Chuck(G) wrote:I wish I could figure out what was being objected to. "Stuffiness" to me has nothing to do (as I've observed many times before) with fluid dynamics, but rather the loss of resonance due to the lowering of the Q of the resonating column.
Ding! Ding! Ding! Ding! Ding! Ding! Give the man a ceeegar (again).
Stuffiness is a lack of resonance, not flow.
(Tom, you don't have to read this if you don't want to.)
There is a balance, however, between resistance and resonance. In electrical parlance, impedance is the sum of resistance and reactance. Reactance is a description of the resonance and total reactance should be low or zero when the tuba resonates well. That leaves only resistance. In circuits, we add resistance to a resonant circuit specifically to lower the resonance quality, or Q. If the Q is too high, the resonance is too narrowbanded and it's also hard to tune it or damp it when needed. Thus, a tuba described as stiff or slotty might be suffering from a bit too much Q. Those tubas are often easier to play with a mouthpiece that has a fat throat, because that lowers the Q.
When I do lip exercises, I find the open instrument more difficult than when I add a few valves, but when I add all the valves, it's more difficult than the open instrument. I first benefit from a little extra resistance because it reduces the grab of the slots in the partial series, but then the resistance overwhelms the impedance and causes too much loss of Q and the result is just fuzz. That's the way it seems to me, anyway.
It may be a function of path length as much as anything. With all the valves down, the path length nearly doubles and the pulse and its reinforcing return reflection (which is what makes it resonant) face more impedance. This is probably what Brian is thinking.
And Chuck is opening whole new vistas of thought with the notion of path length around corners. They aren't original with him, of course, and I've seen several experiments using hard right-angle turns instead of gentle curves that apparently worked reasonably well. When the pressure front reaches a turn, the inside edge of the front gets a bit ahead of the outside edge. If it gets too far, it will damp the resonance altogether. The bigger the curve's radius, the smaller the error with respect to the over length of the path, but I suspect that this accounts for several things that we know from experience: Sousaphones are different than tubas; short, wide tubas are different than tall, narrow tubas; and compensating valves on long instruments (e.g. BBb tubas) tend to add stuffiness.
I think one reason big tubas have their characteristic sound in a concert hall is because of path length. The wide bell and throat of grand orchestral tubas causes all sorts of multipath error, which tends to smooth out the noise in the sound and give it depth. So bending paths may be an advantage or a disadvantage in any particular situation. That's why tuba design involves so much experimentation and empirical adjustment.
The cross-section of the tube isn't a big issue in my mind, as long as the pressure fronts that make up sound aren't smacking into blockages that will reflect them significantly. I've never been able to duplicate the experience some report that a small dent in a large bow changed intonation noticeably. Maybe I'm just not skilled enough to notice (likely).
The point of taper design is to adjust the mix of harmonics that resonate or are damped. That mix of harmonics is what makes the characteristic tuba sound. And that mix of harmonics can also affect the intonation by adding and subtracting normally in-turn or out-of-tune harmonics (with respect to equal temperament, of course). If the ratio of straight to tapered tubing had a really large effect, an F tuba with five or six valves would not be possible.
But it is true that all that extra tubing adds resistance and lowers Q (resonance), either because of twists and turns as Chuck suggests or because of extra length, which I suspect underlies Brian's perspective, or, most likely, both.
Rick "always ready to confuse the issue" Denney
