A string vibrates in two planes that we can see - up-down and side to side - and a third that we cannot see and of which we are largely unaware.
When the string vibrates it stretches, creating variations in tension which reflect the frequencies contained in the harmonic series. Encoded in these cyclic tensile vibrations are mostly high frequency harmonics. Although the visible lateral vibrations of the string are arrested at the bridge and the crown of the chosen fret, the tensile vibrations are not and travel beyond the fret to the tether points of tuner and bridge. Where the string rests on the nut there is a slight deflection where the string is supported and at this point the nut experiences a vector component of the string's tension directed upon it. It follows that the level of string energy absorption at this point will affect the decay rate of the higher harmonics which are responsible for our sense of timbre or tone quality.
Beyond the characteristics of a nut being hard - as opposed to soft - it would be difficult to discern the tonal variation between two different but hard materials.
The replacement nuts I offer fall into three basic categories; bone, synthetic and metallic. Bone is traditionally from the dense part of the bovine femur and is the favoured material for a traditional look and sound.
The synthetic options comprise phenolic (Fender Cyclovac) and Corian. Corian from DuPont is an acrylic polymer with a mineral filler used as a synthetic marble in architectural applications. It's sufficiently highly thought of that it is used a nut material by C F Martin and as a structural material by Morel in the construction of Hi-Fi speakers. The Corian I use has the look of alabaster about it and is very convenient alternative for vegetarians and vegans who dislike the idea of having a piece of dead animal on their guitar...
The traditional alternative metal nut is brass. I offer this option using cold drawn bell bronze however a more modern alternative is Phosphor Bronze. Phosphor bronze, unlike brass which tends to malleable, is quite a good spring material favoured for chemically hostile environments like the springs inside saxophones which are constantly under attack from breath moisture and occasionally saliva. Bronze has a coppery gold colour, is highly resistant to patination and is also self lubricating. I've found it to be an ideal material for guitars fitted with tremolos.
Stainless Steel really is the last word in corrosion resistance and durability. It is also the most intense sounding option. It's not merely a brighter sound than other materials; it's more that it sustains a greater range of natural harmonics which remain in the sound for longer. Compare with my comments on Stainless Steel frets
The top nut is one of the most important components of the guitar. It's job is to reflect the pulse created in the plucked string back towards the bridge to interact with the pulse reflected from the bridge and form the standing wave which generates the sound, which is then amplified either acoustically or electronically.
To function efficiently the nut needs to made of a hard material, not only because hard materials are better at reflecting the string's energy and driving resonance (promoting sustain and efficient retention of high end harmonics) but because good tuning stability demands a precise profile to the slot; it should offer the string sufficient lateral support for it to reflect sound energy while offering the minimal point of contact required for smooth tuning and tremolo stability.
Experience has shown that the optimum profile is approximately parabolic, as shown below. The parabola's single focus point creates a geometry that results in high re-centring forces acting upon the string while maintaining a low surface area contact.
Many manufacturers, even those of high-end guitars, still use soft plastic materials for nuts on production guitars. Such materials tend to deform and grip the string even after they have been recut.
Not all plastic, it must be said, is bad. Hard plastics based on acrylic formulations and phenol-formaldehyde resins (Bakelite) are quite good nut materials and many is the time I have created an emergency nut or saddle out of an electrical pattress box or blanking plate only to find them still in use twenty years later...
Fender use a material called Cyclovac which has properties quite similar to bone and the synthetic material Tusq also has good resonance and restitution characteristics if a little soft.
Material such as ABS and Wilkaloid (a PTFE based compound) favoured by manufacturers of very cheap guitars and, bizarrely, one maker of top of the range guitars, are very poor materials as they are too soft to offer proper support for the string.
Although no-one disputes that the nut composition has a significant effect on tuning stability and the sound of open strings opinion has long been divided on whether the material used has any effect on the fretted notes.
In fact, it does.