Fretboard setup: action, relief, nut-slot-height

This started with some questions:

1) How low can you make the action (fret surface, or nut slot base, to string distance) at the nut and fret 12 before a string “buzzes”, and in particular why are both usually different for the 6 different strings?

2) What determines where any string-fret contact problems will occur?

3) Does adjusting the truss rod neck to modify the neck relief (how much the neck bows away from the string) help or hinder “playability”?

4) What causes “back buzz” (frets buzz between the fret played and the nut), can the issue be quantified, and how do you deal with it?

5) Why is “fall away” (the action at high fret numbers is increased with fret number) sometimes used?

We note some poor assumptions sometimes made when considering these and related questions.

First, it is often stated that a string oscillates with a perturbation that is localized around fret 12, halfway between nut and bridge. This is not what happens unless you only pluck at the 12th fret. You don’t do that.

Second, relief is often shown as the neck taking a downward bow between the nut and neck-body join. Our guitars never show this: We think it is incorrect.

Third, it is often stated that nut slot bases must be higher than the first fret height, typically by 10 thou. inch for the high e string and more for the low E string, to avoid first-fret buzz. We are not convinced this extra clearance is needed unless it is because the nut wears down quickly. And our nuts have not shrunk.

After a lot of gemetry, some experiments, and a few headaches, we develoepd a model for how the nut slot height, the action and the relief interplay. Look at the figure above. Start by comparing the dot-dashed next-fret string displacement line with the solid next-fret clearance lines: First the green, then the black line, and finally the blue line. The red dot-dashed line is the maximum string displacement at fret n+1 when fret n is fingered, based on our best estimate of how we play (pluck displacement divided by pluck distance from the bridge, independent of n). The red dot-dashed line is for a constant pluck distance (1 mm at 100 mm from the bridge), while the orange dot-dashed line assumes a constant pluck force. There is some reduction in the string displacement with increasing fret used if constant force is assumed, because moving up the fretboard increases the string plucked angle.

We need the clearances at fret n+1 when fret n is fingered to be above this, but not so far that we have to push the string further than is needed. That would be uncomfortable, and increase the string tension and thus affect the note being played (the intonation would be adversely affected). The green line is a first cut at setting up the fretboard, with action, relief = 0 and nut slot base height. With zero relief the clearance with n > 0 is constant: For low fret numbers the clearance is too low (string displacement is larger) and for high fret number it is un-necessarily large (string displacement is smaller). With the chosen nut slot the clearance at fret 1 with an open string (n = 0) is comparatively large. The next step, black line, is to increase the relief to 10 thou. inch (0.254 mm) from 0. Now the clearance and string displacement match from n = 1 to n = 12, but not for the open string at fret 1 (n = 0). Next the nut slot base height is reduced from 1.27 mm to the same height as the frets, 1.016 mm (40 thou. inch), and we see good alignment between clearance and string displacement up to n = 12. As discussed above there is only a small difference in the clearance for n > 1 with the changed value of nut slot base height. Above n = 12 the string displacement and clearance diverges, but safely (more than sufficient clearance), and we have not attempted to modify it here with a negative fall away.

But let’s be clear: Play harder and it will all go wrong! But it does show we should reduce the nut slot base height, and we will (later).