dissonance, ambiguity, poetic expression

> [me, TD 246.3]
>
> I think this idea of dissonance=ambiguity can be used as a
> characterization in any kind of tuning system, JI, ET, or other.
>

> [Kraig Grady, TD 246.5]
> Joe!
> I don't agree <snip> for instance yo can have a
> 8-9-10-11 tetrad and completely "know what the tonic is. The
> nearest comparison in 12et c-d-e-f or c-d-e-f# ones ear is
> completely confused as to what is meant.

Kraig:

I can't argue with what you say here, but by ET I didn't mean
solely 12-ET. Other ETs (say, a high number like 72-ET) can
provide pitches which fall quite close to the tetrads you present.

I specifically had in mind, when I said what you quoted from me,
Paul Erlich's observations about arbitrarily-complex-ET vs.
arbitrarily-complex-JI scales approximating each other.

My point was that no matter what system of tuning is under
consideration, the idea, that increasingly greater numerical
complexity equates to increasingly greater ambiguity which equates
to increasingly lesser consonance, seems to hold true.

In a sense, what I'm saying is that sonance is a result or
measure of the numerical complexity of a given interval or set of
intervals, regardless of which type of numerical tuning method
is being used. Each tuning system has inherent within it the
idea that some intervallic relations are more consonant than others.

This is a necessary prerequisite for the interplay of harmonic
and melodic relationships that imbues music with its ambiguous
levels of 'meaning'. We feel certain kinds of emotional sensations
when we hear a particular harmonic or melodic combination of
pitches, and with our typically human desire to process, classify,
and categorize both the feelings and the intervals, and various
patterns which we perceive in their combinations, various 'rules'
are generated. Characterizing this in terms of physics, one might
say that the tones themselves are the matter and the manipulation
of sonance is the energy, of the harmonic/melodic equations.

This is exactly what any music theory is about. It's what
Schoenberg referred to as 'compositional problems'.

Your comment 'The wider the range of poetic expression, the
better the theory.' deeply impressed me. A compositional problem
for Schoenberg was simply: 'how can I express this poetic idea
in musical sounds?'. His _Harmonielehre_, and probably most other
books in music theory, or at least harmony, is the search for what
'rules' may be applicable to untried tonal combinations.

Musical examples in harmony textbooks are generally fragments
from great pieces where a wonderful new poetic idea is expressed
in a way which most listeners would agree is quite exquisite.
The task of the theorist becomes then to tear apart the various
different rhythmic, harmonic, melodic, intonational, metrical, etc.,
aspects of the example, to determine what in the music is causing
the agreement among listeners as to the achievement of the poetic
expression.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

___________________________________________________________________
Get the Internet just the way you want it.
Free software, free e-mail, and free Internet access for a month!
Try Juno Web: http://dl.www.juno.com/dynoget/tagj.

Joe Monzo wrote,

>My point was that no matter what system of tuning is under
>consideration, the idea, that increasingly greater numerical
>complexity equates to increasingly greater ambiguity which equates
>to increasingly lesser consonance, seems to hold true.
>
>
>In a sense, what I'm saying is that sonance is a result or
>measure of the numerical complexity of a given interval or set of
>intervals

Of course, one has to be careful to measure "numerical complexity" correctly
-- in a few cases, something like "an 8:5 flat by 14 cents" gives one a
rough idea of the sonance, but in general, one needs something more
sophisticated. Perhaps harmonic entropy is the best attempt yet to equate
sonance purely with numerical complexity. Anyone care to differ?