Posted by Rick Denney on November 21, 2003 at 12:22:10:
In Reply to: Mouthpieces affecting pitch? posted by Rocky Bivens on November 21, 2003 at 07:50:15:
In reading the literature, it seems ("seems" is an important word here--I think I have all this right but what follows still includes broad generalities) that mouthpieces have a characteristic impedance curve. This curve is a wide, shallow hump centered over the middle register of the instrument. The characteristic impedance curve of the tuba is a series of resonant peaks representing the overtones (for a given valve combination).
The impedance curve of the mouthpiece seems to be controlled by two variables, volume and throat diameter. You can get an idea of the pitch center of the mouthpiece by popping the open cup against your palm and hearing the resulting "pitch" as the air inside resonates. Larger cup volumes lower this pitch, as do smaller throat diameters. That's why some of the largest mouthpieces have surprisingly small throats and are still very effective.
Thus, if you find a mouthpiece that has good intonation characteristics on your horn, you can change the mouthpiece size as long as you offset it with a different throat diameter, and retain those characteristics.
Now, how powerful are those characteristics? It depends on the tuba. Some tubas have very sharp resonance peaks, and tend to slot pitches narrowly. These tubas are pretty resistant to changes in mouthpiece impedance because they are applying so strong an influence of their own. Other instruments have a collection of resonances that allow a wider band of pitches. These are more sensitive to mouthpiece changes, but they are also more sensitive to player changes. If you have a horn like that, changing mouthpieces might not help if you don't have the right pitches in your head.
Larger mouthpiece throats tend to spread out the resonance peaks a little, making the horn a little less slotty. I managed the intonation wierdnesses on my York Master by going to a large mouthpiece with a large throat. It worked because the large volume and throat combination lowered the popping frequency and therefore the pitch tendency in the upper register, and also because the large throat opened up the pitch slots a bit making it easier for me to adjust automatically (assuming any ability to do so).
So, yes, it is quantifiable by looking at the sum of the impedances of mouthpiece and tuba (and also of lips). You'll see several brass-instrument examples in both Benade's Horns, Strings, and Harmony and Fletcher and Rossing's Fundamentals of Musical Acoustics. But measuring it and quantifying it in any useful way will be beyond the reach of nearly all tuba players, myself included, which leaves us with empirical methods, meaning trial and error.
But knowing the broad tendencies helps you select a direction for your experiments.
Rick "thinking impedance is the main measure of behavior in the frequency domain, but hard to understand" Denney