Hello, I have recently picked up drumming and the topic of tuning has peaked my interest. I have gone over numerous sources (academic theses, Wikipedia, HyperPhysics, etc.) trying to piece together what is occurring when drums (right now tom with two heads, batter and resonant, are of most interest to me) are struck. From what I can see, is that circular membranes have many interesting modes of oscillation that are not integer multiples due to their 2-D geometry. HyperPhysics and a few other sources have nice representations of some of these lower modes. With that being said, the above helps explain what the membrane is doing when struck, but in the case of a drum with two heads separated by a length L, the sound is also affected by air moving back and forth in the cavity as a closed tube (with small exit holes). In practice, based on personal preference, drummers will either tune their batter and resonant heads to match or differ from one another. In either case, the open-tone (fundamental) frequency of the drum when struck does not match either of the heads, but ends up being lower. At the end of the day, how do the circular membrane tensions/tunings of both heads along with the closed-tube effect work to produce a fundamental tone of a drum?