While what Gs says may be "textbook true", in my experience, the higher the slew rate, the better off you are. Reasonable amps are rated for AT LEAST a minimum of 40+ V/uS ( Volts per micro-second ). Fast amps are well above 100 V/uS.
You can do all the math that you want, but my experience is that "proper" formula's don't always equate to high levels of transparency. After all, music consists of dynamic transients by its' very nature. If the components can't respond fast enough to major changes in amplitude or polarity, the end result is distortion. Douglas Self
claims that a preamp need only slew at 2 V/uS to be sufficiently fast. Needless to say, i don't agree with him on that at all. Then again, he thinks that Class B amps are "better" than Class A or "high bias AB" amps, so that may give you some idea as to where he's coming from.
As far as slew rate goes, David Spiegel had prototype amps back in 1978 that slewed at 1000+ V/uS. His preamp that was available to the public in 1974 slewed at 350 V/uS. How far has audio technology / circuit design come since then??? To be quite honest, most of it has gone backwards. That's why i bitch about all of this "inferior crap" being marketed today.
Many manufacturers won't quote slew rate, rise time, etc... because it would show how "backwards" their designs really were. As such, something else to look for is "rated power bandwidth" or just "power bandwidth". This tells you how linear the amplifier is over a given frequency range at rated output +/- a tolerance rating in dB's. For an amp to maintain a very wide bandwidth with a very tight tolerance at full rated power, it has to be "fast". Having said that, don't confuse "rated power bandwidth" with "frequency response" though as they are NOT the same thing.
Frequency response is typically measured at 1 watt, which is coasting for most amps. Some amps will measure into the MHz range at 1 watt but won't be able to make it to 80 KHz at rated power with a tight tolerance. Even with full rated power out to 80 KHz, you can still run into dynamic saturation of signals at very high frequencies, especially if they are of very high amplitude and / or the speakers are highly reactive. Yes, the ability of the amplifier to "load up" into the speakers or "power transfer" characteristics of the amplifier / loudspeaker interphase DOES come into play here.
With all of that in mind, slower amps can sound quite "musical" but typically tend to be far less resolving, not nearly as transparent and tend to get "hard, nasty and gritty" with a less cohesive presentation as they are pushed harder. That's because the amplifiers themselves are introducing distortion into the signal path. This distortion effects the harmonic structure, timing and amplitude of the signals that we hear. In most cases, the end result is "smearing" that is less than pleasurable to listen to. In that regard, this is one thing that a system built around "reasonably fast" amps with GOBS of headroom will never run into. Ultra-sonic speed with brute force is a hard combo to beat. That's because you can't stress it dynamically ( speed or amplitude output ).
Speaking of speed ( or lack of it ), most "standard" tube amps with output transformers are "turtles". This has to do with the huge amount of inductance that output transformers bring with them. Inductance limits high frequency response, resolution and speed, so you can pretty much kiss any amp that has an output transformer on it "goodbye" if you want speed and resolution. There might be a few amps using very high quality output transformers, but those would be the exceptions and far from the norm. I think that the new Mac amp i glanced at in Stereophile was actually pretty impressive in terms of bandwidth and high frequency linearity. Can't remember the specifics though, so if you're interested in such things, you might want to check into them yourself.
On the other side of the same "tube" hand, OTL ( Output Transformer-Less ) tube amps have the potential to be MUCH faster. A perfect example of this would be Ralph Karsten's Atma-Sphere amps. I think that they slew at something like 300 - 600 V/uS ( give or take ). That's why they sound SO much better( cleaner, clearer, sharper, more focused ) than so many other slower "toooob" amps. If Ralph could find a way to lower the output impedance on his amps without resorting to using gobs of negative feedback to do so, he'd have the audiophile world eating out of his hands.
Either way, any given spec is nothing to judge a product by. You have to look at the entire array of spec's, know how they inter-act with each other and interpret them on the whole. You can have a product that is ultra low in distortion, super fast, super wide-bandwidth, etc... and still have it sound like crap. That's because the manufacturer might have used gobs of global feedback, which tends to strip the liquidity and natural sound from a component, yet at the same time, helps it to measure "excellently" in terms of VERY low distortion, etc...
I can think of a very well reviewed amp that fits into that category, but i don't want to mention names here in a negative way. There are those that sell / represent some of these products that frequent these forums and they tend to piss and moan when i step on their toes. While they want me to participate & teach, they don't want me to use products that they like and / or represent as "examples" of what is wrong with this industry and modern day product design. I'll give them their "cake" on this one, but that doesn't mean they won't get "eaten" next time : ) Sean