So there was this older post from 2005 that did not seem to have a lot of useful follow up:
Weird double tone in upper frets.
Anyway, from the looks of the thread, I think I am having the same issue. I have a MTD KZ6 6 string bass. I have tapered strings on it. I don't remember if this had been an issue all along as I only recently got decent enough to play up in the fret 15+ range.
So pretty much I get this harmonic noise on the fretted notes on the B, E, A, and D string fretting frets 15+. These are the only ones with tapered ends from the set. The G and C are just like the strings from regular bass guitar string sets.
Moving the pickups down did not seem to work, plus that would not make sense since I hear the harmonic noise unplugged as well. Does anyone know if these tapered core strings are sensitive to this effect? I noticed that the other bass I have with these tapered strings is string-through-body and less of the the taper is exposed. The bridge is not very long and I wonder if the shallow bridge is exposing too much of the taper and creating this issue.
Any thoughts are appreciated. Thanks.