by Bert Eendebak

1 Introduction

In designing your own guitar personal preferences may play an important role. Do you want to play the guitar yourself? Do you (intent to) play just for yourself or do you need extra volume to cope with other instruments of the band or ensemble you are playing with? During the design of a guitar hundreds of large and small decisions have to be made. Sometimes related, sometimes not. (I have “counted” more than 200 different “decision points”!). To bring light in this complex decision process it is good to be aware of 5 main construction principles that have to be taken into account:

- Playability	Playing the guitar should be as easy as can be
- Constructability	In constructing the different parts no unnecessary difficulties should be encountered
- Acoustics	The volume and sound should fulfill your specific and highest expectations
- Durability	The performance has to last for at least 50 years
- Aesthetics	The guitar should be a piece of art and wonderful to look at

 

Sometimes these principles may lead to contradicting decisions and compromises have to be found. However most of the time it is easy to distinguish between “hard” and “soft” demands and to let prevail one principle above other ones. It is part of the design process and fun to make your own balanced decision on conflicting principles. A well-known example of conflicting principles comes up in the design of the soundboard. For a large volume and rich basses you will choose for a light, thin top. That may lead to an instrument with a wonderful sound, a sound however that will last for not more than some weeks because of the deformation due to the pulling forces of the strings. The “balanced” decision that has to be taken on this point and on many others as well will be discussed in the relevant chapters.

Nevertheless there will remain decision points which cannot resolved by calculations, trying to be smart or whatever trick you should have in mind. For this group of “unsolved mysteries” we still have to look to the experience of others (in the past). This is fortunately only in exceptional cases and we will surely draw your attention to it.

Because it is sometimes easier to discuss the design process in terms of specific measures, we will give from time to time specific examples of a realistic design. These examples are taken from some guitars (Guitar EB 2009 and EB 2010), designed and constructed by the author Bert Eendebak.

Whenever measures are given in italics they are taken from that design. So keep in mind that those numbers are just examples and can or should be adapted to your own initial choices.

In the description of the design process as given in this article no use is made of computer-based calculations or inside knowledge of mathematics, physics or acoustics. “Design of a classical guitar” is mostly based on the use of common sense, simple logic and of course a lot of reading.

2 On acoustic principles

There is a fundamental difference between a classical guitar and a violin in the way the sound is produced. In both instruments the energy of the vibrating strings has to be transported via the bridge to the soundboard. However finger picking the guitar strings leads to a short excitement of the strings, where in the case of a violin the energy is more ore less continuously added by the fiddle stick. In the case of a violin the vibration of the strings brings the bridge into a movement, perpendicular to the top. Some people describe the same phenomenon for a guitar but in fact it is the wriggling movement of the bridge that gives rise to the waves in the soundboard of the guitar. In designing a guitar understanding this difference is of primary importance.

Because the wriggling movement of the bridge is the main way the soundboard is excited the dimensions and the other characteristics of the bridge of a guitar play a radical role in the design. Because of the limited energy of separate notes of the guitar string every bit of energy should be used to generate the sound we want to hear. But unfortunately the efficiency of that process is low: for a “standard” classical guitar only 5 to 7% of the energy in the string is converted into sound waves. It will be clear that one of the main challenges in the construction of a guitar is to look and fight for every possible improvement of that efficiency. Prevention of every useless loss is a must.

Firstly, the connection points of the strings have to be fixed. The saddle has to be a hard fixed point related to the nut. That asks for a rigid neck, head and nut. In fact also the construction parts, connecting the neck with the bridge and directed parallel to the longitudinal axis have to be inflexible. Even the saddle and the nut have to be shaped in such a way that the string will not lose energy to the construction itself. The bridge itself is only a tool to transport the energy of the strings to the soundboard and it should not absorb any energy by itself. Not by a large momentum of its own and not by internal heat absorption by compressing or bowing motions. So the bridge and saddle have to be as light and inflexible as can be (see chapter 6 .The brigde).

