uummm this might be an obvious answer but i've never heard or seen it so....
i went to a show last night and the bassist had a really nice warwick bass but he had a wristband/sweatband (like the one tennis players where) around the end of the neck where the fretboard starts (near the head). my first impression was that it reduces buzzing, but he had a fairly nice bass guitar and i didnt think that would be the problem
people do that to avoid excess strings from ringing out so they can go wild and still sound clean.
i used to be a mod, then i took an arrow in the knee.
it deadens the note quicker so you get a cleaner sound when playing fast passages, although with good practice you shouldn't need one
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if your tapping if you hit an open string by accident it will deaden in a flash so if youre not plain any open notes it will show less mistakes
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Sometimes if I'm playing on the D or G strings, the E might be vibrating and producing some rumbling without me noticing, so I can see why'd he'd want to deaden it.
I do the same thing but i do it with one of my sisters scrunchies. It's kinda embarrassing though cause i always keep it on my wrist and its blue with little flowers and stuff on it.

It really helps to reduce or even cut out extra string noise when your doing some tapping and i recommend it to anyone who has just heard of doing something like this.

Also: (if your in a situation like i am) If you go to school you'll probably be asked about why you have such a thing on your wrist. This makes for a good reason to run down to the band hall, get your bass and a little practice amp, and show off a little in front of your class mates xD.
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