Sorry the blog was put on hold — I had a lot to do, including composing over 50 pieces since September of 2018. A creative burst!
A student came to me asking for help with the high range and endurance, especially in the high range. This is probably the most perceived common struggle. I say perceived, because the roots of the problem are really due to a different problem: proper breathing and breath control training.
First, certainly embouchure plays an important role supporting pitch and pitch changes. It requires embouchure placement, stability and flexibility to ease the passage of an air stream over the lip into the mouthpiece, and for that buzzing breath stream to move at the right angle in the mouthpiece.
Embouchure is all about paradoxes. The corners must be firm, yet pliable. The depressor anguli oris must encourage a downward movement in the corners and an upward movement, to prevent misshape of the obicularis oris. The buccinator must be alert to move away from the mouth or forward depending upon the support needed to keep the mouth in place for achieving the right opening and breath motion. The muscle around the mouth itself and attached to the pips, the obicularis oris is ONE muscle, therefore acting as one both on the upper lip and lower lip, while the air stream direction flows over the lip, with in an upstream or downstream, depending upon the player and into the mouthpiece. Then, we buzz lips, but do not squeeze them together. Philip Farkas uses a drawstring in a canvas wrapped around a can to demonstrate how our embouchure must both move inwardly and outwardly to achieve the right opening for the air to pass over the lips sufficiently and efficiently to fill the resonation of the horn and support the correct angle of the air stream going into the mouthpiece.
All that said, however, learning and training our mouths to do so is best left to a development simultaneous with breath control and endurance. Here is where many fail to develop.
Phrasing developed according to the amount of breath we have to produce a musical effect, while falling within the breathing capacity of human beings. The normal adult takes in 4-6 quarts of air. It is no accident that we normally have equal divisions in the way we phrase. As we have an in breath and out breath, we have phrasing developed from call and response. Typically, phrases are 2+2, or 4+4, etc. Sometimes we have an extension or a diminution of a phrase, but even that is subject to our breath capacity.
Then, to produce a musical instrumental sound on a brass instrument, we must maintain an air stream which with continuity fills the horn with vibrations from the buzz. Then and only then may we manipulate articulations, tone color, dynamics, in short, expression.
So, too, correct breathing lends itself to better placing of the fulcrum provided by the lip, enabling the correct angle of air steam into the mouthpiece. Before we even reach the embouchure, we face the daunting task of breath control development. Each muscle in the torso, really in the body, is involved in blowing through the horn, correctly. Yes, the diaphragm is directly involved in our exhale. However, needed are the supports from muscles around the diaphragm and complex muscle systems, often contradicting each other's directions, supporting evenly that layer of breath exhale and inhale. To achieve correct breathing for a consistent tone color in every part of range, we must exercise inhale and exhale while supporting sound and timing of phrases. Little by little, breath control develops in a very complex layered muscular system in our torso and beyond, our bodies. One teacher of mine said he breathes through his toes!
Since the muscles in the torso are layered and move in complex ways, it is best to relax, allow the slow development of muscular control over our breathing. After college, I worked for an organ company. My job consisted of finishing the wooden keys. The builder had his own mix of lacquers, which applied by cloth then sat drying. Once dry, each key got lightly sanded, emory paper, and rubbed down until a hard smooth finish resulted. Then, the process repeated 100 times applied enough finishing to last a lifetime of wear. All done by hand, this required patience and could not be done with any increase of thickness for each layer. Think of breath development with 100 layers carefully developed.
In conclusion, warm-up exercises correctly applied, played daily will develop consistent breath control and power, which then supports the development of a supportive embouchure. Though, once must maintain awareness and support of embouchure development in the same way. Trying to do this the other way around by squeezing or stressing the the lips will prove ineffective. The sound of splitting the tone and the undesired drop of pitch while playing in the upper register are signs of uneven, unstable breath, then exhaled over the lips in such a way as to encourage improper embouchure. Often, we compensate in this moment with pressure against the mouthpiece and by pushing (even forcing) breath into the embouchure. This proves fatal for good tone production and sustaining pitch. Hence the complaint of so many who so far lack the patient exercise and development of breathing capacity for control.
Once layered, developmental practice of breath control rules practice, over time great tone control develops and playing is much easier. Use of graded and progressively challenging technical, flexibility, scale, harmonic series and tonguing exercises rotated according to the needs of the next piece to practice, in daily practice over six weeks or so for muscular development and 9 months or so for ligaments and tendons will render ease of production, range, control and monitoring so focus then naturally shifts to the music.