What is meant by a "fast" pre amp

'good phase purity' comes from wide bandwidth/high slew rate.

In order to get to 20KHz without phase shift, the upper cutoff of the circuit needs to be 10X higher, IOW 200KHz. YOu can use that as a good rule of thumb for seeing a 'fast' preamp in its specs.

Mind you, 'fast' is not the same thing as 'bright', in fact brightness is often caused by phase shift issues due to poor bandwidth. Brightness is also caused by very minimal distortion of the 5th, 7th and 9th harmonics.

All of this can be summed up in one word, MUSIC.

A preamp could have all of the best specs in the world, but if it doesn't sound like music, you have nothing.

If you think your equipment sounds fast then it probably isn't.

Agreed- 'fast' by itself would strike me as being a coloration. 'Fast' with a host of other aspects (detailed, transparent, **relaxed**, wide bandwidth), no worries.