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The Wedge Design

Your embouchure isn't flat. Why should your mouthpiece be?
The round, flat design of brass mouthpieces stems from their origin as the cut off end of an animal horn, and the limited  manufacturing options of early mouthpiece makers.  It was not based on extensive research exploring alternate designs, and has been the predominant, unchallenged shape since the early history of brass instruments... until now.
The Wedge mouthpiece is different. When looking into the cup of a Wedge mouthpiece up you can see that the rim has a slight oval shape, with the oval oriented up and down, not side to side as you might expect.The inner diameter (ID) is therefore larger from top to bottom than side to side. The oval shape extends all the way to the bottom of the cup. The mouthpiece has one or two indented orientation dots to make it easy to position correctly.
There have been oval mouthpieces before. However, the rim design of those mouthpieces was a more crude attempt to match the shape of the lips from side to side, not up and down like the Wedge. They increased contact between the lips and mouthpiece around the entire rim. The whole idea was exactly the opposite of the Wedge.
The key to the Wedge design is a subtle change to the shape of the rim and cup that makes it more biomechanically efficient. The main idea of the Wedge is to decrease pressure and surface contact on the left and right sides of the rim, so that the chops don't get pinned down. I think of it as the logical evolution of the rim shape to finally catch up with the way our embouchure works. It is a subtle change that can produce dramatic results, as thousands of players have
experienced.

These images to show the shape of the Wedge rim from the side, slightly rotated, and from the end. The basic shape is present in all Wedge mouthpieces. 

Viewed from the side in the playing position you can see that the rim is not flat. It curves away from the player at the sides of the rim, where the corners of the embouchure form. That curve is called the lateral dip.

The curve follows the natural shape of the teeth, which in most people forms and arch from top to bottom. This curve transfers pressure away from the sides of the rim at 3 o’clock and 9 o’clock and onto the top and bottom rim at 12 o’clock and 6 o’clock. The rim is extra wide at the top and bottom, and narrower at the sides, so it easily absorbs the pressure on the top and bottom rim.  This makes the rim very comfortable, especially for players with braces.

