fair warning: Here goes.
(Mark me "foe" now, or forever hold your peace.)
"free" buzzing:
It really seems to rile up a few people when I suggest this, but I suspect that when people do this without a mouthpiece or an instrument, they actually ARE causing their lips to bump against each other very fast (blowing them open, and then they close - with this occurring rapidly) to cause the frequencies, which is not what happens when we play our instruments (whereby - when we play our instruments - the lips are vibrating independently at the same frequency, as with a bassoon or (very high range, as with trumpet) oboe reed. I know this, because I know how far apart my lips are when I'm playing very low very loud frequencies (because I have nerve endings and sensation), and there's just no possible way that my lips could be touching when they are that far apart..
Also, when so-called "buzzing" with a mouthpiece, there's no instrument overtone series harmonic vibrating in conjunction with the lips to support the vibration, which thus requires a heroic effort on the part of the player... perhaps the equivalent of the absolute loudest playing that anyone ever might actually do (Think of those marching band sousaphone section contests...), I'm not sure that we really need to practice that very much at all.
Finally, to develop a (no pun intended) "good buzz", how in the heck do we know whether it's "good" or not "good" without hearing how it's interacting with our instrument?
When bassoon and oboe players make there wooden double reeds (vs. our flesh double reeds), they shave a little bit off here or there - based on experience - and constantly test them ON THEIR INSTRUMENT until they are satisfied.
-----------
Here is one case whereby I see value and vibrating the lips into the mouthpiece WITHOUT the instrument:
Shut off most of the end of the (tuba) mouthpiece whereby the resistance feels close to imitating the resistance felt by blowing through the mouthpiece with the instrument attached, and play through some passages - the objective being improving embouchure PITCH CONTROL, without relying so much on the instrument to control the pitches produced.
(I do this.)
Specifically, I decided that I needed to work on this when I switched to B-flat tuba, because the tremendous amount of cylindrical tubing required to play the F sharp up in the staff - when depressing valves 2 & 3 - is nearly as much cylindrical tubing added as when depressing the 4th valve on a C instrument, and that's quite a bit of cylindrical tubing for playing a pitch that high in the range. I realized that my pitch control needed to be spot on to avoid being afraid of that pitch, whereby - if my lip vibration frequency is true - that pitch will sound without faltering.
I don't believe that some of the things I said above are true for TRUMPET players, because their mouthpieces are about four times as long as ours are - in relation to the entire length of their instruments - and I believe they can buzz through their mouthpieces without feeling I need to artificially add resistance.
