Getting the neck relief (if any) right can be challenging. There's a tendency just to follow the plans and hope for the best, but really this only works if (a) the plans are precise, correct and complete, and (b) you follow them precisely. Otherwise it's a bit hit and miss; ideally one would have known measurements to work to.

The problem is that, even if you get exactly the right relief according to the plans, the precise height of the top of the saddle is dependent on the curvature of the soundboard and this tends to be something of an unknown quantity. Since the strings form a straight line from the nut or, when depressed, the frets, to the top of the saddle, their exact height above the other frets (and particularly fret 12) is a little uncertain.

There's an obvious and simple solution to this problem: measure it. Of course you have to be pretty sure what you are measuring, and why. So here's one approach...

Parameters

The reference plane This is the flat surface relative to which the various heights (e.g. the amount of relief) are measured. For example a 3 mm relief means that at the nut the surface of the neck, excluding the fretboard, is 3 mm above the reference plane. The curvature of the soundboard means that the base of the bridge may be either above or below the reference plane. For the plans I am using (Romanillos 2012) it seems to be about 2 mm below. A guitar built according to the Roy Courtnall method (see Roy Courtnall, Making Master Guitars) will be about 2 mm or 3 mm above. But this isn't precise, and there's no straightforward way of measuring it precisely.

For my guitars the reference plane is defined by the top bout, which is flat, strongly reinforced and (once the back is glued on) firmly fixed to the neck at the required angle. For a guitar built using the Roy Courtnall method it will be the plane defined by the top (soundboard edge) of the ribs.

The fingerboard thickness I like fingerboards to be between 5 mm and 7 mm. No particular reason; it just feels right to me. They are usually supplied with a thickness of 9 mm to 10 mm. They have to be planed down anyway as the thickness is variable along the length and, to some extent, across the width. I make the maximum thickness (at the nut end) 7 mm. The thickness at the twelfth fret (and therefore the rate of taper) depends on the required string clearance. It is what we have to determine.

The height of the top of the saddle This is determined by (a) the height of the bridge, (b) where the bridge is mounted on the soundboard, and (c) the amount that the saddle extends above the top of the bridge. My bridges are 9 mm from top to base, and I like the saddles to extend 2 mm more at the bass end than the treble. If we say 1 mm at the treble end and 3 mm at the bass end this gives an addition clearance of 1 mm for the bottom E string compared to the top E string, assuming the thickness of the fingerboard doesn't vary across its width. This means the top of the saddle is 10 mm above the base on the treble side and 12 mm on the bass side. If we work with a figure of 11 mm (the average) we can simply regard the plus or minus 1 mm as compensation to be added as appropriate.

Procedure

We start by preparing two small blocks of wood. One will be about 10 mm or 20 mm wide and about 40 mm or 50 mm long; these dimensions are not critical. It should be exactly 11 mm thick to represent the height of the bridge up to the top of the saddle. The other block will be about 52 mm wide (to fit comfortably on the fretboard at the nut end), about 50 mm long, and 8.7 mm thick. This last figure is the sum of the thickness of the fretboard (7 mm), the height of the crown of a fret (which I am taking to be 1 mm) and standard clearance of the strings at the first fret (0.7 mm). A line can be squared across the block 5 mm from one end, and another at a further 35 mm (i.e. 41 mm from the end).

The guitar is now held in a vice (and/or supported by wood blocks) so that it is horizontal with the soundboard face up. The small block is placed with its front edge a millimetre or two over the intended position of the saddle (652 mm from the nut) and the other block is placed on the neck, butting against the head veneers. The 41 mm line marks the position of the first fret .

We now place a metre rule on its long edge with one end on the 41 mm line and the other covering the small bridge block. We measure (as accurately as possible) the size of the gap between the surface of the neck and the bottom edge of the metre rule. This will be the sum of the fretboard thickness at the twelfth fret, the crown height of the twelfth fret, and the clearance at the twelfth fret. We want a clearance of 3 mm (strictly, 2.9 mm), so with an assumed crown height of 1 mm the thickness of the fretboard at the twelfth fret will be this distance minus 4 mm.

