I have an adult student who is a thoracic doc with whom I have great conversations about breathing. Teaching him has helped me really define, verbally, control of proper air flow for trumpet playing so there isn't a contradiction between medical functionality and teacher description. He has such an understanding of function of the lungs that he processes what I describe through his thorough lens. With all my students I do my best to avoid too much technical vocabulary and keep things simple and easy to understand with my vast wardrobe of analogies.
Vincent Penzarella has said it best, "Exhalation is inhalation without hesitation". Now, this is an advanced concept, so although my students hear me say this, I give lots of examples of what this means. For years I did not breath deep enough and move my air fast enough and still sounded decent. Having a deep understanding of the importance of a very deep, relaxed inhalation and pushing out my exhalation at the end of a note before a breath took my playing to a new level.
The beginning of anything we play is the easiest place to start, but it only begins here. The test and most important implementation of this concept is in the breath between notes. Understanding that how you exhale has everything to do with what type of inhalation you will have. So....I teach my students how to increase exhalation before a breath so that inhalation will be deep, relaxed, efficient, and will need less time, thus interruption of the music is minimized.
Continue that concept to every note you play.....meaning "connection". Think of a relay race. What is the one aspect beyond being a fast runner that makes the team win/work? It's the hand off of the red stick! What does the runner do? The runner with the stick, when getting close to the hand off, increases his/her speed and reaches out with the stick. The runner on the receiving end starts slowing running and reaches out to grab the stick from behind so there is as seamless a hand off as possible.
Try this with each note you play. Start a half note (quarter equals 60) middle g...on beat two increase your air in anticipation of handing it to the next note, a "c" one forth above for a whole note. Do that again, but add a breath at the end of the "c", push out the exhalation at the end of that note and come back in on another "c" whole note. Experiment with this concept with the music you are working on. Does it improve your sound, pitch, relaxation?
Find Parts I, II, and III to this topic by tapping the numbers.