For those not on the yahoo hornlist, I’d like to share a recent post from Richard Hirsh. For those not familiar with him, he is a very highly regarded Horn miracle worker from Chicago. You have probably seen the various horns on hornplayer.net which he has resurrected.

My take-away from this post is that science absolutely has its place in horn building, its just that nobody has figured out how to use it to their advantage. It’s nice to know the amplitudes of every available overtone in a given note, but nobody has any idea how to turn that into usable information for horn builders. And even if we were able to build a horn with perfect acoustics, who can even say for certain that it would sound like a horn? The secret is good old fashioned empirical research (read: trial and error…). If it sounds good and plays good, it is good. Period. (grammar left poor to facilitate wisdom…)

Now words from someone smarter than I…

“For those interested, two classics on musical physics are Vibration and
Sound by Philip Morse (McGraw-Hill 1948, second edition) and Horns,
Strings and Harmony/ by Arthur Benade (ca. 1962).

Benade’s book is very intuitively understandable, but it is based on a
lot of rigorous understanding and analysis. I heard him speak on several
occasions at the Acoustical Society of America. He was a clarinetist,
but had a wide understanding of musical acoustics. Still, when
describing how to make adjustments to clarinet mouthpieces, he answered
one question by saying, “I can show you, but I can’t describe what I do.”

Morse’s book is fairly pure theoretical physics. I struggled through
part of it during my senior year in college as a physics major, and came
away with some understanding of the subject:

(1) In order to come up with “nice” solutions (e.g. strings produce sine
waves, the ideal taper for a horn is a catenoid, etc.), you have to make
many unrealistic assumptions. These include perfect reflection at tubing
ends, perfectly rigid tubing walls, perfectly rigid string bridges,
perfectly flexible string, etc. Even with these simple models, the
mathematics quickly gets heavy when you start to introduce more
realistic modifications, like movable bridges, stiff strings etc.

(2) Physics, like all sciences is descriptive. It relies on models to
describe complicated phenomena, because we need to start with relatively
well understood phenomena in order to progress with some confidence to
more complicated. These may be mathematical, purely descriptive, or more
recently, digital. The classic competing models of light comes to mind -
two different descriptions of light (waves or particles) were developed,
both successful at predicting much behavior using physical models (wave
tanks and rolling balls) and both good for mathematical analysis. Wave
theory was more successful at predicting diffraction, but eventually
particles (photons) had to be reintroduced when very low levels of light
were analyzed. Ultimately the usefulness of a model must be judged on
how well it can predict actual behavior.

FFT (Fourier transform) analysis has been mentioned as a tool in
understanding how sounds are constructed, but one must be careful in
relying too heavily on this method. While it’s information is
intuitively useful (time/amplitude waveform is converted to a
frequency/phase spectrum), it is ultimately only a mathematical trick,
WHICH DOES NOT PRODUCE CONSISTENT OR REVERSIBLE RESULTS. You can get
wildly different analyses of the same sound by changing the size of the
sampling window. And if you Fourier transform your frequency/phase
spectrum back into a time/amplitude waveform, you will find the waveform
has no beginning or end, but repeats endlessly.

Still, the results of mathematical model analysis provide us with some
basis for study and development, which ultimately must be corroborated
by practical experience. Fourier transform analysis does still give us
information about predominance of certain partials etc. For horns,
analysis of tapers etc. shows that making a horn play with a good
harmonic overtone series relies on the taper matching approximately a
catenoid pattern, both for the alignment of the overtone series ,and
the ability to insert varying lengths of straight tubing without
altering the spacing of the harmonic overtone series.

Richard Hirsh, Chicago
A.B. Physics, U. of Penn’a, who remembers precious little of it.”