I built a partscaster for a friend yesterday and realized I have had too low action for a long time. And I mean like REALLY low. Even the guys at the PLEK place thought I was crazy. I've had between 0,5mm and 0,7mm action during the last few years, obsessing about getting as low action as possiblle.. But now I really have to re-think my ways here!
I still need low action to be able to play comfortably, but on my main guitar I simply raised the action, and put on a thinner set of strings (009 as opposed to my good old 010s)
Here's a video where I use another guitar for actually hearing how action affects tone.
So, it doesn't really affect the tone SUPER MUCH, but it differently sacrifices to things:
1. The bottom end omph....
2. And the overtones and other nice things that you really want.
After adjusting my main guitar I got better overtones and harmonics, simply put a more lively sound!
Here's a Wav version of the comparison in the late part of the video: