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Lars Hedelius-Strikkertsen is a Danish guitarist, who plays a 19th century guitar and specialises in the music of that time. Here he is playing a piece by Fernando Sor.

 

 

If you go to his website, you’ll see that he sometimes takes the trouble to dress the part when he gives concerts. Not surprisingly, in view of this attention to authentic period detail, he didn’t like the idea of using an anachronistic metal contraption as a capo d’astro and asked me to make him a cejilla.

 

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I’ve written about these devices before so I won’t repeat myself. But the commission reminded me of what delightful instruments these early romantic guitars are. Anyone interested in finding out more about them might like to take a a look at this excellent online gallery.

A few years ago, I made one of these guitars, which is now owned by the artist, Gill Robinson. The instrument that I copied was made by Louis Panormo around 1840, and it’s now in the Edinburgh University Collection of Historic Musical Instruments.

 

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There’s a photograph of my guitar above, and a video of Rob MacKillop playing the original instrument below.

 

Players of stringed instruments, particularly fretted stringed instruments, have been using capos to raise pitch and change key for a very long time. Some early English guittars, like one below, made in London in 1760¹, actually had holes drilled through the fingerboard and neck to allow a capo to be held in place with a screw and wing-nut.

 

 

Recently, I’ve been experimenting with another type of capo with a long history – the cejilla. Nowadays, they’re mainly used by flamenco guitarists, but a friend, who plays a copy of a nineteenth century guitar, thought that it would be nicer to have a capo that was plausibly of the same period as her instrument instead of a modern metal anachronism.

My first attempt to make one worked well enough as far as stopping the strings was concerned. But it looked clumsy because the peg head was too large. Worse, at least from the player’s point of view, the sharp corners were uncomfortable for the left hand.

 

 

So for the second one, I substituted a smaller peg from a half-size violin and softened the edges of the cejilla with a tapering chamfer. It looks better, I think, and I hope it will be more comfortable to use.

 

 

Cejillas aren’t difficult to make as long as you have a peg shaver and a matching tapered reamer available, and a bit of practice in persuading tuning pegs to turn smoothly in a tapered hole. This is everyday stuff for violin makers but guitar makers who fit worm and wheel tuning machines may not have the necessary kit. Mind you, since a pencil and an elastic band will do much the same thing, they may think cejillas are too much fuss anyway.

 

 

Anybody interested in the history of capos and the diverse and ingenious mechanisms that have been invented to provide what’s really just a moveable nut will enjoy the online Capo museum which has a wonderful collection (237 different designs).

 

As usual, click on the thumbnails for a more detailed view.

 

Footnotes

1. The early English guittar is in the collection of historic musical instruments at the Ashmolean Museum, Oxford

Although many people prefer guitars made of dark coloured wood, lighter colours can make good looking instruments too. The back and ribs of this one are in satinwood (Chloroxylon swietenia), a dense hardwood from Sri Lanka rarely available nowadays but which in Georgian times was widely used as a veneer in furniture making. It’s hard, brittle and difficult to work with hand tools but it bends fairly easily and, because it doesn’t contain large pores, finishes well with French polish. As its name suggests, satinwood is strongly reflective and when polished takes on a shimmering, almost iridescent, quality (sometimes called chatoyance) that’s impossible to capture in a photograph.

The rosette and bridge decoration are burr ash and the bindings are Rio rosewood. The soundboard is European spruce.

As usual, click on the thumbnails for a larger view.

I had intended my previous post to be the last on the V joint. But, as I’ve just completed a guitar using the one that I made for the photographs, the series can end in a rather more satisfactory way by showing how it turned out on an actual instrument.

 

 
Here’s a close-up to show any sceptics that the small extra piece of wood glued on to the male part of the V really is invisible in the finished joint – scroll down to the last couple of photographs in this post if you can’t remember what I’m talking about.

 

Before gluing up the joint, it’s worth taking some trouble to make sure that the two parts fit perfectly. I put the neck in a vise and hold the headstock in place while checking for gaps with a 0.05mm feeler gauge. A bright light behind the joint also helps to reveal places where the fit is defective.