The soundboard forms the vibrating membrane, which makes the music. The waves, introduced in the soundboard should on one side dispose their energy by introducing airwaves, but on the other side fade away slowly to show the desired sustain for the pitch involved. As for the bridge this asks for a piece of wood, that is very light, but with enough strength not to be deformed by external forces it is subjected to.

Here it is important to mention two different construction principles, sometimes described as contradictive. Some guitar builders highlight the essential role of the soundboard by following the frame principle. In that case the guitar body is seen (and constructed) as a solid, inflexible frame on top of which the soundboard is glued. That is in line with the idea that every “unnecessary” loss of energy should be prevented. So the only acoustical function of the guitar body in that case is to reflect the acoustic airwaves. This idea will lead to relatively thick back and sides and makes the construction of these parts relatively easy. However there are some “secondary” effects, which are in favor of a more flexible construction. It is well known, that some famous luthiers in the past, e.g. Torres, Ramirez and Hauser produced instruments with thin and flexible backs and sides. Such an approach has also advantages, of which the following are important. First a thin sidewall combined with a flexible lining allows the edge of the soundboard to turn over a little bit and thus enlarging the “effective” surface of the soundboard. This may give, let it be small, an increase of the sound volume. A second advantage of flexible back and sides is that some standing waves in the guitar body are supported. The end-effect of these different approaches can be characterized as “more volume with flexible linings and more sustain with fixed linings”.

As in life it is good to go for the best in both approaches and instead of choosing one of the two we will look for a combination of rigidity and flexibility of back and sides (see the chapters on top, back and sides).

Vibration modes

For a good understanding of the construction principles as described in this article some basic knowledge of possible vibration modes of the guitar top is needed. The traditional classical guitar top vibrates in many ways, but some fundamental frequencies below 500-600 Hz are of prime importance. These are the (0.0), (1.0), (0.1), (1.1) and (2.0) modes as shown in figure 2.

These figures of basic characteristic oscillations will be used for some design steps in the chapters on the sound bar and the back. Interesting and useful background information on these vibration modes, their relationship and effects on the guitar can be found in the reference 1 till 5.

3 Choice of materials

As a starting point for the choice of materials we assume that a classical guitar exclusively is made of wood, with the exception of the strings, frets, tuning machines, nut and saddle. The choice of the soundboard may be among others spruce, cedar, redwood, cypress or mahogany. In many cases the choice is spruce for the “concert” classical guitar or cypress for a flamenco guitar. Within the spruce (Picea) family various variants are used, like Alpine (Fichte), Sitka or Engelmann spruce. The choice is often made based on the availability and price of wood for the soundboard, but the characteristics of the white “Fichte” are clearly different from the harder and finer grained, slightly red-brown colored Sitka. Using a softer material for the top like red cedar asks for a thicker soundboard and adjusted sound bars.

Important are the large differences between different pieces of wood of the same species in view of grain, stiffness, run out, color and figuring. For the top, stiffness and “tap tones” may be the most important ones. For the back color and figuring may be deciding factors. Of course the characteristics of the wood in terms of e.g. strength, hardness or brittleness are important during the construction but have less influence on the main features of the design. The description of the design as given in this article starts from generally preferred materials as rosewood for back and sides, a spruce top, mahogany neck and ebony for the fingerboard and bridge, but other materials with roughly the same strength may be used as well.

4 Main dimensions

Playability

Do you want to have a big guitar or a small one? A big guitar gives you possibilities to end up with a guitar with a large sound volume and strong, durable, sustaining basses. A small one may lose power, compared to the big one, but still have sparkling trebles and be handy to transport. A small one may also be preferred if you have small hands, and find it hard to play specific accords on a big guitar.

