I broached this subject on another forum about a year ago, and didn't receive much useful feedback. Feedback yes, useful no.
Having switched to euphonium from contrabass tuba, my upward expansion has been slow, but is progressing. But I have hit a significant sandbar as I try to go from F4 to the G or even the Gb above it. And I have begun to wonder about the physics involved.
Specifically: you can play C4 with either 1, or 1-3, or with the compensating 4th. So, if the first valve lowers pitch by a major second, when I play that C with the first valve, am I actually using the vibration speed needed for the D just above it? Or when I use 1-3, am I lowering what would otherwise be an Eb to produce the C? Or since the compensating valve lowers the tone by a 4th, am I using the vibration needed for the F4, but sounding the 4th below it?
My point in all this is: the open F4 is pretty consistent for me, but the next open note, Bb4, is a real challenge. Is the G4 "sandbar" a result of having to actually "play" that Bb4, with the addition of a couple of valves pressed? So moving from F4 to G4 is more like going from the F to the Bb?
I realize, bottom line, it takes patience and practice to attain range, but does my theory have merit? This has been bugging me for a while.
Maybe this is why some teachers have emphasized playing through the harmonic series to build range?
Sorry for being long-winded, but I was hoping to make my point clear.