Here I’ve discovered that the sides of the V are a bit loose…

…while the shoulders are tight.

A couple of fine shavings taken off the shoulders of the headstock using a shooting board…

…improves the fit. As a final check, I rub chalk over the male part of the V joint, locate the female part in position and press the joint together hard.

Where the fit is perfect, chalk will be transferred evenly. High spots, on the other hand, show up as a blotch of chalk surrounded by unchalked wood. Here it looks as if there’s a high point on one side near the mouth of the V.

A small file takes off the bump…

…and a second chalk fitting shows that the joint fits pretty well all over, except for a small low spot on one side at the apex of the V. I decide that I can live with that.

The next step is to dust off the chalk, size all mating surfaces of the joint with hot dilute hide glue and leave them to dry.

This is the clamping arrangement that I use. It’s important that the compression force runs through the centre line of the headstock and bears directly on the shoulders of the joint. Chiselling off the front of the V where it projects through the headstock allows the bar of the clamp to sit close to the surface of the headstock.

Once I’m happy that I can get the clamp into exactly the right position, I un-clamp, brush medium strength hide glue onto all joint surfaces, re-clamp it and leave it undisturbed for a couple of hours.

Here it is after taking the clamp off. The shadow below the right hand shoulder of the joint indicates that the headstock is slightly twisted relative to the neck. I suspected that this would happen while I was making the final adjustments but decided that the inaccuracy would be small enough to plane it out after the joint was glued up.

And I’m pleased to say that it was.

The back of the joint looks a bit weird until the extra block is shaved off.

But these two necks show that it comes out all right in the end. Even with a magnifying glass it’s scarcely possible to see that extra wood has been added and after the final shaping it will be quite invisible.

That’s the last of the series of posts on making a V joint. Thanks to anyone who has followed the story this far. Before finishing, I ought to add that there are many variations in the way this joint can be cut. Some makers, for example, prefer to use a template for marking out rather than a ruler and dividers. Please add a comment if you know how to do it quicker or better.

Click on the thumbnails below for larger pictures.

Moving on from my previous post about marking out a V joint, it’s time to cut and trim it to shape.

First, I saw out the V in the headstock, keeping close to the lines but being careful not to saw past them. I try to be brave in sawing up to the line at the narrow end of the V because that’s the hardest part to clean up later.

Next, I stop to put a fresh edge on the chisel that I’m going to use. When it will slice through tissue paper, I reckon that it’s sharp enough.

I clean up the V, paring from both sides towards the middle. Final cuts are carried out with the chisel resting in the knife line that marked out the joint. A small square is useful to check that the sides of the V are flat. The most difficult part of the joint is the apex of the V but a slicing cut with the corner of the chisel will remove the last bit of waste.

Here’s the female part of the V joint in the headstock finished. It shouldn’t be necessary to touch it again.

Now I cut the male part of the joint on the neck, starting with the angled shoulders. I chisel out a ramp for the saw in the usual way…

… and then saw down to the V, keeping clear of the lines.

I mark the starting point of the cuts for the sides of the V on the endgrain…

… place the neck in a vise, tilting it so that the cut will be vertical, and …

saw off the sides of the V with a tenon saw.

I mark and keep the pieces that I’ve just sawn off. They’ll be useful later.

Now I clean up the V and its shoulders with a chisel, paring in from both sides as I did for the headstock.

Here it is almost finished.

The neck and headstock are now tested for fit. Below is the view from the fingerboard side of the neck.

And here’s the view from the back of the neck.

As you can see, there’s a problem at the apex of the V, where a shadow shows that the neck isn’t quite deep enough to fill up the whole of the female part of the joint in the headstock. (My stock of mahogany for necks is planed up at a thickness of 25mm which means that I always run into this difficulty.)

The solution is to add a little extra depth at the apex of the V. This is where the offcuts that I saved come in handy. I prepare a small piece from one of these…

and glue it on, taking care that the direction of the grain in the extra piece is orientated in the same way as the grain of the neck.

