@JeezyMcNuggles, how exactly does paint "trap" or dampen anything?
And somehow the magic number is 4 coats????
I couldn't find the absorption coefficient of the paint, plenty of acoustic panels specifically use that as a standard.
Good luck to the OP.
Coefficients for sound control also include STC (Sound Transmission Class), NRC (Noise Reduction Coefficient)- look for NRC.
Explaining NRC: Noise Reduction Coefficient | What is NRC?
STC Rating: Understanding Sound Transmission Class Rating | ASI