The problem is in the "definition" of tone. It can be the fundamental and harmonic spectrum of a played note. The problem with this "definition" is that the proportions change with each partial and/or valve combination that we choose. This description is quantifiable and when we practice long and intelligently enough, we gravitate to a balance that sounds "full" regardless of the genre that we choose. Lets not forget that someone playing lead needs a different harmonic balance than someone in a symphony orchestra.
Another, more fuzzy definition is what we perceive when we listen to someone playing. This is much, much more than frequency response. Ever wonder how we can tell who is playing after only a couple of notes? Think about Miles Davis, Chet Baker, Louis Armstrong, Maynard Ferguson, Maurice André, Rafael Mendez. They ALL practiced enough but ended up somewhere different from one another. If this is what was meant with the original question (and I suspect that it is judging from HHSTrumpets other very qualified posting at TrumpetMaster), we can get more into the interpretive/emulative rather than beating the mechanics up.
When a player asks about tone, we really need to find out what they mean before offering any blanket solutions. We are at post 41 in this thread and are posting in circles because we do not know what we should be talking about. Everyone can be right and useless at the same time. In another thread I mentioned that TrumpetMaster is not always Search and Rescue, rather Search and Destroy. 40+ posts and not a bit closer to the requirements of the thread owner seems pretty lame to me...............
I can claim for myself that more practice and/or a teacher would not improve my tone - in any genre. I need to simply play with those doing a fine job in the selected genre and LISTEN instead of DICTATE. An hour of duets with a top lead player/symphonic trumpeter/baroque trumpeter, cornetto-ist will do more for my sound concept/tone than any internet posts.
There is a point where all of us need to take a look from the bell backwards instead of the mouthpiece forward.