Equal vs. Proportional String Spacing

I'm a bassist so these things matter to me more than guitarists. We're sort of used to looking at the world in terms of strings that you can measure with a thrown axe than the fine micrometer-and-loupe stuff used for the twiddly high notes! Nonetheless - how strings are spaced across the nut matters a lot, especially when the gauges from one side to the other are radically different.

The two distinct methods of string spacing are centre-to-centre and "proportional" spacing. I'm more into the latter of the two, so lets start with the first one so I can sell you on my personal favourite later....

Centre-to-centre spacing is exactly what it says on the tin. Regardless of each string's gauge, the centre point of each string is the exact same distance from that of neighbouring strings. Most off-the-shelf guitars come with this setup purely because it's simple, quick to use and works independently of the destined string set gauges. Even bassists can work this out on all four of their fingers!

All that is required is to take your nut width (lets say, 1,75" or 44,5mm) and subtract the spacing from each edge that you prefer (about 0,125" or 3,0mm on guitar). Divide this by the number of strings minus one. In our example:

Metric

(nut width - bass edge - treble edge) / (strings - 1)

(44,5mm - 3,0mm - 3,0mm) / (6 - 1)

38,5mm / 5

= 7,7mm

Imperial

(1,75" - 0,25") / (6 - 1)

1,5" / 5

= 0,3"

This makes it extremely simple to mark out on a nut blank using a pair of calipers. Set up the string to string distance, lock the calipers up and mark the string centres using the sharp points of the jaws one to the next. So what's wrong with this method?

(This is where I get to sell you on the benefits of proportional spacing....)

In short, nothing. It has been used since forever, and the chances are that your hands are used to this spacing anyway. As a bassist however, the disadvantage becomes far more apparent; the heavier gauge strings have smaller gaps between the edges of each string. Basses with five or more strings exhibit this symptom in increasing measure. Extended range guitars can also fall afoul of the centre-to-centre spacing bug with lower strings starting to bunch up. It's definitely an option worth considering because of this.

Instead of marking up each string's centre point by a simple division of string span, the overall spacing between all of the strings is divided instead, taking into account the fact each string's width. The outer strings are in the same positions, however the bass strings are no longer bunched up in comparison to the thinner treble strings.

Does this sound clear as mud? Once you've played with the calculation a couple of times it becomes pretty much as easy as centre-to-centre calculation.

Take your destination string set. I'll use a 7-string set for this example, based on the Optima Gold .009-.054 set on my own 7-string and its 50mm / 2" nut size.

Firstly, total up the diameters/gauges of each string in your string set; 0,188" or 4,8mm for the set mentioned. Subtract both this and the outside spacings from the nut width;

(nut width - string gauge total - bass edge - treble edge)

50,0mm - 4,8mm - 3,0mm - 3,0mm = 39.2mm

or

2" - 0,188" - 0,125" - 0,125" = 1,562"

Now simply divide this value by your number of strings minus one to produce the spacing; 39,2mm / 6 = 6,53mm or 0,260"

The trick here is how to transfer this to your nut! For CAD users, it is a simple matter to draw out a 1:1 representation of the nut, pasting this to the top of the nut blank and using a razor to scribe where the centres are located.

For those used to doing it manually, there are two alternatives; one with a bit of maths and the other requiring a little precision woodworking.

Mathematical version

Working from the 1st string, add up the outside spacing value with half the diameter of the 1st string;

3,0mm + (0,228mm / 2) = 3,1mm

0,125" + (0,009" / 2) = 0,125"

Okay, so not a huge jump.

The centre point of the 2nd string is the outside spacing, 1st string's gauge, equal spacing value and half of the 2nd string's diameter;

3,0mm + 0,228mm + 6,53mm + (0,279mm / 2) = 9,9mm

0,125" + 0,009" + 0,260" + 0,011" = 0,405"

From that point on, each centre point is worked out using the same combination of edge/string-spacing-string-spacing-string-spacing/half-string calculation. Still with me?

To make this process simpler, I have created an Excel spreadsheet to do all of the donkey work for you:

Woodworking version

The most practical method is to work out the spacing between each string and make a precision wooden shim. These can be used in a number of ways to transfer the spacing onto a nut, whether it be guiding fret files or physically spacing strings and marking the nut by a light hammer blow over the nut.

Which method is better here? Ultimately it depends on whether you can produce shims to exacting thicknesses.  Certainly, using shims is a more repeatable method if you're making more than one nut.

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Opinion is pretty much polarised on the two methods of string spacing. Some people (especially bassists) swear by proportional spacing due to the effect of larger differences the lower to heavier gauges accumulate across the string span. Many people initially dislike proportional spacing, having compensated for the spacing differences of centre-to-centre for years. Either way is perfectly relevant and don't let anybody tell you otherwise!

Unless they are a bassist, in which case they are right.