Too much or too little gain?

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Joined 2021
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There is a post from @chris mielke in the ba-3 thread that talks about too much gain from the ba-3. My question is, how does too much or too little gain affect the sound? Does it mean the sound coming out of the speakers has too much influence from the source and pre-amp and not enough from the amp? Or is it just as simple as the amp cannot offer the power it has and it doesn‘t have anything to do with the actual sound?
 
If it has too little gain the weak source won't be able to drive the power amp to full level, surely. Adding more gain shouldn't affect the noise level much as that's set by the input stage of the preamp (i.e. before the gain). In fact having too little gain will reduce the noise at the output as well as the signal.

This is why an active volume control as part of the preamp is such a great idea, it can provide as much gain (or attenuation) as needed without losing headroom.