In regard to Duke's mention of Jon Dahlquist's conclusion that the trailing edge of a bass tone is of more sonic consequence than is it's leading edge: Danny Richie of GR Research, in one of his Tech Talk Tuesday videos (viewable on You Tube), discusses the matter of "fast" bass. He explains why though woofers don't have to move very fast (in comparison with the other drivers), some woofers do indeed sound subjectively "faster" than others. It is his contention that it is the ability of a woofer to "stop" when the signal does (to "track" the signal) and return to "rest" that makes one woofer sound faster than another. All the GR Research subs employ the Rythmik Audio Servo-Feedback woofers and plate amps, known for their ability to produce "stop on a dime" bass.
Owners of planar loudspeakers, particularly big Magneplanars, know how different planar bass is from dynamic woofer bass. Tauter, leaner, a standup bass sounding more like a string instrument than it does when played by most box woofers, which make the string bass sound a little "plump." It may be that some consider the former type bass reproduction "over-damped"; I don't.
In one video, Danny shows spectral decay displays (waterfall plots) of various drivers and complete loudspeakers, THE most telling loudspeaker measurement in his opinion, the one most predictive of how a driver/loudspeaker will sound. Well worth the time searching for the video.