The saxophone actually has a parabolic conical shaped bore

(click above graphic for a large version)

My student Randy, who is an engineer for a pipe organ company, put this drawing together after reading a great book about the history of the saxophone called The Devil's Horn. The book explains how the side of the saxophone that has the tone holes is actually has a parabolic conical shape, rather than just being a conical shape. Adolphe was a true genius.