Double "Harmonics" or something...

[Stevecore]

My bass (Fender Aerodyne Jazz) has been giving me these odd double "harmonics" when tapping - it will ring out with not only the note I should be getting, but a harmonic from the other half of the string's vibrations. It has been recently set up, intonation is dead on, etcetera, so I'm not sure what's causing it to happen, or rather, what should be happening to prevent this.

Obviously, putting something around the strings, some cloth or whatever, keeps them from ringing out, but of course it mutes the strings and renders my harmonics unusable. What else could I do to keep the strings from ringing out like this?

What's worse is the extra ringing is just as loud as the note itself, so I can't hide it under volume. I don't think it's because of my technique, I've watched many other bassists tap and I've never seen someone need to mute the strings - I'm actually watching a Victor Wooten video right now to double check that.

[Andy Will]

You'll find that when tapping you generally need to mute with the left hand (if playing right-handed). Also, in Victor Wooten's case, he also sometimes uses a hair band slid to different positions on the Bass's neck to give allow more left hand freedom for tapping.

Without the left-hand muting it's expected to have overtones unfortunately. Check out Vic's clips a little more to see how efficiently it can be done.

Please note this is a technique question as opposed to set-up/repair

[Stevecore]

Hey, I'm allowed to pretend my technique is perfect :P

Well, I guess that means I'm going to have to find quite a few more videos on tapping, then.

I do find it odd how overpowering the overtone is, though, it's the same volume if not louder compared to the initial note.