Ron Chaplin asks:

>Writing the above, it occurs to me that I do not know the definitions
>of atonal and dodecaphonic music. If you or anyone else, would care to
>let me know, I would appreciate it.

Atonal and dodecaphonic music are two different things.  Not all
dodecaphonic music is atonal and not all atonal music is dodecaphonic.

Atonal music is said to have no key center.  In other words, you can't
decide where "do" is.  It's a fairly nebulous definition.  Ned Rorem
points out (and I agree) that if you hum a pedal point against a background
of atonal music, that pedal becomes "do." It's a bit analogous to abstract
painting, as opposed to representational painting.  You can often "make
pictures" out of abstract works.  Atonal music is often highly dissonant
and highly chromatic, but there are lots of pieces which fit that
description which, according to their composers, are in definite keys.
To me, atonality - tonality is a spectrum rather than, say, two distinct
paint chips, and it's also nothing to fuss about.  Most professional
musicians can't tell an atonal piece purely by listening: they need a
score.  Even then, two analysts might not agree.

Dodecaphonic music refers to music which uses all twelve tones.  It
usually gets used as a label for Schoenberg's "method of composing with
twelve tones." However, there are several twelve-tone systems.  Schoenberg's
is merely the one that seems to have been the most influential.  It's
also sometimes referred to, inaccurately, as serial music.  Schoenberg's
dodecaphonic music is serial, but so are certain Renaissance keyboard
pieces.  In Schoenberg's system, the composer bases his music on a
*series* (hence, serial) of the twelve notes of the chromatic scale.
The order of the notes is important and, in most cases, invariant
(Schoenberg himself, however, sometimes cheated).  Certain variations
of the series are allowed.  The basic variations are:

1.  Starting the series on a different pitch.  The intervals between
notes remain the same.  For example, if your series begins with C-E-G,
you could begin on Eb instead.  Your series would then begin Eb-G-Bb.
This maneuver is called "transposition."

2.  Playing the series from last note to first.  This is called "retrograde."

3.  Playing the series upside-down.  For example, the C-E-G series becomes
C-Ab-F.  This is called "inversion."

You can also do a "retrograde inversion."  In fact, you can do a lot
of stuff.  There's a maneuver called "cancrizen" (crab-like).  Messiaen
has one he called the "fan." Schoenberg also liked to divide up his basic
series in halves and perform individual operations on each half.  Webern
sometimes divided his series into *quarters*.  As I say, there's all
kinds of stuff you can do.  The constant is that every variation derives
in some way from the original series of twelve notes.

Many people view this kind of maneuvering with distaste as determinist
and "anti-art," but it's really no different in kind than learning school
counterpoint.  Nobody would claim that school fugue is real music (at
least most aren't), so it really shouldn't surprise anybody that the
basic maneuvers *in themselves* don't often produce real music.  There's
still plenty of room for composers to express themselves, if they have
anything to say with those techniques.  If a composer has nothing
interesting to say, no technique in the world will make him interesting.
As Schoenberg himself said, "Of course, a soul you have to have."

Steve Schwartz