When the glue is fully hard…

… it’s sawn roughly to shape…

… and trimmed with a chisel. This addition will be invisible in the completed joint.

The last step is to make sure that everything fits to perfection before glueing up. I’ll discuss how to do that in the next post.

Click on any of the thumbnails below for larger pictures.

Although the geometry of the V joint is simple, it’s surprisingly hard to to visualise if you’ve only seen the joint on a finished guitar. So, in an attempt to make the marking out easier to understand, I’ve sketched it below.

As with all joints, the more precisely it’s marked out the better the final result. It’s crucial that the stock is sized and squared up accurately. The headstock needs to be 17 or 18mm thick to give a final thickness of 19 or 20mm after application of the veneer. The neck must be rather thicker – at least 24 or 25mm – or there won’t be enough wood at the apex of the male part of the V where it engages with the female cut out part in the headstock. The side view in the drawings of the joint above will show what I’m getting at. (Even 25mm thickness may not be enough for full engagement but I’ll show how I deal with that problem in my next post.)

It’s also important that the end grain edge at the lower end of the headstock is exactly square to the sides and faces. I ensure this with a low angle plane and a shooting board.

To begin the marking out, I scribe a centre line down both faces of the headstock with a marking gauge, being careful to scribe both faces from the same edge.

Then I mark the corners of the V with dividers, placing points 18mm either side of the centre line to form the base of the V, and a single point 42mm up from the base on the centreline to define the apex. In the photograph, the pinpoints are marked with chalk to make them more visible.

A single bevel marking knife is used to mark the sides of the V, keeping the ruler on the outside of the V. I try not to cut beyond the point of the V, particularly on the back of the headstock. It doesn’t matter so much on the front which will be covered with veneer later.

To ensure that the ruler doesn’t slip, it’s helpful to fix a strip of fine sandpaper to its underside with double-sided tape.

Here’s the V marked out on one face of the headstock. This process needs to be repeated on the other face so that both sides of the headstock are marked. I haven’t bothered to illustrate this.

Now it’s time to mark out the male part of the joint on the neck. Again, I start by scribing a centre line down both faces. Then I square a line across the upper face of the neck slightly more than 38mm from the end.

Using a sliding bevel set for the angle that I want the headstock to make with the neck (10º in this case, so the bevel is set to 80º) I scribe both sides of the neck from the line that I’ve just squared across it.

Then I square across the back of the neck at the point where the angled lines on the sides end. Finally, I mark out the V on both faces using dividers set to exactly the same dimensions that I used on the headstock. The only difference is that, when it comes to scribing the lines with the knife, I keep the ruler on the inside of the V.

Here’s the top of the neck marked out…

…and here’s the back. You can see that, on the back, the V is positioned slightly further down the neck than it is on the front.

In the next post, I’ll show how I cut out the joint.

You can see larger versions of the photographs by clicking on the thumbnails below.

There are two ways to create the angle between the headstock and the upper end of the neck of a guitar. One is to saw it out whole from a large piece of wood; the other is to make it out of two pieces using a glued joint – either the V shaped joint invented by the early guitar makers or a scarf joint. Of these options, the most rational is the scarf joint. It’s quicker and easier to execute than a V joint and wastes less wood than sawing out a neck and headstock whole. What’s more, it has a large glued surface so it doesn’t rely on nanometric accuracy for its strength.

Despite the obvious advantages of a scarf joint, the V joint has become something of a fetish among guitar makers. This is easy to defend where historical accuracy is concerned. After all, if you’re attempting a copy of a 19th century guitar, it’s desirable – even obligatory – to imitate the constructional methods of the original maker. But for a modern instrument, why prefer a weaker joint that takes longer to make?

The answer, I guess, is to show that you can. It’s not a million miles away from the Georgian cabinet makers who made the pins of their dovetails so skinny that they almost vanished at the narrow end, as you can see in this photograph of the drawer of the table at which I’m sitting as I write this post.

