Ok, so, imagine you had a one-stringed violin, except that rather than press your fingers on the string, you used a lever, kinda like a whammy bar. Does anybody know of such an instrument? Otherwise, there's a possibility I'll end up making one.
As pointed out, a washtub bass is what you are thinking of: https://en.wikipedia.org/wiki/Washtub_bass
Though the most common way to play it is to pluck the string, I have seen it played with a cello bow. The sound difference is instead of a steady thump, you get a cello like sound, but with a more primitive rattle.
It's...pretty rough. And I don't have a bow. And it's harder to control than I hoped. And you guys are right; it only has about an octave of feasible range. But! It does kinda work, and science has been done. Thanks for your inputs.
Many years ago I built a one-stringed instrument which didn't have a whammy bar, but similar: you pressed the string down in a trough between two glass rods at the top of the neck, thus changing its pitch.
While fun, it had severe limitations: the useable range was only about an octave, it was very difficult to control the intonation (especially at the bottom of its range) and the string had much less tension at the bottom (a fourth that of an octave higher), making it weak. But don't let me discourage you.