6 The bridge
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 same argument holds for the saddle. Materials most in use are ivory, bone or ebony. But you can take any hard material e.g. horn, mother-of-pearl, glass etc. As long as the saddle can be immovably fixed to the bridge, the choice is open and again mostly based on aesthetic arguments.
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 kinds of different profiles to connect the strings to that mid-section 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.
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 twofold 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 total length of the string, but increasing the relative length of the fretted string.
For guitars with a 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).
From the calculations and measurements 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 image Saddle arrangement.
In this figure the distance between the 0-fret and the front of the bridge is taken as 647 mm. The numbers on the left side give the distance to the front of the bridge. In the design of the EB-guitars the scale length is 648 mm and the compensated scale lengths are: 650.0, 648.8, 648.5, 649.7, 648.9 and 648.5 mm for the strings E-low to E-high.
For the decision on the height of the saddle see the following two paragraphs.
Image: Saddle arrangement
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 (Fstring * 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 I 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. The image Sound level as a function of the height of the saddle 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 e.g 10 to 20 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.
Image: Sound level as a function of the height of the saddle
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 small bridge with a high saddle, preferably as high as the strength of the saddle-bridge combination allows.
The image below 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.
Image: Cross sections of the middle part of the bridge
The cross section of this middle part is decreased from ~1000 mm2 (usual layout) to ~600 mm2 for the optimized cross section.
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. In practice most classical guitars have a total length of 18.5 - 19.0 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 mass added by 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 (1.0) and (2.0) (see Primary modes of the guitar top) it is obvious that a bridge with long wings will hamper these resonances. Applying the 1/4 principle (see chapter The soundboard) on the tripole (2.0) we would end up with a total length of the bridge of ~18 cm. This looks a little bit short compared to the "usual" 19 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 30 x 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 chapter 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.
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.
The image below shows an example of a bridge which is designed according to the principles described and applied in the construction of the EB-guitar series.
Image: Bridge of the EB-guitars
As you can see, the ends of the wings are not massive but partly open. This results in a effective length of the bridge of ~ 16 cm.
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.