There’s no practical advantage either in strength or speed of production in cutting dovetails like this. Indeed, the reverse must be true. But they do provide an understated way by which makers can demonstrate that they care about seldom seen details and show off their skill.

I’ve found myself using a V joint for both these reasons. Here’s a copy of a 19th century guitar that I’ve mentioned in previous posts. The V joint in this instrument was present in the original and it seemed right to keep it.

On the other hand, the V joint in the guitar below could perfectly well have been a scarf joint. The guitarist for whom I made the instrument didn’t notice it until I drew it to her attention. Still, I enjoyed making it and, for reasons that I can’t properly explain, felt that it was worth the extra time and trouble.

I’ve just cut a couple more V joints for guitars that I’ve got planned for 2012 and, although instructions for making this joint already exist (see here, for example), I thought it might be useful if I kept a camera handy to document the process. In the next post, I’ll explain how I mark out the joint.

This splendid photograph was taken by John Runk¹ in Stillwater, Minnesota on an 8 x 10 plate camera in 1912. I came across it in a book, The Photographer’s Eye written by John Szarkowski. Unless the chap in the hat is unusually short, these pine boards must be around 3 feet wide and 15 – 18 feet long. The saw marks run straight across the boards which made me wonder how they had been cut – not with a circular saw obviously. Were large bandsaws in operation at the beginning of the 20th century?

Buying wood a few months ago, I realised that I didn’t know much about modern methods of conversion of timber either. Here are a couple of photographs taken in Andy Fellows’ wood store in Gosport, Hants². He has supplied me with quite a lot of the wood that I’ve used in recent guitars including the Madagascan rosewood for this nylon string guitar and the beautiful walnut for this copy of a 19th century guitar by Panormo. These boards aren’t quite as large as those in Runk’s photograph but they’re still pretty big and I’ve only the vaguest idea of how he goes about transforming them into the book matched guitar sets from which he lets me pick and choose. Next time I visit, I shall try to find out a bit more.

Sometimes, when handing over an completed instrument to its new owner, I catch myself wondering whether they have any idea of the time and trouble that has gone into making it. (Of course, it’s enjoyable time and trouble so I’m not complaining. Even so … ) But I suspect that instrument makers and woodworkers aren’t any better. When we buy wood we’re more likely to whinge about the price than to acknowledge the efforts and skills of the people who selected the log and converted it into sets of conveniently workable dimensions like those below.

1. There’s a brief biography of John Runk here.

2. Andy Fellows also sells wood at his on-line shop, Prime Timbers.

Having established, to my own satisfaction at least, that it would be asking for trouble to make a steel string guitar without a truss rod, the next question was which type to use and whether to arrange to get access to it at the top of the neck or the heel.

My friend Peter Barton, who makes beautiful steel string guitars in Yorkshire, recommended the Hotrod, which is a 2 way adjustable truss rod available from Stewart-MacDonald and looks like this.

But there were a couple of reasons why I had misgivings about this device. One was that it weighs over 100g and I thought it might make a small or medium sized instrument too heavy in the neck. The other was that it’s 11 mm deep and, although it would be easy to rout a deep enough slot to accommodate it, there wouldn’t be room to glue a fillet over it. The top of the slot would have to be covered by the bottom of the fingerboard and I worried that, when the rod was tightened up it might split the fingerboard or cause a bump.

To check, I made a model guitar neck out of a scrap of softwood, routed out a slot, installed the hotrod, glued on a pine ‘fingerboard’ and tightened up the trussrod as hard as I could.

It worked fine. My anxieties were unfounded: no splits or bulges in the fingerboard, even though it was made of nothing more substantial than cheap pine, and I could put a curve in the neck in either direction.

Still, there’s no getting away from that fact that it’s heavy.

An alternative, which is less than half the weight of a hotrod, is a simple tension rod. This what’s recommended by Jonathan Kinkead in his book Build your own Acoustic Guitar (ISBN 0-634-05463-5), where he gives instructions how to make and install it. I liked this idea because of its simplicity and light weight, and because it’s easy to arrange to adjust it through the soundhole, which means that there’s no need to excavate the headstock to provide access to the nut.

