with Rothenberg stuff

It appears to me that phase space and pitch height behave much like
Asgard
and Midgard in "The Long Dark Tea-Time of the Soul"; any change in one
affects the other, but in suprizing and unpredictable ways. Phase space
controls harmony, while pitch height controls melody. Equal temperaments
recognize pitch height but ignore phase space, vice versa for CPS's and
Euler-Fokker genera.

Now I can get along in phase space just fine, but I know nothing of the
tools for pitch height beyond propriety and Constant Structures, on which my
hold is still slippery
at best. The Dictionary, which I can usually depend on to have what I'm
looking for no matter how obscure, is curiously devoid of definitions for
"stability," "efficiency," "redundancy," or anything beginning with
"Rothenberg." Could someone please explain these to me? If it's not
something the rest of the list would benefit from, use mtpepper@prodigy.net
.

"We all like to congregate,' he went on, 'at boundary conditions.'
"'Really?' said Arthur.
"'Where land meets water. Where earth meets air. Where body meets mind.
Where space meets time. We like to be on one side, and look at the other.'"
�"Mostly Harmless", chapter 9

Stay Tuned,
Keenan P.

--- In tuning@egroups.com, "Keenan Pepper" <mtpepper@p...> wrote:

> It appears to me that phase space

You must mean lattice space or harmonic tone space. Phase space is a
totally different concept.

and pitch height behave much like
> Asgard
> and Midgard in "The Long Dark Tea-Time of the Soul"; any change in
one
> affects the other, but in suprizing and unpredictable ways. Phase
space
> controls harmony, while pitch height controls melody. Equal
temperaments
> recognize pitch height but ignore phase space,

Well . . . some of us derive equal temperaments directly from
harmonic
tone space, by constructing Fokker periodicity blocks and then
ironing
out the unison vectors. Of course, only the harmonically "good" ET
come out this way.

> vice versa for CPS's
>and
> Euler-Fokker genera.
>
> Now I can get along in phase space just fine, but I know
nothing of the
> tools for pitch height beyond propriety and Constant Structures, on
which my
> hold is still slippery
> at best. The Dictionary, which I can usually depend on to have what
I'm
> looking for no matter how obscure, is curiously devoid of
definitions for
> "stability," "efficiency," "redundancy," or anything beginning with
> "Rothenberg." Could someone please explain these to me? If it's not
> something the rest of the list would benefit from, use mtpepper@p...

Well, the Rotherberg stuff is interesting, but take a look at my
paper
for a set of melodic (pitch-height) criteria that I find more
plausible and intuitive as a musician. I discuss "tetrachordality" --
the idea that every octave species of a "good" scale should contain
two 4/3 spans with an identical arrangement of step sizes. For
example, the diatonic scale satisfies this property:

(C D E F) (G A B C)
(D E F G) (A B C D)
(E F G A) (B C D E)
F (G A B (C) D E F)
(G A B (C) D E F) G or G (A B C (D) E F G)
A (B C D (E) F G A) or (A B C (D) E F G) A
(B C D (E) F G A) B

The usual pentatonic scales, and one of the two classes of decatonic
scales in my paper, satisfy this property. Many other world scales
are
"tetrachordal" in some, but not all, octave species. One could thus
define a fractional "tetrachordality" measure. Kraig Grady's 7-limit
JI Centaur scale, which we recently discussed, has a decent amount of
tetrachordality both as a 12-tone whole and in its scalar subsets.

Then there are "altered" scales that deviate from this logic in one
spot -- if this deviation has a strong harmonic raison d'etre
(preferably otonal rather than utonal), it is accepted quite readily.

>The Dictionary, which I can usually depend on to have what I'm looking
>for no matter how obscure, is curiously devoid of definitions for
>"stability," "efficiency," "redundancy," or anything beginning with
>"Rothenberg." Could someone please explain these to me?

You can read excerpts of Rothenberg's own article -- I referenced it in
my last post on the topic. Maybe you've read the article, and found it
unclear?

If you understand propriety, then you understand the most important part
of Rothenberg's idea.

-Carl