Shank: trumpet palyers will tell you how important the correct shank can be.....they know that how a mouthpiece fits into the leadpipe receiver of your instrument is vital. If not aligned correctly, a small gap can result between the shank and leadpipe. This small gap can have disastrous effects on intonation and response on your trombone. Make sure your mouthpiece sits firmly into the leadpipe without any excess play and without sticking out too far. (NOTE: for those that play European trombones, a custom shank may have to be fitted for your mouthpiece.........euphonium players experience this with their Besson instruments)
Cup Depth: a deep cup will tend to darken one's sound and open the trombone up in the low register. This comes at the expense of making the high range a bit more difficult and cutting some brightness out of your sound. If you want a mouthpiece to assist in the high register, look for a shallow cup.
Cup Shape: the more "funneled" a mouthpiece's cup, the darker and mellower the sound. The presence of a well-defined SHOULDER in a cup-shaped mouthpiece will brighten the sound by favoring more of the higher overtones in your sound.
Throat: this is the point of most resistance since it's the narrowest aperture through which the air will pass. A big, open throat will allow for more volume, but will require more air from the player. If you venture too far into wide-open throats, you will also experience intonation problems as notes will have a tough time "centering". A smaller throat will make your sound more focused and centered, but you will "break up" on the louder stuff. If you never need to play loudly, a small throat can make your job easier. If you notice that your sound spreads when you play loudly, you might want a bigger throat.
Backbore: the interior of the shank is referred to as the backbore. It begins where the throat ends and serves to "guide" the airstream into your horn. An open backbore that tapers very quickly to it's largest diameter will let you put a lot of air into the horn and thus play loudly with a bigger, darker sound. A backbore too open will lead to control problems and tricky intonation tendencies. A more narrow backbore will "compact" the sound at the expense of some darkness and volume. A delicate balance must be achieved between the dimensions of the throat and the backbore of a mouthpiece. Many drastic changes in response and tone quality can result by experimenting with this balance.
Rim Width: a wide, cushioned rim can feel very comfortable and many players say they have more endurance on these. It has been my experience, though, that the big fat rims can wear you out very quickly and don't allow for much flexibility. Very narrow rims can be uncomfortable and tire you out quickly too. A happy medium should be sought in this regard.
Rim Contour: if you look at your mouthpiece from the side, you'll notice that the rim is not flat. Old sackbut mouthpieces were very often flat, but modern mouthpieces are rarely so. There's a slight "roundness" to the rim and the peak of the roundness should probably be closer to the inner rim. This allows for a nice mixture of comfort and effectiveness.
Bite: the bite is the steepness of angle as the rim meets the cup on your mouthpiece. A 90-degree bite would be severe. A sharp bite like that would allow notes to center very well and notes would "slot" nicely. Staccato attacks would be easy, but legato would be tough on an extremely sharp bite. A round, gentle bite would make legato very smooth indeed, but would make it tough to center notes and play harder articulations with any amount of clarity. Again, since music will demand both centered staccattos and legato passages, a happy medium should be sought. If you notice great difficulty in playing legato, you may want to examine the bite of your mouthpiece.
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