Let’s assume that you want to design a guitar, to construct and play it yourself. The first thing you should do is to have a look at the guitar(s) you have already played. Is playing easy? I mean do you have problems with accords, which ask for a large reach of your fingers, especially at the higher positions? No problem? Or do you like to have the frets closer to each other? May be just a little bit. For some people, due to the size or the restricted movability of their fingers a shorter distance between the frets may be desirable. If the distances between the frets are just fine you should keep it that way, so measure the distance between the nut (or 0-fret) and the 12th fret. The scale length of that specific guitar will be twice as long as that length and also the maximum for the guitar you want to construct. Of course if you have no trouble at all playing challenging accords look around for another guitar to try out and to find your own maximum or optimum scale length.

Now for the next step, let’s assume that a large (sound) volume and rich basses are the characteristics you are most interested in. Then you fix the scale length on the maximum you just decided on or just below that. “Small” changes, e.g. between 63 and 65 cm give small changes in volume, but may change a lot in terms of easy playing.

Because it is easy to talk about a specific length and other dimension let’s for the rest of the design process choose for a scale length of 648 mm. But keep in mind that at this starting point of the design you are completely free to make your own choice.

Because the 12th fret is just in the middle between the nut and the saddle the distance between the 12th fret (exact the edge of the guitar body) and the saddle is also fixed. In our example 324 mm.

Other design characteristics that are solely based on playability are the width of the neck and the dome of the fret board (curvature perpendicular and parallel to the neck). Comparative thick fingers are a good reason to choose for a comparative large width for the neck and a stiff, bowed forefinger on your left hand asks for a curvature of the fret board. For these choices please see page neck and head.

Acoustical considerations

The main dimensions of the guitar body however are more based on acoustical considerations. Let’s think about the function of the guitar body as a (Helmholz) resonator. The dimensions of the guitar body or box determine which frequencies are favored for sound waves inside that box. Some people argue that the dimensions should be chosen such that the important tones (to you or to me?) are amplified. Or, in other words, the resonance frequencies of the guitar box should harmonize with the frequencies you like to be sustained at the most. On the other side you can imagine that favoring specific tones will bring the balance of the sound spectrum we strive for, in unbalance. However the practical classical guitar box with its feminine fluent profile has a whole spectrum of inside dimensions and every tone within that spectrum may, so to speak, find its place to resonance for a while. That may be the case, but it is still wise to give the basses we are looking for a preferred status because they are mainly influenced by the main dimensions.

Many designers choose the dimensions of the guitar body like the width of upper and lower bout, waist, height etc. as a fraction of the overall length of the guitar body. Just to realize that the “partials” also easy find a place to resonance for a while.
For that reason we take the distance between the saddle and the bottom as 25% of the scale length. So the length of the guitar body in our case would be 324 + 162 = 486 mm. Taking into account small corrections in view of edges and linings we end up with a total outside length of 489 mm.

Now starting from an inside length of the guitar box, say 486 mm, you may raise a lot of partial lengths, like 1/2, 1/4, 1/3, 2/3, 3/4 x 486 etc. But the choice is not free! The guitar should look like a guitar and for constructability reasons the sides have to follow a smooth curve. Therefore there are only a few possibilities. For the lower bout we choose a fraction of 3/4, for the width of the upper bout a fraction of 5/9 and for the waist a fraction of 1/2.

Again after corrections for linings we end up with the following dimensions (for the EB-guitars):

Length	489 mm
Width lower bout	368 mm
Width upper bout	273 mm
Width waist	245 mm

Dimensions of “Torres-made” guitars

Now having fixed the main dimensions of your guitar you may wonder to what extent these dimensions differ from or are equal to the dimensions of other guitars, preferably those constructed by famous luthiers. So let’s have a detailed look at the main dimensions of guitars built by Antonio de Torres Of the ~ 300 guitars constructed by or under direct guidance of Torres the construction and dimensions of about 80 guitars are reasonably well-known. Derived from ref 11 we put all main dimensions of Torres-build guitars in spreadsheets. A discussion on these spreadsheets, findings and conclusions are published in ref 12. Because it is obvious that a real small guitar (in length) will also have small widths and heights all these dimensions are normalized on a total body length of 500mm. The results are shown in figure 4. The dimensions of the “EB-guitars” are given as dotted lines.

