I have produced a contour plot and have a colour bar but it's labels are such random numbers which I assume just comes from the data and I've been trying to find a way to relabel it so the numbers go from 1-12 instead and go up in integers. Is there any way I can do this?

I tried changing the limits but it didn't change anything at all.
When the colour bar gradient is smooth, I've found this works well:
If the gradient wasn't as smooth (i.e. fewer levels in the contour plot), this method wouldn't work as well.
Reproducible example