BRIDGES

Bridges of string instruments, especially the baroque ones, are the best place to start looking at an instrument to see why and how it produces sounds the way it does. The baroque models are designed to let the waves created by the vibration of the strings reach the front of the instrument by the shortest way, while modern bridges do quite the opposite. By looking at the different models while bearing in mind how mechanical waves propagate, you can get a pretty good idea of what happens in each different type of bridge. A close examination shows how intelligent those baroque-era designs are, and how each different kind of instrument had a differently designed bridge.
I need to say that to fully understand the shape of a bridge, the importance of a bridge’s design, you need to play the instrument well enough to be able to feel under your bow the differences between one shape of bridge and another, or you need to have people who do play that well to tell you what they feel. Let's start!

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These are the Stradivari bridge models that I could find. Four for cello, three for viola and two for violin.

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In this model for cello I've done some markings. The red point represents one of the inner strings, say D, the second. The rings represent the waves coming from the string, propagating in all directions, as long as no surfaces are encountered: they are the addition of all the waves' trajectories in all directions. Then I have drawn in colors a few of those waves. You can see how those waves will rebound when encountering the surfaces of the bridge: wood to air all around it. The light blue one will reach the ground of the right foot in a direct, undisturbed straight line.

Though I didn't draw them in, notice that there is room for quite a few more waves reaching all the way to the base of the feet. Also notice that the base of the feet are solid-to-solid surfaces (wood to wood), surfaces that most of the incoming waves will cross due to the similar densities that form those surfaces. That's why it is indeed so important that the feet of the bridge perfectly fit the front blade. Otherwise, the surface wood-to-wood becomes smaller, and fewer waves get into the instrument.

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As opposed to the baroque bridge, where lots of the waves coming from the inner strings reach the base of the feet directly, in this modern violin bridge you won't find a single one that directly reaches the feet of the bridge. The holes, especially the heart, actually get in the way of the waves to the feet. In baroque bridges the heart helps waves reach the feet, while in modern bridges the heart hinders them. That's why I think of modern bridges as closed and baroque bridges as open.

Sometimes the holes in a modern bridge just happen to be high enough to allow some waves from the outer strings to reach directly the feet. However, then the chances are that the first string will sound too bright.

See how different the feet of the modern and the baroque bridges are: thick with wide ankles (open) are the baroque ones. Thin with narrow ankles (closed) are modern feet. While it is true that cello and double bass bridges have wide legs, the direct way to the feet remains closed.

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We have already seen that the heart of the modern bridge is in the way of the waves from the top to the feet, while the hole/heart of the baroque one makes the way for them.
If you take a baroque bridge with a hole, and you turn the hole into a heart, the instrument will sound louder, a bit darker and fore sure more robust. Without going too far, the bigger the heart becomes, the louder the instrument sounds. If you go too far, you will find not much difference between a really very big and a far too big heart.

In the next picture you can see how the same waves will rebound differently on a hole than on a heart. This explains the differences in the sound they produce. You can also see the path of a wave colored in green which has entered one arm. See how the wave in the straight-ending arm rebounds immediately back while the one in the arm with fingers stays there a bit longer.

Take another look at the Stradivari bridge models above. Only the bridges for viola and one of the models for cello have straight-ending arms, while the other models for cello and the models for violin have arms ending with fingers. Arms with fingers ask for heavier bowing; flat straight arms produce a clearer articulation with lighter bowing. Violas are heavier to play and articulate less easily than violins. That's why it makes sense to me to use bridges with straight-ending arms for the violas and bridges with fingered arms for the violins.

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This is a design for a bridge of a five-string double bass:

It has straight-ending arms, because double basses need all the help they can get to sound clear. The portion of waves going most directly to the base of the feet of the bridge have been drawn in colors. Blue indicates waves coming from the outer strings. These waves do not reach the base of the feet directly, but reach it by getting reflected on the outside end of the legs, actually the projection of the width of the harmonic bar. Its English name, "Bass bar", now seems inadequate to me, since I see that the frequencies reaching it in the most direct way are the trebles rather than the basses. In fact, these last frequencies reach the sound post most directly.

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The profile of the bridge, meaning the shape of the bridge seen from the side, is also very important. I prefer bridges with a profile in wedge form, with straight back and front. Opening straight lines are indeed very good to send waves down to the feet of the bridge.
Some bridges are made with a belly: the front is curved at the upper part and at a certain point it becomes parallel to the back. This makes a convex surface for us but this surface is concave for the waves, which makes them take a much longer path in their way to the feet. As a result, the articulation is not very clear, and it requires pretty much weight from the right hand, which makes the instrument hard to play. When I asked about the reason for making a bridge with such profile, I was told that this makes the bridge last longer. For me this is a pity...

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Here are the two real baroque bridges I have seen compared to their model. Both of them are made of flamed maple. These bridges have suffered quite a lot in their life, but you do not need to look very closely to see that they are pretty much what they are supposed to be according to the models. The first one is to be seen in the book The 'Secrets' of Stradivari by S. F. Sacconi, Libreria del Covegno, 1979.

The second one, decorated, is the bridge of the Tuscan tenore. I went to the Musical Instruments Museum at the Accademia Gallery in Florence to see that instrument and its bridge. The profile of that bridge was indeed in wedge form, opening in an angle of about 5,5 degrees. After all those years this brigde is now completely bent.

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The next bridge is the bridge I have on my baroque viola. It works really very well.

Even too well: it responds so well that actually my arm and my bow are far too heavy for it. I once played a modern cello mounted with a bridge in this manner with a very light early baroque violin bow. Despite the fact that a cello is not supposed to be played with a very light violin bow, it did feel very well in balance. That is so because modern and "baroque" instruments after the 19th century do not have blades with a thick middle part anymore.

Baroque instruments did have such thick blades before being transformed, which brings in balance the response of the instrument with the weight of the bow and the arm of the player. The intensity of the waves that these bridges bring to the instrument are somewhat too much for the thin blades of the modern instrument. In the section about Jakob Stainer I tell about those thick blades of the ancient instruments.

Jakob Stainer

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This bridge is between the modern and the baroque ones. It has no heart, and therefore it is much more open than modern bridges: both E and G have waves reaching the feet, however A and D don't. Thi bridge has a little hole under the absent heart. As I see it, it breaks the flat surface under it, where most of the waves would rebound back. It is also placed low enough to not hinder waves coming from the armpits from reaching the feet. I has the feet of a modern bridge, and it is made of flamed maple. This sort of wood used to be used instead of stripped maple, which has no flames. Flamed maple produces a darker sound, allowing the bridge to be of a regular thickness without sounding too bright. Open bridges made of stripped maple tend to sound quite bright.

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