I use black nylon tapewounds on a fretless acoustic bass guitar (Tacoma Thunderchief). Very upright-type vibe. I use strings from Status. Here are some gig recordings:
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Don't like tapewounds on my fretted Fender Jazz bass. I prefer ground wounds on that one.
Loved the performance! And on a side-note, your hair is awesome. I recently tried the black nylons and, like you, I didn't dig them on my fretted P-bass. I don't have a fretless bass (yet), so I'll just keep them around until I do.
PBnJBassist, you should try (d'Addario) flats with a small piece of dense foam underneath each string. It's for free and it might bring what you're after.
I actually did this at one point, and I only kind of liked it. Granted, I used Fender's official foam, weather strip from Home Depot, and a sponge from underneath my sink. Experimented with all of those with some medium Chromes and was cool at first, but recently, I ended up finding what I was looking for in GHS Precision Flatwounds.
I loved the tone straight out of the pack and it's been about over a week or so - and I'm still loving them. They have already begun breaking in at an extremely high rate and are literally dead out of the box. These are my ideal flats, and the best part is that I don't need a foam mute. Rolling down the tone knob almost gets the job done on it's own with these flats. Not quite "upright" but I was looking for a string with a lot more "thump" than my Fender flats without having to spend $60 on La Bellas.
Again, thank you to everyone that responded! A lot of questions were answered and testing it out was a fun experience. Now I have to do now is buy me a fretless bass to attach these nylons hanging around.