Of a limited number of these guitars (~17) it is known that they were of exceptional class. They are indicated by ♦ in figure 4. It looks like that there is no strong relationship between this high quality and the dimensions. However the dimensions of the group of “exceptional class” fall in general in the upper range. The length of the bodies did not really change during the time (1850-1892) Torres built these guitars and the variations of the ratios between the different width and the lengths were minor.

It is thanks to the curved shape of the guitar body, that allows many different frequencies to feel happy inside, that you can build with large and with smaller bodies.

The height of the body for these guitars always shows the effect that the height at the top is smaller than at the bottom, varying between 5 and 10%. Also taking into account convenience of holding the guitar and the wish to give preference to strong basses the height of the EB-guitars is taken as 90 mm at the top up to 100 mm at the tail block.

The diameter of the sound hole for the Torres-made guitars varied between 84 and 90 mm with a few exceptions up to 95 mm. When you decrease the diameter of the sound hole of your guitar by partially blocking the opening you will hardly be able to hear the difference as long the variation is not too big. That would be a reason to decrease the sound hole diameter to e.g 60 mm. This would contribute to the strength of the upper bout and a little bit to the acoustical performance of that part of the soundboard. However by doing so you will not be able to go for final adjustments or repair activities inside the box. This last point is the main reason that for the EB-guitars a diameter of 88.2 mm (in fact 2/11 x 485) is chosen.

Final decisions on main dimensions

If you wish to have 18 full length frets, as is usual for a classical guitar, and you position the upper transverse bar and the waist bar 5 mm separated from the edge of the sound hole the other main dimensions can be derived easily. In figure 5 below these dimensions as applicable for the EB-guitars are indicated.

 

5 The neck and head

Dimensions

As explained in the chapter on  acoustic principles the construction of the neck has to guarantee that under string load the neck deflection will be practically zero. From the standpoint of a design that is based on a connection between nut and saddle firm as a rock the design of the neck itself is relatively simple. If you follow the usual instructions in guitar construction manuals you will end up with a neck that can withstand the pulling forces of the strings without any problem. For an impression of actual deflection it is interesting to look in the appropriate spread sheets in”Left-Brain-Lutheri” (ref.15).

For a more or less standard classical guitar neck (mahogany with an ebony fret board) the deflection, measured in change in the action at the 12th fret is about 0.1 mm, which is no problem to deal with during the construction. The choice of the wood and careful construction of the neck and its connections with foot, heel and fret board has to prevent dimensional changes with time. But that is more of a constructional challenge than a design problem.

In order to avoid buzzing of the vibrating strings against the frets we have to provide enough action (distance between the strings and frets). Too much action however hampers the playability and therefore sometimes guitars are provided with a concave fret board. In  ref.13 by Oswald J. Verbejj the author gives theoretical analyses for an optimal finger board curvature. Some of his conclusions were that:

• the optimal fingerboard is slightly concave with positive relief amounting 1/10th of string action at the 6th fret
• the optimal nut height is 1/20th of string action
• the action of an optimal concave finger board may be 27% lower compared to an absolute flat one

These findings are applied for the EB-guitars.

In view of the playability the fret board may also be domed perpendicular to the neck. To what extent is up to the choice of the individual player. The fret boards of the EB-guitars described on this web site have a slight dome. At the position of the high and low E-strings the fret board is thinned with ~1.5 mm compared to the middle of the fret board.

In general, the width and thickness of the neck and fingerboard are chosen in view of the playability of the guitar. From that point of view it is interesting to know how some famous luthiers chose these dimensions. In his book “Making Master guitars” (ref 21) Roy Courtnall gives detailed information on the dimensions of 8 classical guitars, constructed by internationally famous guitar makers. Taken from that reference some dimensions related to the neck and fingerboard are given hereafter (measures in mm).

