Is it an advantage for the headstock geometry to minimize the string deflection between slot and tuning peg?

Question

Almost all of my guitars have the tuning post arranged either in a straight line like this:

Or fanned out like this:

This design requires the strings to deviate dramatically from a straight line after they pass through the nut slots - particularly the two middle strings.

Many electric guitars use a headstock design similar to this:

Which have the advantage of allowing the strings to continue past the nut to the tuning posts while staying in a straight line.

Some acoustic guitars also have a reverse taper to the headstock (Christmas Tree shape) where the tuning pegs converge instead of fan out - like these:

which minimize the angle that the strings deviate from a straight line.

It seems to me that torquing the string to the left or right as opposed to allowing it to remain parallel to (in line with) the nut slot - would put lateral pressure on the side of the string and have an effect on the way it vibrates. I have noticed that if I use a string gauge that is much larger than the nut slot is cut for, that it tends to dampen the string - perhaps because it is pinched in the slot and can't vibrate freely.

So my questions are:

Will this sideways torquing of the string negatively impact the strings resonance or sustain (when played unfretted) by decreasing its ability to vibrate freely?

And if there is an advantage to minimizing the deflection of the string - why don't more guitar makers use a headstock design that allows the tuning pegs to be more in line with their corresponding nut slots?

Answer 1

Every string on every guitar will deviate at the nut. Downwards. There needs to be an angle, be it laterally or downwards, so that the string has a 'node', rather like if the string is fretted, there is a downwards angle formed by the fretting finger, otherwise the note doesn't ring clearly. The nut isn't there to clamp the string tightly, although some of my guitars have a zero fret that does the same job as the nut, so thicker/thinner strings aren't affected. Some makers put string trees on the head, partly to pull strings down, partly to keep them from pinging out of the slots laterally. At the saddle/bridge end the string also has an angle, similar to the nut end, for the same reason.

The main reason it's better to have the angle only down rather than lateral as well is due to the vibrato system on a lot of guitars, which, in use, tightens the strings. A straight as possible line will help the strings slide rather than bind at the nut.

Apart from that, strings won't vibrate past that point, as they are dead there, so the nut ought to be the last spot where string movement is found. Having said that, head mounted tuners feel the vibration! But I believe that's coming back through the body/neck of the guitar. Be interesting to clamp one ONTO a string behind the nut...

Answer 2

Yes, there is an advantage to headstock designs that only have a downward angle, but it has little to do with the vibrations of the string, and more with tuning stability. (As Tim has written, you always need the downward angle, such that the nut is fact a node of the string vibration. And typically, you don't want the string to vibrate too freely, because that will cause funky resonances with the piece of string between the nut and tuner. Some guitarists will even put a piece of cloth there to prevent the resonances. )

When you tune the guitar, the string needs to slip through the slot in the nut along the direction of the string. Likewise, when you play a bend, the string is pulled through the nut a little bit, and then needs to slide back. However, when there is a sideways angle, the string (particularly the thicker strings, which have a significant stiffness and a large bending radius) can get stuck in the slot in an out-of-tune position. This is well-known phenomenon - search on Youtube for "Les Paul tuning problems". It can reportedly be remedied by taking a nut file to the slot, or by applying a bit of graphite or other lubricant to the nut slot.

The downward angle can also cause problems if it is too large - it puts stress on the wood. (Search for "Les Paul broken headstock" for examples.) A smaller angle, or a construction with string trees, solves these issues.

So why are there still guitars that are designed that way? Because people who buy a Les Paul want it to look the way a Les Paul has always looked, essentially.