The gap on my guitar was 10.5 mm. so the required thickness was 10.5 - 4.0 = 6.5 mm, which meant that the fretboard would have to be tapered by just 0.5 mm (from 7.0 mm to 6.5 mm). This was less than I was expecting but it explains why on my previous build I found I had rather too high an action.

Variations

The obvious question this raises is why (or whether) we need a 3 mm relief. The design I have been using was largely based on the plans included in Jose Romanillos's book Making a Spanish Guitar, but although he is quite clear about the neck relief the exact curvature of the soundboard is not very clearly defined. Sometimes he talks about using a radius dish (without, as far as I can remember, saying what the radius is), but at the same time he stipulates a particular solera arrangement that will result in a not very clearly defined curvature, but is clearly not spherical.

I suspect this is the problem. It appears that for the solera I have constructed the relief of 3 mm is too great. It's clearly not that I am tapering the fretboard too much, since Romanillos suggested more, not less, tapering. But on the other hand reducing the relief would have an immediate effect: for each 1 mm reduction in the relief the twelfth fret thickness, for the same clearance (3.0 mm), would reduce by 0.5 mm, as follows.

Fortunately my solera allows the relief to be adjusted easily simply by adding veneer shims at the nut end of the neck extension. A close inspection of the Romanillos 2012 plans seems to suggest that the fretboard thickness at the twelfth fret is 6 mm, which (from this table) would imply a 2 mm relief, not 3 mm. This is consistent with back-of-envelop calculations assuming a base height of -2 mm for the bridge, so it seems reasonable to suppose that the discrepancy results from the difference between the bridge height on Romanillos's solera and on mine.

For other solera arrangements, such as Roy Courtnall's, where the bridge base height will probably be around +2 mm, the required fret 12 thickness needs to be established using the spacing blocks as described above and measuring the F12 gap.

What about fret 19?

Good question. As long as the relief is non-zero, the surface of the neck (and therefore the underside of the fretboard) will be at an angle to the reference plane -- i.e. the surface of the top bout. Since the part of the fretboard from frets 12 to 19 must lie flat along this surface an additional taper must be applied over this section.

The amount of this additional taper is easily calculated. The distance from fret 12 to fret 19 is seven frets, and therefore exactly half of the distance from the nut to the seventh fret, which is half of the distance from the nut to F12 (i.e. 32.5/4 = 8.125 cm). This means we will require an additional taper which is one quarter of the relief. So for example if the relief is 3 mm we need an additional taper of 3/4 = 0.75 mm over the last 8.125 cm of the neck. Since without this adjustment the taper over this section would already be one quarter of the taper from F0 to F12, i.e. 0.5/4 = 0.0625, this brings the actual taper at F19 to 3.5/4 = 0.875 cm.

We can now extend the table to include the end taper (still assuming fretboard thickness at F0 to be 7 mm).

In practice, of course, we need not work to quite this level of precision.

An alternative approach using geometry

Alternatively we can just work it all out geometrically. If we do (see diagram) we find that if the bridge base is 2 mm below the reference plane, the thickness of the fretboard at F12 is 6.35 mm, rather than 6.5 mm. This suggests that the bridge base is a little less than our estimated 2 mm below the reference plane. We could use the formula in reverse to work out the actual displacement and then recalculate the F12 and F19 thicknesses to confirm the figures given in the table. Feel free to treat this as an 'exercise for the reader'!

Note, however that the diagram draws attention to some very minor sources of inaccuracy. For example, if the thickness at F1 is, as we assume, 7.0 mm, it will be very slightly more than 7.0 mm at F0. Further, we have not taken account of the fact that the thicknesses should be measured perpendicular to the reference plane, not (as we would do in practice) perpendicular to the plane of the neck surface. We could make corrections for the errors but they will be so small as to be negligible, and therefore hardly worth the effort.