Stability. To be 'stable'- unwavering. Consistent. Steady. Like a foundation of a house, or a pyramid. Environmental variability will not cause a change in course. I define stability as the ability to remain at a level of homeostasis regardless of the presence of factors of variability.
As a musician (particularly a wind musician), we need an embouchure (when the muscles in our face create a stable formation that can allow a consistent flow of air to pass through an opening (aperture), which creates a consistent vibration in the lips, thus a consistent sound). The muscles in the face need to be coordinated in a very specific manner that allows for consistency as well as flexibility.
This entire concept of stability is a matter of scaling. If we think about anything that is stable it has to be relative to time. A bridge is stable, unless you are referring to a period of a million years. In that case, a bridge is actually not stable at all- it is quite flimsy. For our purposes as musicians, we can relate to things that seem consistent over a period of seconds or minutes as this most closely relates to the amount of time in between breaths or tiny breaks in musical lines. In the grand scheme of life, the amount of stability we need is actually quite small.
As a brass musician, I need to be able to play tones that are unwavering in frequency or timbre or volume. They need to have clarity and efficiency. I shouldn't have to work too hard to make these sounds. I noticed a funny thing- I have been playing trombone for decades and only recently discovered how bad I am at playing really stable tones. I basically have NO stability! In fact, as I work with my students, I am starting to discover that almost none of them have stability in their playing either.
I have paid keen attention to great players as of late for this very reason and I started noticing the best players do have great stability- they way they play is so smooth that even notes that change pitch etc. appear to be all 'the same' as if there is no movement in the face. I am not sure if they meant to develop stability or not, but they DID, and if you want to sound like them, stability is one skill you need to master.
The body is designed to operate under variable constraints and can usually deal with a changing environment to produce consistent results (product over process). It is fine when the system accommodates tiny adjustments and variability (that is most likely imperceptible), but if you want to play at the highest levels, you have to have an exceptional balance of stability and agility such that there is no audible involuntary deviation from your sound. That means being able to play sustained tones with no 'funny business' in your face. Minimal shifting around in your embouchure in order to sustain tones. It makes sense that this would also help agility as increased shifting around while you play, the more cumbersome it becomes to move around the range of the instrument (thus less agility).
I offer private consultations for people that need a 'personal trainer' to either develop stability, improve their current stability, or rehabilitate after injury. Please click on the following link to learn more about my services.