Hornlist Post by Richard Hirsh and Horn Physics.
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.)
For those interested, two classics on musical physics are Vibration and Sound by Philip Morse and Horns, Strings and Harmony by Arthur Benade.
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 understandings of the subject. I have included two examples of the more profound concepts below.
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.
-Jacob
January 27, 2009