Kevin Sutton replies to Ron Chaplin:

>>>Can you give me some examples of tonal centers?
>
>A tonal center is a primary key area upon which the harmonic structure
>of a work is based.  To give an example that most everyone would recognize,
>Beethoven's fifth symphony is in the key of C minor. When Beethoven moves
>into other keys, these keys are related, harmonically, to c minor. In
>the common practice of western music, certain key relationships are
>stronger than others, and it takes some clever use of related chords to
>successfully wander too far outside of the realm of easily related keys.

and so on.

Kevin basically talks about common practice -- that period from roughly
Corelli to just before Wagner.  I'll elaborate on tonal centers in modern
music.  Essentially why this is important is that the structure of
classical music is marked by shifts in tonal centers.  That is, typically
we find in scherzo and trio movements the scherzo in one key and the
trio in another with the scherzo returning in the original key.  Think
of it a bit like the blues, where the first strain is in one key (that
is, "do" is on a particular pitch), the repeat is centered in another,
related key ("do" moves a fourth up), the third line moves "do" to the
fifth, but returns to the original "do" by the end.  We can see this in
the song "Fine and Mellow":

  My man don't love me, he treats me awful mean.  (original "do")
  My man don't love me, he treats me awful mean.  ("do" up a fourth)
  He's the lowest man I think I've ever ("do" up a fifth from original)
seen  (original "do")

Now, in classical music, these "do"'s take a while to shift.  When they
do, you can reasonably bet you're in a new section.  For example, in
Beethoven's Fifth, the center doesn't really shift from initial c-minor
until the horn call.  The problem is that these do's began to move around
very quickly, much more quickly than delineating the parts of a symphonic
movement requires.  Try, for example, to find "do" in Wagner's prelude
to Tristan.  Harmonically speaking, things are changing rapidly.  The
unsettled feeling you get is due in large part to these quick shifts.
You don't find your feet all that easily.  Indeed, you may find it hard
to figure out where "do" is at all.

Furthermore, as Kevin points out, certain shifts are felt as "stronger"
or "more natural." Shifting a fourth or a fifth -- well, these days we
hardly notice that.  Shifting by thirds is a little unusual.  Often
composers reserve this shift for a special moment -- as Faure does in
the Agnus Dei section of his Requiem, at the words "lux aeterna" (eternal
light); the whole line sudden seems to light up in ecstasy.

In Modern music, the key you may be in at any moment is hidden by
the increased level of dissonance.  In that case, it's often possible
to talk about a "tonal center" as a kind of average over a span.  In
Nielsen's Fifth, for example, the first movement is largely a conflict
between *two* tonal centers, F and G.  Why "tonal centers" and not "keys?"
After all, for Beethoven, these are pretty much the same thing.  Well,
for one thing, Nielsen's F often has notes out of key in it, most notably
a B-natural rather than the "designated" B-flat.  The G often has an F
rather than an F#.  For Nielsen, these two different tonal centers,
adjacent to each other on the keyboard, often share exactly the same
notes, while the keys do not (they share only five).  The tonality becomes
fluid and ambiguous, while remaining tonal.  This furthers not only an
indecisive quality to the music, but also drama.  Which center will win
out?  Will either one, or will there be a transforming resolution to
something completely different?

Atonal music doesn't really care about these things, and thus finds other
structural principles, even though Schoenberg in his final period started
incorporating something very much like tonal centers into his dodecaphonic
music, in structuring both his basic set of pitches and his larger
movements.

Anyway, my contribution.

Steve Schwartz