If you go for this solution, you have to find a way to anchor the rod at the top of the neck. Kinkead recommends a metal dowel tapped to receive the threaded end of the rod. I made one out of silver steel and repeated the earlier experiment.

It’s easy to install, although it’s important to judge the depth of the hole for the dowel accurately to avoid drilling right through the neck.

And it seemed to work OK too, although obviously it’s only able to bend the neck in one direction. However, when I took the fingerboard off, this is what I saw.

The fixing at the top end of the neck had been pulled out of its cavity and had begun to travel down the neck. Of course, this experimental neck is made of softwood and the problem might be less severe in a real mahogany neck. Even so, I thought there had to be a better solution.

It was the shape that was wrong. The cylindrical nut had acted a bit like a wedge. When I made a rectangular shaped nut out of mild steel, it stayed put.

As you can see, the first nut was unnecessarily wide. A narrower version worked just as well.

That’s what I decided to use in this guitar: a tension rod made of 5mm studding, anchored at the top of the neck with a square nut and adjusted through the soundhole. The nut at the top of the neck was silver soldered to the studding to prevent it moving during any adjustments at the lower end. Tension in the rod is controlled by turning a 5mm column hex nut bearing on a substantial washer at its lower end.

This arrangement worked well in the finished instrument and was more than powerful enough to keep the neck straight against the pull of the strings. Next time I make a steel string guitar, I shall be tempted to use 4mm studding instead of 5mm, which would mean even less weight in the neck.

As you’ll have gathered from my last post, I’ve been making a steel string guitar recently. That’s something I hadn’t done for a long time, and it got me thinking about truss rods. One puzzle is how they got their name. Doesn’t the word truss conjure up something like the Forth bridge or the roof structure of this magnificent medieval tithe barn¹?

Wikipedia says that, used in an engineering context, a truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes. So it’s surely an exaggeration to call a rod in the neck of a guitar a truss. Still, it’s not seriously misleading and I expect that most readers will think I’m quibbling.

Another puzzle surrounds the purpose they serve. As far as I know, no classical guitar maker finds them necessary. So why is it that steel string guitar makers never build a guitar without one? The straightforward answer is that steel strings exert more tension when tuned up to pitch than nylon strings and that a truss rod is necessary to counteract this extra force.

But I wondered if this explanation really held water. Using information provided by d’Addario, a reasonable estimate of the combined tension of 6 nylon guitar strings is about 40 kgs, while 6 steel strings exert nearly double that at 70kg. A load of 70 kgs certainly sounds a lot – the weight of an adult man – but don’t forget that it’s acting at a mechanical disadvantage when it comes to bending or breaking the neck of a guitar. The pull is only a few degrees away from parallel to the neck’s longitudinal axis and the compressive forces will be substantially greater than the bending forces.

Using simple beam theory, I made some rough calculations to get a sense of how much the string tension of a steel string guitar would bend the neck. These calculations didn’t attempt to take the taper of the neck into account – I simply pretended that the dimensions of the neck at the first fret remained constant all the way along the neck until it joined the body of the guitar – and they ignored the fact that the fingerboard and the neck are of different woods that have different material properties. (More details of the calculation are given at the end of this post in a footnote, if anyone is interested enough to check².)

The answer turned out to be that, tuned up to pitch, string tension would deflect the nut end of the neck about 1.6 mm forwards of its unloaded position. Although this is bound to be an over-estimate (because the calculation neglected the stiffening effect of the fingerboard and the increasing dimensions of the neck as it descends), I was surprised how large the deflection was. And I wondered if I’d got something seriously wrong. To check, I made a primitive model of a guitar neck to make some actual measurements. As you can see in the photographs below, the experimental neck is smaller in cross section than a real neck but it’s modelled realistically with an angled headstock and nut. Loaded with a 14lb weight, I measured a deflection of 1.47 mm at the nut, which compared fairly well with a theoretical value of 1.26mm derived using the dimensions of the model neck. So I’m moderately confident that my calculations for a real guitar neck aren’t too far out.

