This was a little tidbit from my lesson with Nick Atkinson, but it’s really affecting me. Nick suggested I breath from the corners of my mouth without really pulling away from the mouthpiece. The conclusion I drew from this is that my embouchure is maintained while I’m taking a breath. This is very useful when needing to take a quick breath while in the outer ends of the tuba’s range because, for me at least, it reduces the chance of kacking or fluffing the next note because I’ve reset my embouchure when I pulled away (just a bit, but still) from the mouthpiece to breath.
But this is also helping me in another way — slurred octaves and fifths when warming up on the harmonic series. C-G-C, etc. I’m trying to remember the details of that moment with Nick, but I believe it also involved not sitting so lightly on the mouthpiece (but not so deep that the pressure adversely affects a free buzz). Get inside a little bit. This is really helping my harmonic series slurs (first three notes of each) by reducing the “flip” sound when switching notes (smoother and quicker transition). I’m going to explore this further.