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Pierre Divenyi writes:

> The
>Mussorgsky example of Steve Smoliar only raises the question
>whether the smallest played units should be considered
>the REAL units (in a musico-perceptuo-cognitive sense).

That was one of my intentions.

>Thus, the problem to be solved is to establish units of
>t i m i n g  -- for the sake of musical meaning and perceptual
>organization. Grouping rules cannot (and should not) ever be
>drawn up in disregard of such timing units.

Furthermore, the ability of the metrical structure rules to capture those units
in any perceptually relevant way is also questionable.  Part of the problem is
that we tend to succumb to the urge to focus only on short examples which are
relatively neat.  Another interesting element of Mussorgsky's "Gnome" is that
the whole movement proceeds in fits and starts.  Taken as a whole, there are NO
units of timing which really encompass the entire "picture."  In this case the
most salient cue to segmentation at the highest level is SILENCE.  Pauses break
the whole into fragments.  Furthermore (and this may be the most interesting
part), some of those fragments are too brief to establish units of timing
within their own local scope.

I think the primary lesson here is that while (or perhaps because) most music
has a beat, there are acts of music behavior which seem deliberately calculated
to escape that beat (just as there can be calculated efforts to escape
conventions of consonance and dissonance).  We even find performances
of jazz which are often aimed at getting away from the beat, despite
any assumptions that you cannot have jazz WITHOUT a beat!  So I suppose
the key question we face is whether or not, in such situations, silence
is all we have.  I am not sure this is the case.  The metrical modulations
of Elliott Carter are also quite disruptive of beat conventions, and he often
implements them in rather think instrumental textures which eschew silence.
This may be quite a sticky problem which would provide an excellent opportunity
to survey the literature of music.

> Yes, the
>Mussorgsky notes in the last measures of Gnome are audible
>only to the very best trained ears (I used to be capable of such tricks
>thirty some years ago...) and, therefore, we can assume that the
>timing units are quite a bit larger than the eight-note element.

It helps if you know in advance what the notes are (say, from having practiced
the passage).

>Larger chunks would also work for music with uncertain unit
>onsets, such as the Schoenberg piece cited, or the "composed
>harmonic structures" (harmonics of a complex played by different
>instruments) in pieces of composers like Gerard Grisey.
What is interesting about the Schoenberg example is that it does not abandon
the beat.  While he tries to conceal the onset, the overall quality of timbre
is modulated by dynamic swells.  Thus, through more gradual controls of
dynamics than you would find in attack curves, he sets up a pulse which,
in this case, DOES pervade the entire movement.

>The 64,000-dollar question is: what are those larger timing units
>and how to determine them experimentally. The hunch is yours!
I would think that, before designing experiments, one might do well to
interview people who actually make music.  How do pianists (or conductors)
organize the passage of time through Mussorgsky's "Gnome?"  What sorts of
channels of communication are set up within a jazz combo which is pushing
the limits of its beat?  How does a conductor maintain control of Carter's
"Variations for Orchestra?"  How does he know what to listen to in or to
establish whether or not he is IN control?  I would recommend that any search
for an answer to that question should begin in the concert hall before it moves
to the laboratory!

Stephen W. Smoliar; Institute of Systems Science
National University of Singapore; Heng Mui Keng Terrace
Kent Ridge, SINGAPORE 0511
Internet:  smoliar@iss.nus.sg   FAX:  +65-473-9897