On May 29, 2007, at 4:47 AM, Ken Moore wrote:
Christopher Smith <[EMAIL PROTECTED]> wrote:
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.
Yes I concede that I exaggerated when I said that most vibrating
OBJECTS produce the overtone series, but given the overwhelming
number of instruments that use vibrating pipes, strings, membranes,
and bars (in ALL music, not just European music!) that DO produce the
overtone series, I still maintain that he is correct that our
perception of harmony comes from the harmonic series.
I am NOT saying that every composer has to use root-position major
triads in the accepted spacing; I am just saying that these are our
primary colours. Obviously I would not insist that every painter use
red, yellow and blue, but I do think our perception of colour stems
from these basics, too.
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.
Now you are the one who is exaggerating! Brass instrument
manufacturers fine-tune the taper to bring the tone and tuning closer
to what players want, but ANY overblown tube will produce the
harmonic series quite naturally in tuning close enough to be
identified. I can confirm this, having blown cow horns, garden hoses,
bamboo, termite-hollowed branches (digeridoo), vacuum cleaner pipes,
conch shells, numerous beer bottles, clarinets without the mouthpiece
on, and any number of plumbing supplies. Some harmonics are out of
tune, some are absent or hard to produce, but there is no mistaking
the relationship to the harmonic series.
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.
I don't think the relationships need to be exactly equal to be heard.
You may be putting too much emphasis on the precision of the
intervals produced.
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).
Thanks for the reference. I will definitely check that out.
Here is a book that deals with more than just tuning that I enjoyed.
It is a bit of a slog, but you seem to be an erudite fellow, and
shouldn't have any problems with the density of the prose.
http://www.amazon.com/Demonstrations-Auditory-Scene-Analysis-
Organization/dp/0262522217/ref=pd_sim_b_1/104-0630595-3786335
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.
It doesn't need to be a scientific theory to be analytical. I think
you are confusing scientific theory with music theory (which is
better called analysis anyway, IMHO). To be able to say "Music like
this (point at piece of music) is like this (point to generality)" is
actually a very powerful tool. It doesn't need to be true 100%, or
even >50%, as long as it points out anything that pokes a tendril up
out of the general confusion. Granted, I prefer my tools to be little
sharper than that, but I'll take what I can get.
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.
Heh, heh, I'm with you there! But I don't need to love the guy, I
just want to use his way of hearing things (well, SOME of his ways of
hearing things!)
Christopher
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