I’m just thinking loud here about pre-amps and all their different sounds and how they contribute to todays recordings and overall production aesthetics.
There are actually two types of such devices in general which are coming to my mind. On the one side there are the more unobtrusive ones which are adding almost nothing to the sound but just tighten and focusing the lowend a little bit or enhancing slightly the mid range in a good way. The other ones (mostly tube/valve types) are tending to saturate and distort the incoming signal if driven with higher input gain which may contribute to the desired sound in some cases while in others not.
A ‘610’ replica I do have here in my lab for example adds cool harmonics to a bass guitar or a male voice recording but there is too much distortion added to use it on female vocal stackings. Other models are more reserved and gentle in adding such effects but still can be used to excite and color the input signal slightly. Most of this goodness comes from certain side effects of transformer coupled tube stages.
The capability of adding overall extra harmonic audio content is just one single side effect and there are different and more complex ones. A transformer for example does have a very complex and non-linear overall behaviour and especially in the very low frequency range. This is due to the fact that it does not let DC pass through and the more near a frequency actually is to DC the more weird a real transformer responds to this signal. The result is a type of distortion which includes both even and odd harmonics and can perceived (in the good case) as a pleasant low-mid enhancement. Due to psycho-accoustics this can even improve the bass perception on speaker systems or headphones which are not capable of dealing with very low frequencies at all.
Leakage or bleeding effects in a circuit does have impact as well on how the device responds to the input signal and saturation effects can have a significant impact e.g. on how depth and stereo imaging is perceived when talking about stereo recordings. Uneven frequency and phase response of such devices counts in as well of course and is probably the most important aspect of the sonic ‘color’ impression we do have from a certain unit.
To me the ideal pre-amp would be a flexible one that would let me dial in or out those effects depending on the input, the recording or mixing situation or so. In the analog domain this is hardly (and expensive) to achieve but in digital domain we can at least simulate this by proper signal modelling.