Guitar	W0	W12	Ws0	Wb	Wsb	Th.fb0	Th.fb9
Antonio de Torres, 1864	49	60.5	42.5	82	56	24	27
Santos Hernández,1933	50	61	41	83	58	23.5	25.5
Hermann Hauser, 1931	52.5	63	43.5	85	59	22	27.5
Hernandéz Y Aguado,1963	52.5	62.5	45	83	59	21.7	23
Ignacio Fleta, 1968	52.5	62.5	43.5	80	59	21.2	26
Robert Bouchet, 1963	50.5	61	44	81.5	56.5	22.8	23.5
Daniel Friedrich, 1992	51.5	61.5	42.5	81	57.5	21.6	21.7
José Romanillos, 1973	52.5	62.5	43.5	87	59	20.5	25
EB-guitars	53	59	44	75	56	21	25

The distance between the E strings for the EB-guitars is chosen to be 44 mm at the 0-fret position and 50 mm at the 12th fret position. So the distance between the E-strings at the saddle position is 56 mm and the distance between the individual strings at that position 56/5 = 11.2 mm.

Position of neck and guitar body

The position of the neck in relation to the guitar body is a more complicated story! There are many variables that are related to the neck-body angle. In figure 8 a schematic drawing of these variables is given.

In this figure the following symbols are used:

fb0	thickness of the fret board at the 0-fret
fb12	thickness of the fret board at the 12th fret
f0	thickness of the 0 fret
f	thickness of all other frets
a12	action of the string at the 12th fret
bn	body-neck angle (divergence at the saddle position)
d	dome (maximum height of the top above the edge)
hs	height of the saddle above the soundboard

 

Geometrical laws tells us that the sum of the left and right side of the trapezium in figure 8 equals two times the vertical right in the middle of the trapezium (so exact at the position of the 12th fret). In that way the formula that describes the relationship between the variables can easily be derived from that drawing and reads as follows:

( fb0 + f0 ) + ( bn + d + hs ) = 2 x ( fb12 + f + a12 )

Now the question raises which parameters are decided upon and which will be calculated. Answering that question can be made more easily by fixing those variables, which can be decided on independently of the other decisions. In the following we will describe a possible approach. If view of commercial available fret wire and playability we may fix the following variables:

• f0 = 1.5 mm
• f = 1.0 mm
• a12 = 3.5/4.0/4.5 mm (for the E-high, the G/D respectively E-low strings)

Based on a standard thickness of an unshaped fret board we choose fb0 = 5.5/7/5.5 mm and as a starting point for the construction bn = 0.

By filling in these numbers in the formula we get the following relationships:

• hs = 2fb12 − d + 2 (E-high string)
• hs = 2fb12 − d + 1.5 (G/D strings)
• hs = 2fb12 − d + 4 (E-low string)

In these formulas we can see the relationship between the height of the saddle, the thickness of the fret board and the dome of the soundboard. Some possible combinations are shown in figure 9.

Be aware that figure 9 gives an example of the middle of the fret board and saddle. Based on the assumptions for the dome of the fret board and the different actions for the strings the height of the saddle for the E-high string is 2.5 mm lower than for the G/D strings. The saddle height for the E-low string is 0.5 mm lower than for the G/D strings.

Some constraints in the choice of these combinations have to be mentioned. The dome of the top should be within limits. E.g. not less than 2 mm and not more than 5 mm  (see chapter 8 ) . When we choose in figure 9 for a thickness of the fret board of 5 mm (at the G/D position!), we have to realize that at the E string positions the thickness of the fret board at the 12th fret is only 4 mm and at the 6th fret even less (~3.6 mm). This is about the minimum we allow in view of the role of the fret board in strengthening the neck.
With these constraints in our mind we may choose our combination of dome and saddle height within the shaded area indicated in figure 9. For the EB-guitars with a dome of 4 mm and a fb12 of 5.5/7/5.5 mm we end up with a saddle height of 9/10.5/11.5/11.5/11.2/11.0 mm.

