Since desaster stroke, I got to cut a new nut.Well, bone nuts are on their way, some post partner will surely deliver them when I am not at home, and I’ll have to fetch them from some obscure and remote place again … until then I can think about how the nut should look.
In principle, there are two possibilities to cut string slots into the nut: you can simply divide the available space into (number of strings minus one) equal parts and put slots (two in case of a 12-string guitar) at each of the resulting marks (that would be called “equal spacing”), or you can place it so that the space between the string( pair)s remains constant. Since the strings have a varying thickness, this is not the same!
The demolished plastic nut seems to have had the slots in equal spacing, as far as I can determine. So the space between the string pairs would have varied, much less between the thicker strings than between the thinner ones. Might be mathematically pleasing, but is less so for the fingers. The string pairs themselves would have had the a rather uniform spacing between the two strings. That’s not optimal, since the plucked strings have varying displacements – the thicker ones need more space. So maybe the thicker strings would have vibrated against each other, while the thinner ones could have been placed closer together without doing so. Oh well, I’ll never know …
Anyway – if I have to carve a new one, then the result should be as good as possible. So let’s calculate an ideal distribution!
Proportional String Spacing
For that, Stewart-MacDonald would offer a really nice thing: a string spacing rule with continuously reduced gaps between the strings that you can easily apply marks onto the nut with. There are only two little problems with that:
- Stew-Mac is located in the US of A. Transport takes some time and costs quite some money.
- The rule is designed for 6-string guitars. Using it for my 12-string one would have meant additional headscratching …
… and if I’ve got to scratch my head anyway, I can as well do it in my favorite way. Computational problems have to be killed with a computer 😎 – in this case, a spreadsheet is sufficient. So which values do I need for the calculation?
- the string gauge. Since it would be quite cumbersome to craft a nut for each possible string set, I’ll go with an average string thickness – and adjust that to the files that I have
- the neck width. That’s given – I can’t add wood to the neck and I definitely wouldn’t want to remove anything. The kit’s neck is 48 mm wide at the nut; luckily, this is a standard size, so I ordered nuts in this size
- the distance between the neck border and the strings. The outermost strings have to be placed a bit inside, since the fret ends aren’t vertical – and since I’d slide off the fret board quite easily with my clumsy fingers when trying to push down the string. The kit’s nut has reserved around 3.6 mm for that; I’ll keep this distance
- the distance between the strings of a string pair. For that, StewMac has a helpful web page that gives, as a rule of thumb, a middle-to-middle distance of 7/64″ for the 4 wound string pairs and 5/64 for the 2 highest plain string pairs. Now … if I’m calculating anyway, why not make this distance proportional as well?
Additionally, I’d have to adjust for the fret board radius as well; the fret board seems to have been done with a 12″ radius (guesswork at the moment – the tools to measure that are on a boat from China 😎 ) which means that a rule (or paper sheet) put on top of the nut would have to be a little bit wider than on a totally flat nut. Based on my calculations, however, the deviation is approximately 0.03 mm, so it’s negligible.
Equipped with these considerations, I created a spreadsheet that should allow the creation of a perfectly slotted nut; and while I was at it, for 6-, 7-, an 8-string guitars as well. Maybe I’ll build one some day. Perfection to 3 places behind the decimal point … now let’s see whether my dexterity can keep up with my plans 🙂 …
For 12-string guitars (and mandolins, 8-, 10-, or 12-string basses), one more subtlety has to be considered: since the 4 lower strings are accompanied by a second string that’s tuned an octave higher, there are two possibilities to place the strings of a pair: with the lower or the higher string on the “upper” side. For E-guitars, it seems to be custom to place the higher string first, although Rickenbacker does it the other way round; my old acoustic 12-string EKO guitar does it like the majority. Of course, the two methods require a mirrored layout, since the strings have a different thickness. I could, in theory, shrug my shoulders and carve two wider slots (the kit’s original nut was done that way); in practice, I’ll create a nut tailored to the “standard” layout first, but do the calculation for the Rickenbacker-style layout as well.
The LibreOffice spreadsheet can be found here: Nut Proportional – it’s configurable in every detail, so that I can easily adjust it to other situations (who knows, I might do another guitar one day).
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