slew rate and rise time

Damping is very important but it is more related to speaker design than anything else. It is determined by Q factor. Above 10 you start to get diminshing returns on an amp - above 50 you are more less getting close to inaudible improvements in damping from going higher. A speaker will have a Q of .707 to be critically damped. Many speakers have a bump in the bass and are underdamped - no amplifier can compensate for the sloppy resonant sound of this type speaker.

Rleff - Keep in mind what "damping" is, as opposed to "damping factor". If you look at the response of a system, any system, to an input signal, the question is how well does the output follow that input - both in terms of time and magnitude. At the extremes systems that are not properly damped are will either be too slow or will have too much overshoot. Damping can be accomplished by mechanical, electrical, pneumatic, etc, methods. Damping factor on the other hand, at least in terms of audio amplifiers (as opposed to the definition found in control system theory) is simply a ratio of impedances and at least one of the impedences is never fixed.

Jj2468 - in response to the other half of your question - a low output impedance will be somewhere less than 0.04 ohms. Most solid state amps will be there without a problem. You are more likely to have high output impedances with tube amps.

Shadorne, At least you get it.
Once above a certain minimal value, who cares?
The Speaker has the last word here. I have heard a speaker alledged to have a 'Q' of .707 and it sounded almost bass thin.
Does a low 'Q' speaker have what I have heard referred to as 'bloom'?

Once above a certain minimal value, who cares?

Exactly. However one caveat is that you are using a speaker with a "reasonable" impedance curve. Some speakers designs dip down to 2 ohms (not a good thing)- in this case a much higher damping factor than 10 will certainly help.

The Speaker has the last word here. I have heard a speaker alledged to have a 'Q' of .707 and it sounded almost bass thin.

Yes that is how they will be perceived because many speakers are not designed this way. A Q of 0.707 is "critically damped". It means the woofer goes the most quickly to zero after power is removed without any overshoot (no added oscillations or extra bass notes). Some speakers are designed with a higher Q. This allows them to have much more bass response (higher efficiency with a typical hump in the bass response on a freq plot) but the signal continues to oscillate after the power is removed. (It also allows for a smaller box to achieve good bass output) This means transients and decays are not represented properly (timbre will be wrong) but you get a pleasing thick and impressively powerful bass sound (it sells in A/B shop floor scenarios). Sound is two things amplitude and duration - the longer the bass note lasts the louder or more prominent (impressive) it will seem in the mix.

Does a low 'Q' speaker have what I have heard referred to as 'bloom'?

A low Q speaker is over damped. It will be rather inefficient and will require lots of power to drive it. (This type design is extremely rare) The response will go to zero when power is removed and it will not overshoot, however, it will be sluggish compared to "critically damped". Think of a a typical North American storm door and how it closes very slowly - this is overdamped. It will sound even thinner than "critically damped" a very dry and tight punchy sound given the right copious amount of power to control it. It will not sound like "bloom". Bass "bloom" or one note bass would be from a Q of say 0.9 - 1.2 (actually so common that this may be percieved by many as being "correct" sounding bass whereas Q = 0.707 will be perceived as being bass light or wrong sounding bass)

My guess is that the term "damping factor" was at some time in the past appropriated by audio manufacturers for marketing purposes. The term is defined in automatic control system theory where as the product of the damping ratio and the natural undamped frequency. The damping factor is the distance in the left half of the s or plane along the real axis. It is a term specified wholly in terms of mathematics and is completely generic. It's application is in determining the transient response of a system to a step imput and requires that the system first be expressed in terms of a characteristic equation. Factors that are found in a typical electromechanical system include the torque constant, load intertia, amplifier gain, armature resistance, back emf constant etc, acted upon by appropriate factors.

In short, damping factor as it is understood by engineers in all disciplines is not reduced to a simple ratio of two numbers. Since the term has an actual scientifically accepted meaning, my guess is that the term was appropriated to lend scientific status to what someone was trying to sell.

That all being said, knowing the input and output impedances of the components of a home audio system is helpful in choosing which items to connect together in a system, how to connect the items, and how to avoid or address problems.