During the construction some extra height should be left, leaving room for final adjustment of the action after set up of the strings.

6 The bridge

 

Introduction

Guitars need a bridge to connect the strings with the soundboard. If the bridge of a guitar is too heavy, too weak or not connected properly to the strings or top it will seriously hurt the acoustic characteristics. Always take care that it will not be the source of any energy loss. Above that, the reaction on the movement of the strings should be as fast as possible. A flexible piece of wood will absorb energy; so we have to look for a light bridge, made of hard material. Ebony and rosewood are most in use. The choice between these types of wood may be influenced by aesthetic arguments. For instance by choosing the same wood for the bridge as for the back, sides, head veneer, the finger board or the sound-hole rosette.

The strings have to be connected to the bridge. This obvious starting point is leading in the design of the length and the profile of the middle part of the bridge. Just take a piece of scribbling paper and draw all kind of different profiles to connect the strings to that midsection at the same time minimizing the cross-section. You will undoubtedly end up with a profile that is very close to the well-known bridge forms in current classical guitars. The length of that middle part will be at least 6 cm and the width (parallel to the longitudinal axis of the guitar) 20 to 30 mm. In the following we will discuss in detail the different aspects you have to deal with.

 

Compensation

First the location and profile of the saddle have to be chosen. Here the question of compensation is important. Because the fretted strings are stretched the pitch of that string will be slightly increased. By moving the saddle a little away from the head you can compensate for that effect. It looks like a minor problem, but it is complicated because this compensation is different for the individual strings and also because the stiffness of the strings asks for an extra compensation. In a thorough study of  Greg Beyers (ref. 7 ) a two fold compensation is recommended:

• Compensation by moving the saddle (contact point) away from the neck, so increasing the length of the string
• Compensation by moving the nut contact point towards the neck, so decreasing the length of the string

For guitars with 0-fret, compensation at the nut must be the same for all strings. In the design of the EB-guitars this compensation is limited to a fixed shortening of 0.5 mm (by which the 0-fret is moved towards the first fret). For the disgn as described on website the saddle point compensation is more important.

From the calculations and measures as given in ref.7  it can be derived that an arrangement of two straight separated saddles is enough to provide the necessary compensation. This saddle arrangement is shown in figure 10.

For the decision on the height of the saddle see the coming two paragraphs.

 

The height of the saddle

The width of the middle part of the bridge of classical guitars varies between 25 and 30 mm. This number is important for the efficiency with which the energy of the strings is passed via the saddle to the soundboard. For a specific string the moment (F_string * hs) should be transferred to waves in the top. With a rigid bridge the energy loss in this process depends on the extent to which this moment conforms to the width of the bridge and the wavelength of the specific pitch in the soundboard. The energy loss during this transport is frequency dependent, but for most of the pitches involved we like to minimize the width of the bridge anyway. The same holds with regards to our wish to minimize the mass of the bridge. From a physical point of view the height of the saddle should be in the same magnitude as the width of the bridge. Increasing the height of the saddle will influence the sound level in different ways. If the height of the saddle is increased from 10 to 20 mm the length of the strings will increase with ~ .25 mm, resulting in a completely negligible change of the sound volume so the most important effect is due to the change in the just called efficiency.

 

 

To get an impression of this effect we took an (old!) classical guitar and measured the sound level at a distance of 1 meter from the bridge as a function of the height of the saddle above the soundboard. Figure 11 shows trend lines to give an impression of this effect for the E-low, D- and E-high strings. The trend of an increasing output for higher saddle heights is obvious (as to be expected) but small. Now, if you increase the saddle height of your own guitar for all strings with several mm you have a good chance the bridge will tear away from the top or the saddle will break away from the bridge. Clearly because the design has strived for an optimum bridge for a given height of the saddle. So the best way to come to a “balanced” decision on the saddle height is to optimize the bridge first (see the  next paragraph ) and then look for a saddle as high as possible within the applicable mechanical constraints.

