So the question remains did these manufactures put these string mutes in the bridge just to dampen the output of the string or was it to immitate the sound of a stand up this becomes more interesting given that these string mutes were put mostly on older basses, maybe to accomadate the switch from stand up to the new fangled electric bass.
They put the mutes because that's what a bass was "supposed" to sound like back then. Remember that John Entwistle, Jaco, Fieldy, etc. had not yet come along to revolutionize the sound of the instrument.
"mwah" is not caused by an effect but rather by setup and technique. There are many existing threads, but in a nutshell, mwah is facilitated by roundwound strings, low action, a coated fingerboard, using the bridge pickup, and using left-and-right-hand techniques that emphasize the mwah.
If you're not doing it already, try fingering notes with the fleshy flat part of your finger rather than the finger tip as you would on a fretted bass. Takes a little getting used to, but really brings out the characteristic 'muah'.
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