"Fast" is only part of the sonic story, but an important part I think. It might be easy to confuse the term "Fast" with "Bright" and "Slow" with Dull". I think the later comparison is stronger than the former. I agree with the previous posts that my definition of "Fast" is the ability of a system to accurately reproduce the leading edge transients in music. My view is that getting leading edge transients "right" is a joint effort from source to loudspeaker, but seems to have its greatest test within the amplifier.
My limited experience is that solid state and some digital amps can be very good at leading edge transients, but can have a harder time handling harmonics and trailing edge decay. Cheaper digital amps and sources can sound "Fast" and exciting at first listen, but reveal artifacts or sins of omission in the overall reproduction that on closer listening turn out to provide an overly "Bright" sound, lacking body, natural smoothness, sustain and decay.
Conversely, tube gear, especially older versions, can be syrup "Smooth" and "Sweet" but doesn't always get the attack altogether right. Nowadays, the more you spend on tube or transistor gear, generally the less these artifacts impede on the sound in either direction.
So "Fast" is and important aspect of reproduced sound, but not by a long ways the only important aspect.
My limited experience is that solid state and some digital amps can be very good at leading edge transients, but can have a harder time handling harmonics and trailing edge decay. Cheaper digital amps and sources can sound "Fast" and exciting at first listen, but reveal artifacts or sins of omission in the overall reproduction that on closer listening turn out to provide an overly "Bright" sound, lacking body, natural smoothness, sustain and decay.
Conversely, tube gear, especially older versions, can be syrup "Smooth" and "Sweet" but doesn't always get the attack altogether right. Nowadays, the more you spend on tube or transistor gear, generally the less these artifacts impede on the sound in either direction.
So "Fast" is and important aspect of reproduced sound, but not by a long ways the only important aspect.