Posted by Rick Denney on August 01, 2002 at 11:33:55:
In Reply to: Re: Re: Duct Tape on Bell Wall posted by Jay Bertolet on August 01, 2002 at 07:55:56:
There's a difference between leather belts and brass rods. The leather damps vibration, particularly in high frequencies, and the brass adds stiffness and mass which changes resonance.
If we think of sound as a complex mix of harmonics, where the upper harmonics merge with the lower harmonics to produce the timbre of the instrument, then anything that influences that mix will change the sound of the horn.
Here are my definitions, to avoid confusion:
Dark means a sound with a lot of lower harmonics compared to upper harmonics. My Miraphone is darker than my York Master, based on actual acoustical measurement. Colorful means a sound with a lot of favorable harmonic complexity. In many ways, colorfulness is related to depth which is a sense of a broad bottom that I think comes as much from wide radiation patterns as from the tone color of the instrument, and is therefore more tied in my mind to the bell shape than its resonance. The York Master is deeper than the Miraphone by a healthy margin, despite that it is less dark. Get the difference? Bright means a sound with an absence of lower harmonics, or, more accurately to my thinking, a harmonic structure which partially cancels the lower harmonics. These may be good or not depending on what you want.
The brass of a tuba vibrates because the air within it vibrates. That vibration resonates only at high frequencies and at very low frequencies. I've felt subsonic vibration in tuba bodies, and I hear it ring with a nearly shrill clang when I rap it with my knuckle. These are a direct result of brass resonance. This resonance may occur at frequencies that are not compatible with the harmonic structure of particular notes (or even with most notes), and may result in either cancelling or emphasizing those high frequency harmonics. The result is a change in the apparent tone color of the instrument.
A belt is a damping device (and so is duct tape, but to a lesser extent). It absorbs vibrational energy and turns it into (miniscule amounts of) heat. Thus, that energy is pulled out of the sound entirely, never to be seen again. The result is a horn without some of those harmonics. The result is a darker sound, but likely not as deep, depending on which harmonics are influence. It gets tricky here. If the harmonics were favorable to the note being played, the result may be a darker sound because of a greater emphasis on lower harmonics, and also a less colorful and deep sound because it is now missing something useful. If the absorbed harmonics detract from the quality of the sound, the result could be an improvement in both color and depth.
Changing the mass and stiffness of the vibrating body by using weights or brass rods changes its resonance, but in ways that are still elastic. Nothing is absorbed. The increased stiffness raises the resonant frequency, and the increased mass lowers it. Brass rods are stiff in relation to their weight, so they will increase the resonant frequency. Monsterweights and heavy mouthpieces are heavy without adding any stiffness, so that lower the resonant frequencies and also increase the energy required to excite that resonance. Brass rods may well increase the resonance to frequencies beyond the range of harmonics in the tuba sound, such that the brass no longer colors the sound. Or, they may modify the resonance so that its influence is positive rather than negative. They also increase the energy required to excite the vibration at a given magnitude, so they minimize the influence of the brass resonance. Again, this may help a horn or hurt it depending on the tone of the instrument with a given player.
My tendency would be to prefer the elastic route, with brass rods or metal weights to adjust the resonance of the brass, because they don't remove any energy from the system--they redirect it in more useful ways. Vibration dampers like belts and duct tape take something away.
The problem with all these modifications is that it is almost impossible to predict whether the effect will be positive or negative until you do it. That's the popularity of belts and duct tape--they are easily removed.
Rick "resisting the temptation to discuss a belt's tensile hoop stress on the bell" Denney