String Angle Tutorial

This is something that is never covered. I've never seen it anywhere, but still string angles are given for each instrument, along with string lengths, afterlengths, saddle heights, projections, and overstand. I think drawings work best, so that is what I will use. Here it is with a basic Stradivarius, the only one where the "rules" easily work.

There is a lot of stuff there.

There is a side view that I use to find what works. Things will only work within a small range. The saddle has a range. The bridge has a range. The overstand has a range. The nut location has a range. Finding a place where everything is in range when the "givens" are plugged in is the goal.

The givens on a standard Strad might be something like this:
357 long
195 stop
130 neck
158 degree included string angle

I added a 32mm bridge which gives a 2:1 bridge:arch height ratio, and a 26.9 projection. Maybe the projection is a little high. Before we do anything we need some corrections. The radius on the top of the fingerboard gives us one correction. The radius is the same, but the width is different. Use Pathagorus, and we get .8 degrees. Same goes for the string clearance, I settled on .9 degrees. Add them up and it is 1.7 degrees.

Do the saddle end first, then subtract the rest of the included angle. Here, 22 minus 14.1 equals 7.9 on the string side. With that we can figure out the top of the nut. And then we calculate the bottom of the nut by subtracting 7.6 from it, the height of the nut. From there subtract the 1.7 from the strings (7.9) to get the neck angle (6.2); and from there we can figure out the overstand (6.0). I just say the belly is 4mm. It may seem complicated at first, but I'm sure you could do it in high school geometry class.

Many instruments drop the ribs from the top corner to the neck. This will increase the overstand by whatever the drop was. It will also make the nut "seem" like it is a little more than twice that drop higher. I believe the nut should be around zero. So plus on the top, and minus on the bottom is great.

Now we have the neck angle and mortice. I always cringe when people ask what angle to cut the end of the neck at. It depends. How are you cutting the mortise? I use a system that Michael Darnton recommended, with my own stuff (my wife says I can't leave anything alone). He cuts the bottom of the mortise the same depth as the overhang. I use the overhang plus the ribs. At the top I make my neck half the length of the fingerboard. So on this one it is 135mm. If the ribs and overhang are 3.5mm, I figure I need to go .75mm into the block on the top. Doing some calculations the angle of the mortice will be a little over 5 degrees, and the neck has to be cut about 1.15 degrees short of 90 degrees.

The last thing I look for is a 2:1 ratio of the strings to the other end. Then I want a 2:1 ratio there between the tailpiece and the afterlength. I think that may create a rocking couple that may make the strings more active. Maybe it doesn't, but I'll try that first.

Next what happens with the small del Gesu.