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Nut question re slanting the string groove.

I've only built one instrument—a type of solid-body 6-string bass—but I have what I hope will be a quick question regarding the slant in the grooves of the nut:

I have the impression that it's important to slant the string grooves in the nut downward toward the back of the nut, i.e., downward toward the tuning machines. Otherwise, the string may not contact the front edge of the nut, and it seems to me that if you don't do this you risk the string contacting the back edge of the nut instead, which could make the scale a quarter inch or so longer than intended and throw intonation off. Am I right about that?

And is this also why some nut blanks are tapered on the back side—i.e., the side toward the tuning machines—to make the top edge of the nut a bit thinner and make the slotting easier to slant downward toward the back of the nut?
 
Yes, you are correct. The string needs to have full contact along the length of the slot. This is important for both tone and wear (of the nut). But the critical thing is that the highest point of the slot needs to be right at the front edge of the nut, at the beginning of the fingerboard. If the slot gets rounded down at the front edge, so that the highest point is back from the edge, it will cause buzzing problems and the intonation will be off.
 
Thanks, Bruce. It's great that you pro luthiers will help us out like you did for me. Makes me feel a whole lot better about my project. I've already adjusted the nut a good deal, but I may just make a new one from the beginning, now that I have a better idea of what I should be doing with it.
 
Well, Bruce, I've now spent a couple of hours adjusting the grooves in the nut along the lines you suggested, and it's already made a big difference in evening out the intonation along each string as well as from string to adjacent string. Still a bit more to do, but I'm letting the strings settle into the newly-modified groves at pitch for a day or two in between nut-adjusting sessions. My two bass-most strings are nylon-wrapped, flat-wound steel at 0.135" and 0.115" gauge, respectively, and it seems to me that they take awhile at pitch to shape themselves to the newly-modified grooves.

Thanks, again, Bruce.