What I hear from the use of tube dampers is a slight reduction in high-frequency microphonic noise (vibration) from the tubes themselves. Sonically this comes across as a lessening of harmonics that might be perceived as 'air', 'tizz' or venue atmospherics at the very top of the frequency range. Its not music but rather amplified tube noise.
Dampening may, at first, seem to cause a loss of air surrounding an instrument - I sense this most pronouncedly on top-end strings - almost as the very top is cut off. Further listening reveals - to me anyway - a quieter presentation with a bit more musical information because actually there is less non-musical 'hash'.
I believe you can over-dampen with either too many dampers on a given tube or too many dampers overall. Here the result is a slight deadening or removal of top-end 'life' or sparkle.
I've used the CJ supplied dampers on the 6H30 in the ACT2 and the ARC dampers for the same tube in the Ref Phono 2. I'd stick with what the manufacturer provides - at least for the result they intend for their units. Otherwise, the Herbie dampers work very very well. In my Atma-Sphere MP1 I use them to good effect on two of the four 12AT7s in the phono section and on two of the five 6SN7s (per channel) in the linestage. That seems to strike the best balance between noise reduction and retaining a slight top-end liveliness.
I don't think dampers are a solution to increase warmth or the change tonal balance of a given piece of gear. Bottom line is: its easy to experiment, so let your ear be the guide to what sounds most realistic to you.
