All throughout my music education, the diaphragm, ribcage and embouchure were all things that had to be controlled.
"Expand your ribcage"
"Expand your belly"
"Form the smallest aperture"
Breathing is a natural process. As long as I can breathe through the whole range of my capacity while keeping my throat and glottis open and body relaxed, my muscles will instinctively move in the most efficient manner.
I've seen a number of articles that support this breathing philosophy.
This one provides sources to peer-reviewed work with respect to this philosophy as well as other ideas to improve breathing for musicians:
In order to develop a working embouchure, I am going to relinquish conscious control of it and approach it with the following definition:
"The embouchure is a three-dimensional entity in motion which only exists if fed by the airflow. The air blows the tissue into the right shape and size to produce the right note."
I've also seen this definition on several websites with various paraphrasing, including from the dissertation "The Effect of Focal Task-Specific Embouchure Dystonia Upon Brass Musicians: A Literature Review and Case Study" by Seth Fletcher which can be found at