Granite tiles: how to clean them?

Does anyone know of a good way to clean soap scum and limescale off granite tiles?

Washing up liquid and soft detergents don't do the trick. Admittedly I've also let the dirt build up too much... That's partly because I once used a spray that 'leaked' behind the granite surface, this background drip is now stuck inside there forever and, since then, I've been weary of using anything remotely powerful. But now I really need to deal with it!

It's black granite and I'm not sure about its origin and quality. I know some are being artificially darkened and can react with harsh products. The leak/drip behind the surface certainly appears lighter than the black, I don't know whether this is due to discolouration or is an actual stain/remains of the spray – but I can live with it. What I really want to clean off is the scum and limescale on the surface.

Any advice or recommended products appreciated!

Thanks.