The other day I receiverd a very interesting e-mail from Richard Gosnay, commenting on the article I wrote called The "feel" of a bore. In that e-mail he offered a different perspective on the subject at hand. The relevant part of his e-mail is copied below.
The comments about the feel of a bore [in the article The"feel" of a bore] are very consistent with terms used by brass musicians and teachers. However, they do not follow laws of physics. I think that a more practical and scientific approach to brass playing is more instructive to us all. Resistance is a very, very over-used term in brass playing. Whenever I hear a person say that an axe has a lot of resistance, I hold it with my mouth completely around the mouthpiece. Then I huff as hard as I can into it. Almost without variation, my huff finds no resistance. And this, of course is far more air than we use to actually play a note. An instrument with resistence would be tight in the low register because that is a large volume of air. But brass players think they find resistance in the high register. When we feel like a brass instrument is resisting our airstream, it is because we are not playing in tune. This could be due to our limitation in technique. More likely, it is due to intrinsic limitations to the instrument (which is why some instruments seem open and some tight to the same player). Instruments also have dead notes if they have solders that unfortunately deaden the bell precisely at locations of nodes for particular wavelength!
Bernouli, or Birnouli, or whatever that physicist's name was, developed principles regarding matter (i.e. our airstream) passing through fixed volumes. With respect to resistance, the bore or any instrument has no effect. This is because the throat of the mouthpiece is smaller than the bore. Any airstream passing through the mouthpiece is not going to resist passing into the bore. As the air passes through the throat, the pressure immediately drops. And remember, when we are playing high notes, the aperture between our lips is even smaller than the mouthpiece throat! Whether the bore is cylindrical or conical has no bearing on resistance (as long as it does not shrink smaller than the size of the mouthpice throat).
When we have instruments that play tight, or we must force air into with great force, the answer is NOT to address resistance to the airstream. The answer is to address the limitations of the physical and acoustical properties of the instrument. This could mean adjusting the wavelengths so that they fit the frequency (i.e. playing in tune). A valved instrument may need a section of tubing slightly cut. Braces on the bell section might need to be moved or removed. Sometimes, we just need to simply use alternate fingerings or slide positions to more accurately form the optimal wavelength. Many mouthpieces, these days are hopelessly inappropriate to the instrument's acoustical properties. I have an anecdote of my own:
When I was in music school, one of my best talents was versatility. I studied tenor trombone. But I was the orchestra's substitute bass trombonist too. And I played any euphonium parts that were needed. So, when I was impressed by the sound of some European orchestras, I became interested in playing alto trombone. I found a used Yamaha at a good price, and I was on my way. When I would practice, I became convinced that I had bought a lemon. The thing was hopelessly out of tune all the time. I couldn't keep any position consistent. Instead of having a trombone with 7 positions, I had an alto with about 100 different positions. Then, I tried something that had amazing results. I heaved all the small Bach mouthpieces that I felt comfortable with because of my tenor playing. I picked up the Yamaha mouthpiece that came with the instrument. Immediately, all the positions fell into place. The instrument became as loud and resonant as I wanted. I might add that the mouthpiece is a real pea-shooter. And, of course, the bore of the alto is small. But they have absolutely no resistance.
I learned that all instruments have mouthpieces that fit into the wavelengths created by the column such that they easily produce desired frequencies. And it is futile to fight these conditions. I no longer try to shoe-horn mouthpieces with which I am comfortable into instruments. My bass has a bigger mouthpiece than I like. My alto has a smaller one. But they sound much more resonant, and play better in tune, and give less of a feeling of resistance than they would if I used other mouthpieces. I adapt to the physics, because the physics will not adapt for me.
Music is made of sound. And the things that we change are time, frequency, and amplitude. If we simplify our understanding to these ideas, it is much easier to play our instruments. When teachers exhort us to fill the horn, they are not helping. The richness of tone is not a matter of filling the horn (which can't be filled because it has a big hole in the end). We need to think of increasing air volume only to increase amplitude of the sound waves (loudness=amplitude). We do not use more air to make the tones sound better. That is done by buzzing frequencies with our lips that are acoustically supported by the length of tubes that form our instruments because they match the wavelengths of the frequencies.
My alto is not any easier to play than my tenor for any particular high note. If I play well, it just sounds better. This is because the instrument is pitched higher. So, any given note, say a high E flat, is lower in the overtone series on the alto than on the tenor. It rings more overtones, so it sounds nicer. That's all there is to it. The same E flat on my tenor is just as easiy to produce. It just sounds thinner and wimpier. And there is nothing I can do about it because of physics.