Calligraphy art is not at all limited to paper and ink, but when it comes to calligraphic ink, it can be simple and complicated.
Simply put, any non-waterproof medium is ideal for calligraphy, because it can be washed off the nib with the help of, yes, water. We normally avoid using waterproof medium to prevent nib-damage, but I’ve seen calligraphers go against the odds so as to write clearly on non-waterproof background. I guess it might be okay if you make sure to clean the nib quickly before the ink dries on it.
On a more complex note, the nib does want a certain level of consistency so it can readily and steadily flow. That might be why ‘premixed’ / ‘calligraphy’ ink are more expensive – because they are consistent. And to pack that amount of pigment in a somewhat still watery consistency must be tough. If you feel like complicating things, just try mixing your own ink – and don’t forget to put it in an airtight container lest your hardwork dries up.
Now, how do you know of an ink is non-waterproof?
There is a very simple test. Just dab a drop of ink on a waterproof surface, anything that won’t stain, maybe a piece of plastic. Wait until completely dry, then attempt to rub it off with water (on your finger or paper tissue). If it comes off with the water, it is non-waterproof and therefore safe for your nib. If the blob stays there in spite of the water, maybe forming a rubbery layer (like acrylic does) it’s probably not the best choice for calligraphy.