 

The middle part of the bridge

If you want to optimize the design of the bridge (middle section) the following points should be taken into account:

• The weight of the bridge and therefore the cross section area of the middle part of the bridge has to be minimized
• The height of the saddle has a maximum at the position of the G and D string and a minimum for the high and low E strings (2.5 and 0.5 mm less)
• The stiffness of the bridge has to be much higher than the stiffness of the top, parallel as well as perpendicular to the grain of the top
• The compensation of the saddle as described above, asks for an extra width of the saddle block of ~ 2 mm
• Any slippage of the string over the top of the saddle should be avoided. In that respect we will look for an increased (min. 30°) angle at which the string leaves the saddle top and for an extended contact at the top of the saddle.

The length of the middle part is based on the distance between the strings. For a classical guitar that distance varies between 40 to 45 mm at the 0-fret position and increases to about 57 mm above the bridge. The choice of these numbers has to be based on the playability of the guitar for the future owner. For the EB-guitars these numbers are 44 and 56 mm.

To avoid a weak saddle to bridge connection the total length of the middle section has to be at least 20 mm more (than the distance between the E-strings), so a length of ~ 75 mm is advised. The width of the bridge for the EB-guitars is 15 mm for the saddle block and 10 mm for the tie block, resulting in a total width of 25 mm. The outcome is a relatively high saddle, preferably as high as the strength of the saddle-bridge combination allows.

Figure 12 shows a profile of a bridge as is used in current classical guitars and a second one in which is strived for a minimum cross section within the constraints mentioned above.

The cross section of this middle part is decreased from ~1000 mm² (usual lay out) to ~600 mm² for the optimized cross section.

 

Wings

The pulling force of the strings has to be guided to the guitar body. That is the main reason that a bridge has to have “wings”. If you have some experience in repairing old guitars, you know that a rather usual failure is formed by cracks in the top, just at the end of the wings. The shorter the wings the more risk you run in this aspect. A general rule sometimes mentioned is that the length of the bridge should equal about three times the length of the central part. Three times 7.5 cm makes a total width of 22.5 cm. In order to decrease the possibility on cracks in the top at the end of the wings it is advised to taper the thickness at the end of the wings (last cm) to the same thickness the top has at that place or less.
If you build a guitar with an arched top the bridge has also a function in retaining the desired arch. This can only be achieved when the stiffness of the bridge is clearly larger than the stiffness of the top (perpendicular to the longitudinal axis), which in itself is in contradiction to the desired homogeneous flexibility of the top. Therefore the added mass of the bridge has to be compensated by thinning locally the thickness of the top.

An important starting point in designing a bridge has to do with acoustics. The main function of the bridge is to trig the vibration of the top. Now looking at the main wood resonances (0.1) and (0.2) (see figure 2) it is obvious that a bridge with long wings will hamper these resonances. Applying the 1/4 principle (see the chapter on the sound board ) we would end up with a total length of the bridge of 18 to 19 cm. This looks a little bit short compared with the “usual” 20 cm but it is better from an acoustical point of view and allowable as long as we make sure that gluing the bridge on the top is executed professionally.