Optional Angled Rim for Trumpet, Cornet, and Flugelhorn 
We offer angled rims for players who experience specific problems due to a severe overbite. Such problems include a low horn angle that interferes with reading music or playing over the stand, TMJ or neck strain, and too much upper lip pressure. Angled rims will correct horn angle by 5 or 10 degrees.
How will your playing change?  
Better Range
The oval shape of the Wedge rim, with the oval oriented up and down, gives the efficiency of a relatively smaller mouthpiece, providing an increase in range and endurance. The bigger dimension up and down maintains cup volume despite the smaller ID side to side, so a big, resonant sound is preserved despite the smaller ID.
There are two things that drive the trumpeter’s ability to control pitch: the tension or force in the lips and the mass of the vibrating portion of the lips. Ultimately, it is the vibrating mass that really controls things. The player controls the aperture size (hence the vibrating mass). This requires fine control of the embouchure.
The Wedge rim contour provides more freedom of motion of the corners (allowing better control of the center of the embouchure and air stream), while maintaining a comfortable, secure grip on the rim. Freedom at the corners means it takes less work to adjust the embouchure, because you not working against the constraints of the mouthpiece.
Both lower register and upper register performance is enhanced, producing a bigger sound throughout the entire range of the horn. The ability to improve the ease and sound of the upper and lower at the same time is a unique property of the Wedge rim that is not provided by any other design.
Better Endurance
Any time our muscles do not have to work as hard they are going to last longer. The more efficient shape of the rim produces a significant and often dramatic improvement in endurance.
A More Even Response and Fuller Sound in All Registers
The usual way to improve the ease of the upper register is to use a shallower cup. This of course produces a brighter sound and sacrifices the fullness of the low register. The unique oval shape of the Wedge design gives the efficiency of a relatively smaller mouthpiece and the resonance of a relatively larger mouthpiece.
The Wedge sloping side rims “get out of the way” of your embouchure at the sides, reducing your work and providing better freedom and control. The vertical oval rim shape means that the distance between the edge of the lips in the centre of the embouchure and the mouthpiece rim at 12 o’clock and 6 o’clock is increased compared to a conventional rim with the same side to side ID. As a result the lip tissue has more freedom to vibrate, increasing responsiveness and adding depth to the sound in all registers.
Less Swelling
Reducing rim pressure at the sides improves circulation and reduces swelling of the embouchure. The lips get fresh blood from the arteries that run from the corners of the lips to the middle. Venous blood and lymph, which are responsible for swelling of the lips, are drained away in the opposite direction.
The pressure of a conventional rim where it crosses the blood and lymphatic vessels at the side of the rim blocks their flow, as if stepping on a garden hose. The blockage of flow in and out causes fatigue and swelling. The Wedge rim reduces mouthpiece pressure at the sides of the embouchure, which improves circulation in and out of the lip tissue contained by the rim. It takes the foot off the garden hose and greatly reduces swelling.
Less Stiffness After Prolonged Playing
Our muscles get stiff when we overuse them as a result a combination of micro-trauma to muscle fibres, changes in cellular and extracellular enzymes and minerals, and edema (extra fluid), leading to swelling. Increased lactic acid may also play some role, although this is now somewhat uncertain. Chop stiffness is also partly due to residual swelling of lip structures other than muscle, including subcutaneous tissue and skin.
The increase efficiency of the Wedge rim means that less work is required by the muscles of the embouchure. Most players use less pressure with the Wedge rim, resulting in less micro-trauma to tissues in contact with the rim. The Wedge improves circulation in and out of the central embouchure, improving oxygenation to central lip tissues and reducing swelling. Together all of these effects reduce lip stiffness after playing. An added benefit is that recovery after playing time is reduced.
Better Articulation
The unique rim and cup shape improve responsiveness in all registers by providing more cup volume for a smaller, more efficient side to side ID. The Wedge mouthpiece therefore has the resonance and responsiveness of a larger mouthpiece with a conventional rim, improving the clarity of articulation.
Better Comfort
The most common location for rim discomfort and orbicularis oris injuries is at 10 o’clock and 2 o’clock on the upper lip where the mouthpiece rim crosses the upper teeth. The shape of the Wedge rim follows the natural contour of the teeth and reduces pressure at those points, greatly improving comfort.
Easy Adaptation
You play the Wedge just like any other mouthpiece without making any intentional adjustments. Decreased pressure at the sides of the mouthpiece encourages the player to activate the corners of the embouchure, producing a subtle, automatic change to a more efficient, finely tuned aperture. The rim shape also discourages young players from using too much pressure, and from using a “smiling” embouchure, since neither of these undesirable playing habits work with the Wedge.
Reduces Symptoms of Focal Dystonia
The exact cause of focal dystonia is not fully understood by the medical profession. We do know that there seems to be some sort of corruption or interference with the nerve impulses sent to the muscles controlling the embouchure and the feedback to the brain.
There are many proposed methods of treating this disorder, which requires somehow repairing this pathway. Experience has shown that players with focal dystonia who switch to a Wedge mouthpiece often report a significant improvement in symptoms, perhaps because the unique shape of the rim activates a slightly different and undamaged neural pathway.
Easier to Take Breaths
The improved mobility at the corners and solid contact with the top and bottom lip make it easier to open the corners and to return them to the optimal playing position when taking a quick breath.
Ability to Down-size if Desired
While smaller mouthpieces do enhance upper register response a bit, they can also be constrictive and make it more difficult for the player to adjust the aperture size as needed. This often means reduced flexibility difficulty in accessing the lower register.
With the Wedge rim the player has more flexibility as result of the rim contour and the oval shape, so that a smaller diameter can be used without the usual decrease in flexibility. Despite the relatively narrower width, the longer vertical axis provides a big sound and feel of a larger mouthpiece.