It looks as if the obvious answer is at least partly right. You almost certainly do need a truss rod to counteract the bending effect of string tension on the neck of a steel string guitar.

I suspect there’s another reason for truss rods too, and that is to prevent creep. Wood that bears a constant load for a long period tends to deform gradually even when the load is far short of its breaking strain. This is the reason why the ridges of old roofs tend to sag in the middle. In his book, Structures, J E Gordon explains that it’s also the reason why the Ancient Greeks took the wheels off their chariots at night. The wheels were lightly built with only 4 spokes and a thin wooden rim. If left standing still for too long, the wheels became elliptical in shape.

So perhaps I’ve ended up proving something that most guitar makers knew already. However, I don’t feel that the exercise has been a complete waste of time. Musical instruments shouldn’t contain anything that isn’t either necessary or beautiful. Since truss rods certainly don’t fit into the latter category, it’s good to know that they qualify for the former.

Footnotes

1. Thanks to Kirsty Hall for the image of the tithe barn.

2. Details of calculation of neck deflection.

Neck: width = 44mm; depth = 21.5mm; length (to 14th fret) = 355mm
Force exerted by string tension = 700 N
Nut taken as being 8mm above centroid of neck
To work out the area moment of inertia, I assumed that the neck was semi-elliptical in cross section and that the neutral axis ran through the centroid.
Modulus of elasticity of the neck was taken as 10,000 MPa.
Deflection was calculated as Ml²/2EI, where M = moment exerted by strings at the nut, l = length of neck to neck/body join, E = modulus of elasticity of material of neck (taken as 10,000 Mpa) and I = area moment of inertia of neck (assumed to be a half ellipse).

Here are a few photographs of a recently completed steel string guitar. It’s based on a Martin ‘OO’ model but I’ve added, although that’s surely the wrong word, a venetian cutaway. The soundboard is Sitka spruce and the back and ribs are English walnut. I used holly for the bindings and tail stripe, and Rio rosewood for the bridge.





My friend, Dave Crispin, came to the workshop to try it out a few days ago and while he was playing I captured a few moments on an Edirol recorder.



James Gordon, an engineer, materials scientist and naval architect, wrote two books that I highly recommend. I was about to write …to woodworkers but, actually, I highly recommend them to anyone who has the slightest interest in buildings, ships, aeroplanes or other artefacts of the ancient and modern world. My copies have been read and consulted so often that they’re falling apart. They are The New Science of Strong Materials or Why you don’t fall through the floor (first published in 1968, but still in print: ISBN-13: 978-0140135978) and Structures or Why things don’t fall down (first published in 1978 and also still in print: ISBN-13: 978-0140136289). Both are written for a non-expert readership and there’s very little algebra or mathematics. They’re fun too: Gordon writes clearly, wears his learning lightly and the text is spiced by his whimsical sense of humour.

The New Science of Strong Materials has many interesting things to say about the properties of wood and why it’s such a wonderful and versatile material. There’s stuff about how wood is able to cope with stress concentrations and limit crack propagation, about how glues work, the distribution of stress in a glued joint, and many other things of deep background interest, if not of immediate practical significance, to people who use timber.

The second book, Structures, is equally gripping. It explains how medieval masons got gothic cathedrals to stay standing, why blackbirds find it as much of a struggle to pull short worms out of a lawn as long ones, and the reason that eggs are easier to break from the inside than the outside. Of more direct relevance to woodworkers is its straightforward account of how beams work – which means that, if you’re thinking of making something like a bed or a bookcase, you can calculate whether the dimensions of the boards that you’re planning to use are up to the load they will have to bear, which is obviously useful in making sure that your structure is strong and stiff enough.

Slightly less obviously, it’s also helpful in giving you the confidence to pare down the amount of material that you might otherwise have used. A common fault of amateur woodworkers, it seems to me, is that when designing and making something small, they tend to use wood that is far thicker than it needs to be, which means that the finished object looks heavy and clumsy. Conversely, when making something large, they tend to use wood that is less thick than it should be, and the structure often ends up rickety and unstable.

