Hmm, ok, some big questions there;OK I'm really intrigued now as to the relationship between shell diameter; shell depth and the pitch range in which a drum 'sings' particularly as you (Andy) seem to have a great deal of expertise in the physics of drum sounds. Does the ratio of head area to shell area matter? Is the primary driver of pitch the drum's diameter - and if so why do we play 14 inch snare drums? And what do you think has driven the move (over the last couple of decades) towards smaller diameter drums (I'm thinking in particular of the move to 10.12 rather than, as was conventional when I first started playing, 12, 13).
Yes, the primary driver of the drum's pitch range is head diameter, but the biggest driver of resultant pitch, as perceived by us, is head tension. Without going into the fine details of the relationship of various construction features (I haven't got time right now, & I'd bore the pants off most of you), it's useful to relate drums to a stringed instrument. A piano is a perfect example. Head diameter = string length. Head tension = string tension. String thickness = head thickness. That helps clarify the basics of pitch, but the resultant pitch is then affected by many other elements that augment the creation, disturbance, & absorption of overtones by various mechanisms.
"Ratio of head area to shell area matter"? Short answer = yes. That falls into the category of augmentation of overtones, but is just one element of the whole.
"Why do we play 14" snare drums"? Many perceive 14" to offer the optimum combination of tuning range for a typical modern snare sound. I suppose that's true, but there's many that play 13" & 15" too. Snare drums down to 10" are not uncommon.
"Move to smaller tom sizes". Well, I think that's largely a music fashion choice, but it's certainly true that advances in shell construction, bearing edges, & head quality/selection have allowed far greater pitch & tone possibilities to be extracted from smaller drums.
Sorry for the succinct answers, but I've got to run.