TubaTinker wrote:sloan wrote:TubaTinker wrote:
No way. Cutting a bell has much LESS affect on the pitch than cutting the smaller bugle tubing. It has to do with something called 'bell effect' that I understand but can't explain. Maybe Rick Denny can take a shot at that!
http://lmgtfy.com/?q=Bell+effect+brass
I know what the theory is. But can you explain it in terms that EVERYONE can understand? I spend several years doing acoustics research for a living and I still can't begin to map it all out in layman's terms.
Well, in order to do it in "layman's terms" we need to accept a certain hand-wavyness.
How does this sound (I apologize - this is off the top of my head and might be completely bogus). The basic bugle has a collection of partials which are very far from the target harmonic series. The "bell effect" (and the mouthpiece effect) is a shifting of partials so that they line up with the harmonic series. The question is: how does the bell shift the partials? The answer is in the question: where is the "end" of the bell?
So...where *is* the "end" of the bell. The answer is that it is frequency dependent. The effective end of the bell is where pressure is equalized with the surrounding air.
This depends on the relationship between the wavelength of the sound and the diameter of the bell. So - it's easy to see that different frequencies see a different "end" of the bell and hence a different overall length of the bugle.
That should be enough to convince you that the bell will MOVE some of the partials. Alas, my Benade books are out on loan - my recollection is that he has a nice discussion of this. My apologies to him, and you, if I've somehow mangled it. In any event - it's hard to go much further on the details of how and why the mouthpiece and bell take the partials of the basic bugle (my standard model is that these are the odd harmonics of a fundamental that is lower(?) than the target) and compress them to an approximation of all (except 1...) of the harmonics of the fundamental that names the key of the instrument. The "bell effect" pushes the high frequencies lower, and the mouthpiece tends to push the low frequencies higher.
Appealing to Fletcher&Rossing again: (I ask your indulgence here for one of my favorite paragraphs - it has no equations, so perhaps it qualifies as "layman's terms")
"While some brass instruments have Bessel-like flare constants not far from unity, instruments of the trumpet and trombone families typically have [gamma] closer to 0.7 (Young, 1960), so that they flare more abruptly at the mouth, as shown in Fig. 14.2. Such horns can fit even more smoothly onto cylindrical tubing, but they require shape adjustment to tune the resonances, as is indeed true for any such compound horn (Young, 1960); Kent, 1961; Cardwell, 1970; Pyle, 1975). Adjustment of the shape is usually carried out in the course of design to produce a mode series approximating (0.7, 2, 3, 4,...) f0. The first resonance is very much out of alighment, produces a very weak sound, and is not used in playing. Good players can, however, use the nonlinear effects we shall discuss later in this chapter to produce a pedal note at frequency f0 by relying upon cooperation with the harmonically related higher resonances."
What I take out of this (the hands now begin to wave faster and faster, pay no attention to the man behind the curtain) is:
a) simple computations based on length of the bugle canNOT be very precise. There's too much engineering and re-shaping of the resonances going on. A tuba is not an ideal string.
b) even in theory, the first partial is NOT at f0. There is NO RESONANCE AT f0 - no matter how much your ears tell you there is (see the last sentence of the quote).
c) instead, it seems that we can identify the "false tone" with the actual first partial. Notice that buzzing 0.7 f0 will access this partial - but the note should suffer from
a LACK of supporting higher harmonics. Where will the {1.4, 2.1, 2.8, 3.5, 4.2,...} f0
come from?
And so on...
