OK..... here's everything you NEED to know about damping factor.
A higher damping factor means that the amplifier has a lower output impedance, so it controls the speaker more tightly, and will probably sound cleaner.
(It controls the speaker by shorting out the back EMF, which creates a current flow in the speaker, which acts like "electric brakes" on the cone movement, and forces the speaker to stop moving more quickly when the music stops.)
A typical tube amplifier had a damping factor between 4 and 8 - which is quite low by today's standards.
When paired with a vintage speaker, designed to work with those specs, and so having a lot of internal mechanical damping, they can sound pretty good.
However, when paired with a modern speaker, which has very little internal damping, and EXPECTS to be tightly controlled by the amplifier, they tend to have "loose" or "fluffy" sounding bass,
This will vary a lot between different speakers.
Most modern solid state amplifiers have a very high damping factor - of at least 100 - and usually FAR higher (a DF of 500 to 1000 is pretty common).
Therefore, when paired with a modern speaker, whose powerful motor is designed to work with an amplifier that provides tight control and powerful braking, they tend to sound very clean and crisp.
(But, if you pair a modern amplifier with a vintage speaker, which already has lots of mechanical damping, it may sound "overdamped" - with too little bass.)
(And, if you pair a modern speaker with a vintage amp, with a low DF, the bass tends to sound exaggerates, under-controlled, and muddy.
What can be confusing is that the numbers aren't at all linear and the effects vary considerably with different speakers....
However, in general, with a typical modern speaker...
- an amplifier with a DF of 4 or 5 will sound "loose" "blubbery" and "boomy"
(you often get what seems to be more bass, but it's sort of "soft" and "sloppy", and not what most of us would call "tight" or "crisp")
- an amp with a DF of 8 or 10 will sound better, but still "undercontrolled" and "sloppy"
- once you get up to a DF of 40 or 50, it should start sounding pretty much like it should
- once you reach a DF of about 100, values above that tend to be meaningless, and not to make an audible difference
(once you get much past that number "other factors take over" and increasing the DF past that makes little practical difference)
Therefore, in practical terms, any DF above a few hundred might just as well be described as "very high".
And, when we rate the DF on our amps as "above 500" - that's a nice way of saying "it's ridiculously high - so don't worry about it".
As you can probably tell, there's no strict answer for "what's too low".......
- because different speakers respond differently to very low DF
- because, if someone likes the way their speaker sounds with a tube amp, then they LIKE what a low DF sounds like (with many speakers that's softer, smoother bass, but more of it)
- but, if you like "clean solid state sound", you probably want an amp with a DF of at least 50 or 100, and anything over about 200 isn't going to matter at all
Mathematically, the damping factor is "the ratio of the output impedance of the amplifier to the impedance of the speaker" (which determines how much "electric braking" the amp can apply to the speaker).
In practical terms, the "output impedance of the amplifier" is really the sum of the output impedance of the amplifier and of the speaker wire and connections between it and the speaker.
So, for example, if you have an 8 Ohm speaker, and the output impedance of your amp is 0.1 Ohms, the damping factor would theoretically be 80 (8 / 0.1 = 80).
However, if your speaker wire has a resistance of 0.1 Ohms, then you must add that to the impedance of the amp itself.
So the TOTAL source impedance then becomes 0.2 Ohms, and the damping factor is actually 40 and not 80 (8 / 0.2 = 40).
(And, yes, we're talking about the total resistance of the speaker wire, in both directions, added to the resistance of all the connections along the way.)
(And, yes, for a given amplifier and piece of wire, the DF with a 4 Ohm speaker will be 1/2 of what it is with an 8 Ohm speaker.)
The bottom line of all this is that, if you like "tight, clean bass", you should get an amp with a rated DF of at least 200 into 8 Ohms....
And you should keep the total resistance of your speaker wire well under 0.05 Ohms or so.
Also note that damping factor actually varies with frequency....
However, because the woofer is most sensitive to DF, DF is generally higher at lower frequencies with modern equipment, and measuring DF at various frequencies is complicated, we generally quote a single number.
The question THAN becomes one of 'limits' and at what point does a DF become TOO LOW?
My previous post shows the maths and just how quickly the damping factor can drop. I have had stereo amps with "quoted" damping factors under 50, real world under 20, that sounded very woolly overall, with especially muddy bass. But other amps with "quoted" damping factors over 100 and up to 500 I really can't tell the difference with the woolliness gone and the bass quite tight. My speakers are 8 ohm nominal and at that the XPA-1L's are quoted at "over 500" damping factor and with the short 10 ga speaker cables I have what I consider to be "more than enough".
Cheers
Gary