Can you take a cheap high carbon steel katana and temper it so you a real hamon on it?

Answer 1

No, you can retemper a blade to help reset a bend but the hamon is a the unique product of a proper clay forging. You can wirebrush yourself one though, not much point to it. Look into the kaze katana. One of the most practical 'legit' hamon katanas on the market.

EDIT:

Actually, the hamon is a result of the tempering and it is possible to create one on a lower quality sword. However, it will only be good for appearances and nothing more. In a true katana, the hamon is formed when the front edge of the blade is cooled more quickly than the back part of the blade, this causes a slightly different temper in the front making it more brittle and better able to hold an edge while the back is softer and more resilient to impacts. The same effect of different tempers making slightly different "shades" of metal can be achieved by retempering, but this tempering process is also what makes a curve in the blade, as the metal that cooled more quickly won't shrink as much as the metal that cools more slowly, causing the blade to bend backwards when the front ends up being larger/longer than the back. This is because the crystaline structure does not have time to "settle" in the front as it does in the back, causing the formation of iron carbide (I might be remembering ths part wrong but I'm pretty sure that's what is formed). Because of this, you can accidentally make the blade have a VERY extreme curve to it that ends up making it look very strange, even with a more "realistic" hamon. The BASIC process of adding a hamon to a blade is by coating the front of the blade with a thinner mixture of water and clay (sometimes other things such as ash or plant matter) while coating the back with a thicker layer of thicker clay/water mix. the blade is then carefully heated to a very precise temperature (traditionally with sight alone) until it is heated to be around 800 *C (1500 *F) or bright red but not quite yellow hot. the blade is then immediately quenched afterwards in warm (100 *F) water for about 3-4 seconds, then removed to prevent stress fractures by leaving some heat in the blade. Even doing this and somehow preventing over-curving the blade, it still will not be anywhere near a real katana blade, and will at best work as a decorative blade (after using a chemical abrasive to "bring out" the hamon) and at worst (and most likely) be a waste of clay, charcoal, steel, and time as it takes a long time to learn how to make a realistic LOOKING hamon, let alone the real hamon you were asking about.