Knowing a bit about beams might also be advantageous for guitar and violin makers. Here’s an example: take a strut or harmonic bar, rectangular in section, that you’re intending to glue onto the soundboard of a guitar. How is its stiffness related to its shape and its dimensions? What’s the best way to maximise stiffness while minimising weight?

Elementary beam theory tells us that, for a given length, stiffness is proportional to the width of the beam and to the cube of its depth. So if you double the width, the stiffness also doubles. On the other hand, doubling the depth, increases stiffness 8 times. If stiffness is what you’re after, it’s a lot more efficient to make the bar deeper than it is to make it wider.

This cubic relation between depth and stiffness could be something worth keeping in mind when planing down soundboard braces after they’ve been glued. If a brace is, say, 6 mm high to start with, planing it down by 1.5 mm to a height of 4.5mm will reduce its stiffness to less than a half of what it was originally. And shaping the braces to make them triangular or arched in cross section also reduces their stiffness considerably.

Mind you, like so many attempts to understand guitars from a scientific point of view, things rapidly get complicated. A structural engineer with whom I discussed the matter agreed with what I’ve just said about the depth of the beam being a powerful determinant of its stiffness. But he pointed out that where a beam is an integral part of a structure, the stiffening effect is much greater than you would guess from calculations that assume the beam is simply supported at its ends. This is certainly the case of guitars, where the braces are glued to the soundboard along their entire length and clearly count as an integral part of the soundboard structure. In such circumstances, he explained, the overall stiffening effect provided by multiple braces will be large and might well overwhelm the influence of the stiffness of any individual brace.

I thought that this was a very interesting idea and that it might begin to explain why so many different bracing systems work remarkably well. In Roy Courtnall’s book, Making Master Guitars, he give plans of soundboard strutting taken from guitars by a number of famous makers. Superficially they’re fairly similar, all being based on a fan-like pattern of 5, 7 or 9 struts. There are minor variations, of course. Some are slightly asymmetrical, some have bridge plates and closing bars and so on. But the  biggest differences lie in the dimensions of the braces. Courtnall shows a soundboard by Ignacio Fleta that has 9 fan struts and 2 closing bars which are 6mm in depth and an upper diagonal bar 15mm depth. By contrast, a soundboard of similar size by Santos Hernández has only 7 fan struts 3.5mm in depth and triangular in section. Applying simple beam theory would lead one to guess that Fleta’s bracing would add more than 10 times the stiffness that Hernández’s does. But perhaps that’s a misleading way to look at it. If one were able to measure or calculate the stiffness of the whole structure, by which I mean the soundboard with its bracing when attached to the ribs, the difference in stiffness between them might turn out to be much less.

It’s a question that might be tackled by finite element analysis and I’d be glad to hear from anyone who has tried. Some work along these lines has been done on modelling a steel string guitar, which at least shows that the approach is feasible.

In the meantime, without a proper theory, we’re stuck with the primitive method of trial and error. Below are some of the bracing patterns that I’ve experimented with. All produced decent sounding instruments but I’d be at a loss if I were asked which particular tonal characteristics were produced by each of the different patterns. It may be that William Cumpiano was right when he wrote (in his book, Guitarmaking, Tradition and Technology):

Specific elements of brace design, in and of themselves, are not all that important. One has only to look at the myriad designs employed on great guitars to recognise that there is no design secret that will unlock the door to world-class consistency.

All this means that I’ve been arguing in a circle. Perhaps the conclusion is that beam theory isn’t very useful to guitar makers after all. Still, if you take up the recommendation to get hold of Gordon’s books, the time you’ve spent reading this post won’t have been entirely wasted.

Rather to my surprise, since it’s a pretty arcane subject, my last post on the elastic properties of spruce and how these vary according to the orientation of the growth rings attracted a lot of attention. Thanks to everyone who took the trouble to email me with their thoughts or to post comments. Stimulated by your interest, I thought that I might expand on a few things.

