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Chromes produce a weird overtone

I put Chromes (40-100) on my Bacchus Jazz Bass. I love the tone, but when I play the open E, I get an unpleasing high-pitched overtone. Other notes on the E string sound fine. The bass has a TUSQ nut and I cleaned the low E string nut slot, but I hear the same overtone. I've used Hi-Beams, Pure Blues and Dunlop Super Bright strings on the same bass, and never had a similar problem before. Anyway, am I correct to assume that it is the E string nut slot that is causing the problem? I cannot think of any other potential cause.
 
I just checked all the tuners. Nothing is loose. I gently smoothened the nut slot with a piece of 600 grit sandpaper, to no avail. The nut slot height is fine. The open E string doesn't touch any fret when I pluck it. I guess the next step would be to install a new nut and see what happens...
 
I have an old Fender nut that I pulled from my MIA P. So, I put it in the Bacchus. The Fender P nut was, of course, a little bit too tall and wide, but all I needed was to see if the original E string nut slot was an issue. Amazingly, I heard the exactly same overtone from the open E string with the new nut! This time, I grabbed my Stew-Mac .105" nut slot file to smoothen the old Fender nut slot....again to no avail.

If the E string is faulty or twisted, how come fretted notes sound fine? The overtone is, as I described, very high-pitched, and the oddest thing about it is that it goes down in pitch very quickly (almost sounds like a downward filter sweep). I've never heard this kind of overtone in my life. Many odd things have happened to my basses and guitars over the past 20 years, and this got to be one the most weird things.
 
A string must be allowed to rotate as it is wound onto the post.
Like a garden hose which, while it is being coiled flat on the ground, must also spin.

While winding onto the post I used to hold the string some 10 inches or so (wasn't thinking about it) down it's length.
If that pinch is not released, several revolutions of the string must try to build up in that 10" or so.

I think "it's a thing".

*
Another idea: check your pickup height. The brighter string might be exposing something you hadn't noticed before.
 
I just checked all the tuners. Nothing is loose. I gently smoothened the nut slot with a piece of 600 grit sandpaper, to no avail. The nut slot height is fine. The open E string doesn't touch any fret when I pluck it. I guess the next step would be to install a new nut and see what happens...
Squeeze your bridge together, and see what happens. Also, try loosening that string and pulling the ball. It might be slightly twisted.
 
I sometimes experience an overtone like that when the nut is cut for slightly heavier gauge strings.

.105 nut slot + .100 string MIGHT cause this problem. I don't think I've ever experienced it on an E-string though. It's more typically seen on a Fender A-string where the break angle over the nut is too shallow by design and the string REALLY needs to fit the nut slot perfectly to avoid problems.

It might at least be worth checking... but I have a feeling it's something else to be honest.
 
Seconding the bridge saddle squeezing, and check the volume and tone pot knobs and shafts. I haven’t had this happen on a bass yet, but I had a weird resonance from a guitar’s metal dome knob that was a little loose on the pot shaft (the split halves were slightly crushed together and the set screen was a little loose) and both pots on my lap steel have enough free play in their shafts to make an audible buzz on one or two notes. If I rest my fingertips on them it doesn’t do it. New pots time for that thing. It didn’t do it until I changed to a new tuning.