Re: Billy Ward here!
HI Drum Mum (great name BTW!!) Well, the first thing IS about the gear. While Elvin's kit at the lesson was really beat up, it no doubt had been tuned properly for Elvin's tastes. In general a jazzy kit will be tuned very high in pitch. Many guys go as high as the head will go - and then try to go even higher! :)
A funky beat up drum set with questionable bearing edges and such will still more easily sound like a drum when tuned high. This is one of my pet peeves for independent, boutique snare drum makers. They tune their snare drums high - and honestly, almost any snare drum can sound like a snare drum when tuned high. Tuning in the middle to lower register will truly separate the "men from the boys"
Now then , your grip is very very important and I DO recommend having an eperienced drummer in your area check your grip so that the stick is doing what it is supposed to be doing.
After this, I think it comes down to tapping your drums - playing them, and not feeling guilty about spending ten hours with a drum key.
It goes without saying that if your drum heads are pitted, then you have NO CHANCE at groovy tone - again, unless tuned waaaay high.
Thanks - Billy