Because of the primitive way I carried out these experiments, there must be some questions about the validity of the measurements. One reason why I couldn’t show a difference between the stiffness of the wood in the different growth ring orientations might have been that my measurements weren’t sensitive enough. Another might have been that my preparation of the test bars of wood lacked accuracy or consistency. These possibilities seemed worth checking.

First, I re-planed the 9 test bars so that they were as square and straight and, this time, as uniform in their dimensions as I could reasonably manage.

Then I made an estimate of their stiffness, in the same way as before, by clamping them in a vice one at a time and measuring the downward deflection produced by a load of 2lbs applied 20 cms from the vice jaws. Again, every piece was measured 4 times, rotating it through 90° between measurements. For each individual bar, I calculated the mean deflection (in inches) for the 2 measurements in the different growth ring orientations. 3 days later, I measured them again without reference to the earlier readings. The results are set out in the table below, rounded to the nearest hundredth of an inch.

These results seemed encouragingly consistent. The bars that were stiffer in the first set of measurements came out stiffer in the second set too. So it doesn’t look as if the readings are being swamped by random errors introduced by deficiencies in the experimental set-up or that any differences are due to lack of precision. And the actual values in the 2 sets of measurements were quite close too, so the findings are fairly reproducible.

As you can see, there was some variation in stiffness between bars. The deflections recorded for bars 1 and 4, for example, are somewhere between 10% and 20% less than those recorded for bars 5 and 9. It occurred to me that this might have been because my planing had been inaccurate, but when I checked the dimensions with vernier calipers I didn’t find that the stiffer bars were any larger. It may be that this variation is simply a reflection of how the properties of small pieces of wood differ slightly even when cut from the same board.

Although hardly necessary, since it’s obvious from the table that there’s no consistent difference in stiffness between quarter-sawn and flat-sawn orientations for individual bars, I carried out a straightforward analysis using a paired t test, which confirmed that there was no statistically significant difference. [Difference (quarter sawn minus flat sawn) = -0.004 (95% confidence interval : -0.015 to 0.007) p=0.38 df=8]

Guitar makers often flex wood in their hands to get a feel for its stiffness and I wondered if I would be able to identify the stiffest and the least stiff of the test bars by doing just that. Not a chance! I was quite unable to distinguish differences in stiffness between these bars by feeling how much they bent in my hands. It might be worth doing some more experiments to find out what sort of differences in stiffness can be reliably identified in this way. Perhaps we’re not as good at judging stiffness as we’d like to think?

One final thing, which someone kindly emailed me to point out, is that any shrinkage or expansion across the grain because of a change in moisture content of wood tends to be less at right angles to the growth rings than in parallel with them. So, where the growth rings are orientated vertically in the strut, any change in the width of the strut at the glue line with the soundboard will be smaller than if the growth rings had been orientated horizontally. Now in a guitar it’s hard to see that this will matter much because the struts are small, not usually subject to large changes in humidity and are glued in all sorts of different relations to the direction of grain of the soundboard itself, which is also going to move in response to changes in moisture content. But where the strut lies in the same north-south axis as the grain and growth rings of the soundboard – as, for example, in the bass bars of violins or cellos – I can see that there might be an advantage in keeping the growth rings of the strut in the same orientation as the soundboard. This is the best reason I’ve yet heard for keeping growth rings in bass bars vertical, although as I mentioned in my last post, it wasn’t a rule always followed by the great luthiers of the past.

When working on the top of a guitar, I put the instrument on a carpet covered bench and prop up the neck on a block of wood that has a shallow, foam-lined curve cut into the top – as you can see in the photograph above. But I’ve recently learnt a better method. The device below, made out of 2 semi-circles of 18mm plywood, radius about 3 inches, adjusts itself automatically to the taper of the neck and supports it in a far more stable way.

The danger when using the simple block is that it tips over if the instrument is moved along its longitudinal axis. Of course, one can always clamp the block, but with the new neck cradle there’s no need. I’m grateful to Richard Nice (who invented the plane that I wrote about in my last post) for this bright idea.

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