Since my math has seemed to have caused some controversy, I thought I might chime in to the discussion with my experiences.
When I first started out in the audio hobby as a teenager into car audio, I read all the magazines I could get my hands on and fully bought into needing the highest possible damping factor. I went out and bought very good amplifiers from Rockford Fosgate, Precision Power, ADS, Linear Power and a host of other top notch brands. Most sounded excellent. Very tight and controlled bass and excellent sound, in general.
When I got into home audio, my first few projects were subwoofer builds based on knowledge I had gained on the basslist from some of the wisest audio fanatics I have ever had the pleasure of conversing with. I felt like I was back in 1950 exchanging letters with James Lansing, Paul Klipsch, and the like. I was 18-25 years old and holding conversations with the likes of Ken Kantor of NHT, Dan Wiggins of Adire Audio, Ray Wagner of eminence, and Terry Olson of 3M ( I presume he was from 3M based on his love of Bondo) and a host of other wildly knowledgeable, witty and friendly gents. At the time, there was a definite positive vibe towards pro amplifiers, so when I built my Shiva subwoofers, it seemed to be only natural to choose a pro amp to power them. They were very attractive to me, they were well built, sounded good (generally), and best yet, they had a high DF which was absolutely critical for good control, right?
I got a couple of good deals on Crown's, Crest's, and QSCs, swapped them in and out. The Crown was the one I kept and with the money from selling others, I decided to buy a pair of 100w class A monoblock amps (it could have been a Norman Thagard design that was published in one of the old audio rags) from a local. The damping factor was not nearly as high as the crown, but when I connected my subwoofers to these amps, the bass response was subjectively signficantly better. Tighter, deeper, and generally of noticeably better sound quality. How could this be? I think the crown was on the order of 4-5x higher damping factor (possibly more). At the time, I bought into whatever might explain it from some audiophile friends. "The Class A amps have more current!" or "The Class A amps have much less distortion!". I received a number of answers that were nothing short of completely uneducated guesses.
The next few years were filled with examples of amps that seemed to defy the higher damping factors having much better and tighter bass. There were many cases where the higher DF did have better bass, many where they clearly did not. Not really knowing how to explain my experiences led me to asking the basslist members about their experiences and in one of the first replies, I got my answer. The series resistance of the speaker wire, even when very low, was still in most cases, an order of magnitude greater than the output impedance of the amp. What did this mean to me? Well, as you can see in my math, it proved that in the real world, by time you hit the terminals of the speakers, the differences between ultra high DF amps, high DF amps, and something with middle of the road DF is virtually null. My experience with literally many dozens of amplifiers coupled with the math had satisfied the uncertainty of my experiences. I came to the realization that while damping factor can have an audible effect when it starts getting very low, that audible effect isn't necessarily going to be in the negative direction.
As Terry has tried to emphasize, there is no doubt that many of you have experienced improved performance with a higher DF, you can be reasonably sure that you just have an amplifier that sounds better and it's very likely the improvement can be attributed to something other than DF.
FWIW, it took me a few more years to figure out that THD level and sound quality have absolutely no correlation, so you could say I'm a slow learner.