Finally some words about the form of the wings. Almost all designs, ancient as well as modern, show symmetric wings, in most cases thin, with a cross-section of 20×3 mm and more or less rounded at the top and at both ends. One clear exception is the so-called Kasha-bridge (see ref 8 and 9 ) that has a much broader wing at the bass side. The reasoning behind this is that the bass strings introduce the lower frequencies, so the longer waves in the soundboard. An argument to the contrary is that measurements shows up to ~500 Hz perfect symmetry of the Chladni patterns (see ref 5 and 9) and moreover that the bridge is stiff enough to transport all low frequency waves practical without loss to the treble side of the top. Experience falls too short to decide upon, but in my view the argument of the Chladni patterns does not hold. It is the symmetry of the soundboard itself that leads to these symmetrical patterns. Also the argument of the stiffness of the bridge is questionable. If the bridge would be 100% stiff and the soundboard almost symmetrical, the broader part of the bridge could be placed on the treble side as well.

In spite of all those arguments having a bridge with a varying width makes sense. The width of the broader part of the wings is more efficient in starting the low wood frequency waves. With an a-symmetrical top (a-symmetrical in thickness and/or sound bar pattern) it is not logical to go for a symmetrical bridge. First because of the role the bridge plays in strengthening the top and secondly because of its function in triggering the whole spectrum of sound waves in the top. To trigger the main wood resonances and keeping the 1/4 principle in mind (see page The soundboard), the width of the wing on the bass side should be between 25 and 40 mm. All experiences in the past indicate that it is not a big deal to vary between these numbers as long as you keep in mind: as light and inflexible a possible.

 

Bridge patch

Parallel with the design of the bridge you have to decide on the use of a bridge patch under the bridge. A bridge patch is a construction bar, glued underneath the top, exactly under the bridge. Sometimes the patch is made a little longer than the bridge itself to prevent crack forming in the top. You may wonder what the advantage is of a bridge combined with a patch, compared with a bridge without such a patch, but with a thickness that is increased to end up with the same strength as the combination. In my opinion there are no advantages at all as long as you taper the end of the wings. And therefore I do not recommend the use of a patch. The bridge itself should do the job.

In figure 13 an example is given of a bridge which is designed according to the principles described and applied in the construction of the EB-guitar series.

Finally, if you like to decorate the soundboard by adding elegant curly wings like those in use in baroque guitars: no objections. But unless these extensions also have a different function as a construction or sound bar they should be thinned (say less than 0.5 mm) in order not to hamper the flexibility of the top.

7 Construction and sound bars

Sound bars have the function of leading the vibration of the bridge to all parts of the soundboard. A second function may be to separate the soundboard in different parts to optimize the response to specific frequencies.

On sound bars there are decisions to be made on profiles and cross sections. It will be clear that the strength of a sound bar and certainly that of a construction bar has to dominate the strength of the plate it has to strengthen. The resistance against bowing of a right-angled bar is given by the formula:

R = 1/12 * w * h³ (see e.g. ref 15 )

In choosing the shape of the cross section for the bars there are several points to consider:

• The bars should be as light as possible, at least those which are connected to the soundboard and the lower part of the back.
• Construction bars should just be stiff enough to fulfill their strengthening function.
• If you want to increase the strength of a bar increasing the height is much more effective than increasing the width.
• In order to avoid twisting of the bar the height/width ratio should be limited (to ~4).
• The maximum pulling forces will be located in the top of the bars. So the cross section should not be decreased towards the top.
• The bars have to be glued on the plate. If you expect (may be during the lifetime of your instrument) unavoidable strong local forces you should aim for a large gluing surface.
• Depending on the expected bowing forces the height of the bar should vary along the length.

Based on these considerations there is playing room for the choice of the cross section, but only within a narrow scope. In figure 14 examples are given of cross sections and profiles based on the aforementioned starting points. For the large cross bars the profile shown in figure 14 and indicated as “flattened pawn” should be aimed at, but of course this profile will gradually flatten at the ends.

In the construction of the EB-guitars all sound bars are based on the flattened pawn contour adjusted to the specific function and location of a sound bar. The sound bars have a width of 3 to 4 mm and a waist of less than 3 mm. The maximum height of these sounds bars is 5 to 5.5 mm, decreasing at the end of the sound bars. An impression of the application of these sound bars is given in figure 15.