Christopher Smith <[EMAIL PROTECTED]> wrote:
Then how about Hindemith? He said the same thing about > the 4th - we tend to
hear the top note of a P4th as the > acoustic root of the interval.
I don't have Schenker to hand, but what I was getting at was the way he uses
the harmonic series (rather mystically) to assigning significance the perfect
fifth and the major third, while denying it to the fourth. Hindemith, with
considerable justification in later psycho-acoustic experiments, gives perfect
fifth and fourth almost equal rank. They may have agreed in other matters.
Schenker is much maligned (by, among others, you) but
like Freud, he wasn't so much right or precise as
revolutionary. He opened some doors and changed the
way we (well, I) thought about music. Sure he was
weak on some things, but I think his essential points
stand.
He certainly changed the way I and my fellow students thought about analysis. At the end
of the year in which they took the analysis course, they got together and decided,
"There are no facts in analysis, only strongly expressed opinions". I wasn't
there, but I would have agreed.
The two big criticisms you make of him are not really
fatal to his ideas, I think. The biggest one is his
assertion that our perception of harmony comes from
the harmonic series. Behaviour of a closed pipe
or bells notwithstanding, the major triad IS the
overwhelming sound that most vibrating objects produce
in their harmonics. In a closed pipe, eliminating the
even-numbered partials STILL leaves us with a major
triad, so Schenker's assertion stands.
Both these statements are exaggerations. Forced vibrations at constant
amplitude of any structure often follow a repeating pattern (there are
non-linear devices of which this is not true), so that they can be Fourier
analysed into harmonically related components, but free vibrations, in general,
do not, and in these the resonant frequencies usually show no simple
relationships. Western musical instruments are a selected subset, in that many
of the ones that vibrate freely (most of them plucked or struck strings), are
carefully built so that their partials approximate to the harmonic frequencies
that are present in the spectra of the dominant, forced vibration, instruments.
Similarly, brass instruments overblow in close approximations to harmonic
frequencies because their designers know what musicians will want. Note that
closing a parallel organ pipe does not eliminate the even partials totally, but
since it eliminates their resonances they become weak. Similarly, unrei!
nforced even partials are present in clarinet tone, since they are present in
the repeated motion of the reed, but the odd partials are close to resonances
of the near parallel closed type tube,* so are much stronger.
* Not exactly equal in frequency. The tapered bell and mouthpiece bring the
resonances closer than 1 : 3 : 5. Two consequences are the relative weakness
of the throat notes and the tendency of many clarinets to go flat at higher
dynamic levels.
Much more damaging to this theory is how do we
hear a MINOR triad as being so resonant and basic, when
the harmonic series doesn't produce one until much
higher in the series? Your points about different-sized
thirds and seconds are not germane, as we can hear many
different-sized intervals as still being major thirds,
minor thirds, or any interval really. Out-of-tuneness
obviously adds to our sense of dissonance (as you noted
through Helmholtz), but I still think the essential
idea of our sense of consonance being based on the
harmonic series is sound.
Many psycho-acoustic experiments in the last 50 years have demonstrated departures from
that simple view. In particular, see William Sethares' book, /"Tuning, Timbre,
Spectrum, Scale/." (London: Springer, 1999).
One very interesting point
you made but did not follow through on, that a
culture with music based on inharmonic resonances would
have a different scale and harmony; gamelan music is an
excellent example.
The gamelan tradition contradicts the idea that consonance derives directly
from the harmonic series. Sethares shows that gamelan scales relate to the
non-harmonic partials of the principal metallophones of the gamelan. I (and
others) believe that our recognition of consonance is derived from the harmonic
series via the instruments that dominate our orchestras: forced vibration bowed
strings and blown wind that produce harmonic spectra and therefore sound smooth
(acoustically consonant) in harmonic frequency ratios.
Obviously Schenker had no knowledge of this, and of course
in this style his harmonic theories go out the window.
Yes, but there is lots of music to which his theories don't apply, and he gives no independent
criteria for choice of the ones that do, so his "theory" amounts to "Music like this
is like this." Since this is irrefutable, no orthodox (Popperian) philosopher of science
would consider it a theory.
The other weakness that you point out, that he chose his
examples based on their adherence to his theories and
ranked the "masters" according to who fit into his
analysis the best, well that's just stupidity (his, that
is, not yours!) Every analyst picks examples that
illustrate their points,
Maybe every analyst of music, but in scientific experiment you are supposed to
choose your examples randomly: if you are found to have selectively reported
only the experiments that work, you lose your research grant.
but to assert that failure to fit in with the theory is a
sign of poor art or craft, well, that's just ego talking.
Actually, a big point that I make with my students is that
it's the moments when things seem to fall OUT of the norm
that music starts to get interesting. Analysis can help
point out those moments, and why.
Agreed.
Theoretical analysis is only a tool, not a way of life
(which some of my theorist colleagues don't seem to agree
with!)
Schoenberg mentioned that his biggest problem with
Schenker's analyses was that he left out all the parts that
he (Schoenberg) found the most interesting. That is an
excellent point, and only supports my view further; that
any one approach is not THE right way. Each approach is
only a spotlight that illuminates some dark corners and
leaves others unrevealed.
Likewise
Yup, Schenker was a chauvinist. But then, aren't we all in
some way?
Maybe, but not to the extent of considering Paganini and Crueger "masters"
while denying that status to Debussy.
--
Ken Moore
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