TUNING digest 1586

Paul Erlich writes

> I haven't been taking about triads too much -- mostly "consonant"
> tetrads and pentads -- but suffice it to say that I feel the
> Balzano/Clough/Douthett approach to scales is bunk. The acoustical
> nature of simple intervals is a much stronger organizing force in music
> (at least the music I enjoy) than abstract set and group constructs.
> Harry Partch devoted his life to exploring microtonality and the results
> he puts forward are not to be taken lightly. For the most part, he is in
> agreement with a millenia-old tradition of musician/mathematicians for
> whom the acoustical "pull" of simple ratios is undeniable. At present,
> at least three distinct psychoacoustical phenomena have been identified
> which contribute to this impression, and octave equivalence is a fourth
> factor which Balzano happily accepts while rejecting the others. Partch
> has shown that music with a simple-ratio basis need not be
> backward-looking, but can be as exciting and unexpected as any 20th
> century music. It is heartening that most on this list seem to
> understand that there is a relationship between frequency ratios and
> consonance and are not content to choose frequencies just because their
> logarithms make pretty necklace-like patterns (although that can be
> important too).

First of all, Paul, although I disagree with you on what I consider to be
minor points -- congratulations (-- no trick -- I'm not being cynical --
I'm serious, and you'll see why in a moment.)

You may be missing the point I was trying to make. I'm well aware of the
fact that you like to work with tetras and pentas -- and, while I am
attempting to challenge the list in a colleagial way, I'm not trying to
pick a fight with you or anyone. I chose your particular post to use as a
POSITIVE example because it presents systems with more than a few fruitful
possibilities (a point I think you were making as well -- and it shouldn't
be lost).

As far as the "Balzano/Clough/Douthett approach to scales" being "bunk," I
more than disagree, but NOT because I think B/C/D are right and you are
wrong. Rather, after reading your approach, I can't find any DEEP
incompatabilities between you and B/C/D, beyond the fact that C & D use
the term "maximally even" in an understandably more restricted (pitch
class) sense than you do. But I sympathize with your approach as
well (at least up to, but not including, your tuning demands) in that I
consider an interval string such as, say, <1131113> to have important
*intervallically* "maximally even" properties. By C & D's definition,
this string would not be ME, but I know for a fact that that does not
imply that C & D would not consider it an interesting string. In my
opinion, it seems that the whole argument you have with their approach
(beside the tuning aspects) boils down to the fact that yours is an
intervallic approach and theirs is a pitch-class approach. And whether
pc-set theory or ic-set theory, set theory is set theory, so whether or
not you realize it, you're already heavily into set theory.

If you want to take the time, you can check out my "White Note Fantasy --
Part I" in Music Theory Online 4.3 which, among other things, shows why
strings like <1131113>, <9949994>, <3323332>, etc., including the "usual
(maligned) diatonic" <2212221>, share some important invariant
properties since they can all be derived from the same generic (identity)
interval string. This is to say that all of these strings (scales) are
simply versions of the same "complex string" which itself is a
version of the string . The 22@41 scale you described, beside its
individual properties, is simply a version of . Not only is it
an interesting structure for the reasons you discuss (and those I hinted
at and many more), but it should also be investigated in its simpler forms
to see what interesting invariant features can be spotted and used in
the more complex version. AND it suggests other transformations -- but only
if we are willing to bracket tuning considerations while we thoroughly
investigate the geometry (set theory). So unless Paul objects, in the
future when I describe these tri-fold hyperdiatonic structures (resulting
from a modified cloning transformation), I'll call them "Erlich strings."

Then...

> Joe Monzo wrote, > > >I found this article while snooping around > >on
the web. Many of you should find it most amusing. > >
>http://humanitas.ucsb.edu/users/steen/Abstracts/Tonality_96.html > > I
think it's much more important that it is amusing, though Stephen >
Soderberg may disagree.

I checked this out also and wasn't going to comment, but again, Paul
Erlich seems to think he has scored some sort of point with his comment.
So...

Given the choice between baby formula, pablum, strained carrots, apple
juice, etc. and beef bourgignon, stuffed pork chops, single malt scotch, a
complex wine, etc. -- I'll take the complexity of the adult diet any day.
I would no more try to make a child sip whiskey than I would try to make
him/her listen to Schoenberg. Would you draw any conclusions from 200
children who spit out pate other than that children probably don't like
pate?????

Steve Soderberg