Hey, uke, long time no see.
One thing I'd like to add, is the narrower the coil, the more wraps you can get, too (i.e. a coil wrapped on a needle vs. a coil wrapped on a toothpick). The resistance of the wire is caused by the overall length and thickness of the wire, not by how many wraps are in the coil.
That's true Plan, so given the same ID inner diameter coil, the thicker wire will require more wraps and over a longer distance than the thinner wire to achieve the same resistance