Quartz is a 7. It can be scratched by topaz, corundum, and diamond. Quartz will scratch minerals that have a lower number on the scale.
Can a diamond scratch corundum?
The only hardness test that will identify a diamond is scratching corundum. Corundum, which includes all rubys and sapphires, is 9 on the hardiness scale. If your suspected diamond crystal can scratch corundum, then there is a good chance that you found a diamond. But NO OTHER HARDNESS TEST will identify a diamond.
Can corundum scratch itself?
Only a diamond can scratch a diamond. Corundum can scratch itself, topaz (8), quartz (7), and anything softer.