Bass - and "Q"
Technically this whole business of bass quality/quantity/extension is all wrapped up in one phrase - "filter Q". A loudspeaker cannot reproduce down to one or two Hz., so it is by definition it must be a 'high-pass filter' with all the characteristics of an electrical filter set to, say, 50Hz. It will let through higher frequencies but it cannot pass the really low ones as sound.
As with all electrical (and all other mechanical filters) the peakiness of the filter at and around the knee of the filter (in our example, 50Hz) defines its time response. The one-note-bass phenomena of which you mention implies a loudspeaker whose filter-action at one frequency is peaky. A peaky frequency response implies a ringy time response. That is, after the note has ceased the speaker continues to ring-on.
The nearest analogy is the shock absorbers on your car: a highly damped suspension (of the type found on a luxury car) gives a ride with a 'low-Q'; conversely a cheap car with a defective shock absorber has a 'high-Q' (ride) response and at a critical frequency the car can be set into uncontrollable resonance.
The designer can play around with the bass filter-action of his speaker system by changing the weight of the cone, the magnetic strength or if ported, the tuning of the ports and the damping (stuffing) in the box etc. etc.. Each designer would aim for a different combination of characteristics. There is no 'right answer'
Alan A. Shaw
Harbeth Audio UK