As I'm working on my Cepheid 5 bass, one thing I wanted to make sure I did on this build is to cut a compound scarf joint. These are used on multiscale instruments where the headstock angle breaks just behind the nut the whole way along the slanted nut line. Instructions on how to make them are few and far between, and usually just buried in a build thread somewhere. Nothing wrong with that, but from all of my research, there isn't a treatment singularly on cutting the scarf joint. I was told there was an article in American Lutherie at one point, but it's a subscription article. So, as a trained experimental physicist, I decided that I really wanted to understand what was going on. After I did, I thought I should post something that people can reference for a straightforward, illustrated reference, but also with equations to eliminate a bunch of guesswork and trial and error (NOTE: I'm not responsible for any error ). But before we get going, there are three (3) primary ways a compound scarf can be safely cut for a guitar or bass neck: Table saw with tilted blade Band saw with tilted table Router on sled wedges My approach here will work with both the table saw and band saw, though examples are shown on the table saw because that is how I chose to do it. My requirements were to get the headstock and neck shaft from the same board with minimal waste. A lot of the recommendations online are to simply put the compound angle on the neck shaft and use a solid block for the headstock. That's cool and I have no issue with it, but my neck blank was not sufficiently long to do this, thus the approach for minimized waste. I haven't tried it on a laminated neck, but this may work for it, it would be cool if someone gave it a whirl at some point. Basic Information Now, when cutting the compound scarf joint, there are three angles that come in to play: Tilt-back or headstock angle (theta): This is the normal headstock angle that one chooses. My examples use 12 degrees because that is what I wanted. This is assumed to be known. Zero fret or nut angle (phi): This is the angle from the line perpendicular to the center line (like the original nut line, which would be 0 degrees). This angle is given by the likes of fretfind2D and assumed to be known. Blade angle (beta): This is the tricky bit. This is NOT the same as the zero fret angle, as I first assumed. This actually is a trigonometric function of the other two angles. This is where I got confused and where there was zero concrete info. It seemed that the few examples I found determined this angle through trial and error, just like I did at first. So I got to work deriving what that function would be. Here is a quick illustrated cheat sheet that I put together that shows the angles, the equation relating them all, and the sequence for cutting the scarf joint. Cheat Sheet Note how there are two cuts to be made. The first cut will result in the correct compound angle on the neck shaft. The second cut will result in the correct compound angle on the headstock. There will be a pentahedral piece of waste that results from these two cuts.