Some years ago I conducted several controlled blind listening tests investigating damping material for a vented, stand-mount home audio speaker that was intended to be used with subs. I had never before made a speaker with such a small box volume relative to the woofer size, and I figured that getting the damping material right was going to be critical. Damping materials used in the tests included Black Hole 5 (a multi-layered cabinet damping product), No-Rez (basically a less expensive variation on the Black Hole 5 theme), several different types of acoustic foam, polyester fiberfill, and several combinations that I no longer remember.
Here's a photo of the speaker (they were built in mirror-imaged pairs):
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I placed the two speakers side-by-side, facing the listener (didn't use the built-in "toe-in" for the testing), and let the listener tell me when to switch back and forth between the two speakers. The program material was a good recording of multiple voices singing in harmony, summed to mono, and the listener was to choose which sounded the most natural. I knew which speaker had which damping material in it, but the listeners did not.
Zero damping material sounded the most natural, to the listeners and to me. This impression held up with other program material as well. I never would have guessed it. I only tried zero damping material when the data from the earlier tests was pointing in that direction. I speculate that the non-parallel front baffle played a role.
Each design is different, and I've only had one wideband speaker system since then that sounded best to me with zero damping material, and that was a bass cab that combined an 18" woofer with cone mids. The internal dimensions were pretty close to a golden ratio, with a chunk taken out for the mid chamber.
Relying on "science" to tell me what damping material, how much, and where, generally hasn't produced good results. My impression is that our models of the internal acoustics of a loudspeaker box, and/or the psychoacoustic implications thereof, are not yet as mature as our models of vented boxes, for example. So for now at least, when it comes to damping material, I have more confidence in trial-and-error.