On stability
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The response of the mouthpiece is something we've always been very attune to when testing and designing. Our mouthpieces are known for their exceptionally fast response to player input, a result we've arrived at through a combination of back bore setups, highly efficient cups and our very low cup weights.
One thing that's emerged as an important consideration in the last year and a bit of doing this is that the mouthpiece can affect the stability of the pitch and attacks. Not simply in terms of just "how wide the slots are" or how the intonation of the horn sits but actually the responsiveness to changes in the player's input.
Imagine you were trying to do vibrato; a mouthpiece that was "less stable" or "more responsive" would be conducive to doing so; as you bent to the highest and lowest points the horn immediately and easily would follow you, producing the desired result. If you play some of the old French double horn designs (like the Thevet Selmers) you'll see they were designed around specifically producing such an effect. On the flip side, in many modern playing situations we want to have as-stable a pitch as possible. It would be great if we input a vibrato and it would be diminished by the inherent stability of the system.
Now - you don't want this to be achieved by simply narrowing the slots; we need the full ability to manipulate the pitch to blend with those around us. And in-fact a stable mouthpiece can really help with that because it can help you lock in, even when the played pitch isn't centered in the slot.
So - what makes a stable mouthpiece, and what makes an unstable one? And further what other variables might be coupled?
1 - The stability of the mouthpiece seems to be higher on designs that use a high impedance; conical bores, funnel or even convex designs, etc. Designs that are adding resistance are more stable for the same bore size.
2 - As stability goes up, the clarity/ping of the attacks goes down. It seems that stability is gained at the cost of clarity. If you want whip-crack precise articulation, the piece is necessarily less stable. This isn't to say that all designs have an equal amount of stability and clarity and we're simply trading a zero sum - we've certainly played pieces that were neither - but it's important to know what the two ends of the seesaw are when designing.
What does this mean for someone selecting a new mouthpiece?
As always with equipment choices, you'll be picking what you want to focus on in practice. If your articulation is already amazing but pitch stability has been an issue, you might choose a more stable mouthpiece and then be able to focus on your best attribute (clarity) without having to spend as much work on your weakness. Similarly if you're able naturally to hold a very steady airstream, you might find the clarity is what you trade for.
Next, you'll need to know how the mouthpieces perform on it. Below is a rough gauge of the 3 style we have that make this trade at the foremost of their designs.
Stable: GA, GH, CV
Neutral: G, GM, LA
Responsive: CR
The GC, GS, and GD are all aiming for different design objectives so the stability / response trade isn't the forefront of their designs.