Spice rack design using screws (3/4"). In pics I use 12mm stainless, but made versions for 3/8" and 1/2" dowel, and 1/2" copper. The size of pipes seems overkill but it makes the spices roll out nicely!

Screw approx 4mm x 19mm (3/4) but print and match screw second because the offset varies at different sizes. Don't go through your door :)

I hotglued one side to the pipe.

Let me know any tolerance issues! I left 1/32" but I don't have access to the wooden dowels.