Synthesis of drum sound from solution of wave equation on disk

actual drum recording

I tried, but I just cannot match the spectrum of the real drum:

with the theoretical spectrum of the circular membrane:

I have to conclude that the either or both of the facts that (i) a drumhead is not a "membrane" (rather a combination of a membrane and a disk which resists being bent) and (ii) the membrane is interacting with a half-closed column of air, result in a spectrum that is quite different that the theoretical one for a stretched membrane alone. :-(