Chapter 6

Distribution of Strength

The bow that shoots arrows and the bow that plays stringed instruments have something in common. The former is also tightened so that it can be used for hunting. When the wild boar breaks out from the thicket, the string is pulled and and an arrow is shot. But when the hunter tightens his bow too much and it breaks, he has a serious problem. All he can do is climb up a tree. When the violin bow is pulled too tight and breaks during a councert it's also pretty bad, and no trees around.

The moment of shooting an arrow corresponds more or less to playing a stringed instrument in a concert, even if the audience facing the player is less dangerous. The comparison could be taken still further, but I will limit myself for the moment to the problem of the breaking point. The tension and force that a bow sustains cannot be greater than the tolerance at the weakest point (for familiar reasons).

Normally, the head is the weakest point. The grain of the wood runs along, or more accurately, through the stick and on to the head. But it is unattached to the lower part of the head.

Therefore, the midpoint of the head is usually the weakest point. The extent of the danger has to do in part with the position of the annual rings (see the chapter on wood), but also the form of the head. A robust stick requires a larger head. A soft stick will tolerate a finer head, because less force is brought to bear on the vulnerable point. If the risk of a break were all that is involved, the head would be as low as possible. In baroque bows, this is actually the case. But over the course of time, bows have been built to produce a bigger sound with as much tension and camber as possible. The vibration of the hair increases the tension on the head. The more pressure the player exerts, the greater the tension.

The higher the lower part "b" in relation to the upper part "a," the greater the leverage. The greater the leverage, the more powerfully the vibrations are transferred to the stick. The height of the head therefore has a major effect on the movement of the stick. Moving a more robust stick requires a more powerful "input." There is otherwise too little amplifier for a too large loudspeaker.

Two conflicting criteria must therefore be considered for the function of the head. One is the risk of breakage, that can be met by lowering the head. On the other hand, a higher head transmits vibrations much better. This makes the bow more sensitive, even when it is powerfully built.

The strength of a bow is impossible to express in numbers. Usually a player says that a bow is powerful if the stick remains above the string even when playing forte. But a more flexible bow can also give the sense of power if other relationships are right. The first important point is that the strength of the bow must be equally distributed across its length. Lateral stability is equally important. A powerful bow that bends laterally is more likely to overplay than a softer bow with lateral stability. To analyze a bow, these characteristics have to be considered.

When a bow is loosened, the strength of the stick in vertical direction can be measured by resting the bow on its ends, and hanging a 250-gram weight from the middle. A violin bow will gave way by about one and a half to two centimeters, a cello bow by half of that. Many bowmakers use such a device. Anything measurable seems to us nicely objective, but the objectivity should not be overestimated. No one plays with a loosened bow.

As soon as the bow is tightened, its strength become a function of the stick's elasticity, the thickness of the wood and the camber. The match between wood strength and camber can be tested by tightening the bow until the stick is straight. But please don't do it yourself! Even if the bow is well-insured, the test is best left to the bowmaker. If the stick is really straight, camber and wood strength are properly matched.

There are various possibilities for distributing the camber and the thickness of the wood along the stick. The bows of the last century (19th) mostly have the most curve in the middle of the bow, but in the course of time, this point has shifted towards the tip. My own impression is that bows with little wood and a lot of camber at the tip respond well, but sound somewhat thin. More camber in the middle produces a fuller sound, although the response is not as accurate. But these are general tendencies, because a bow's sound and response depend on many factors. Any concept can work well if the relationship of the camber to the quality and conformation of the wood is right. When this is not the case, the player has the feeling of losing contact with the string at a certain point.

Even when the camber and the quality of the wood are properly coordinated, what matters is how much bend there is in the bow. When the loosened bow touches the hair, this is called a full camber. The opposite state consists, for example, in a five-millimeter separation between the hair and the stick. The appropriate camber can vary from bow to bow. Too much will make the bow nervous, make it scratch, and cause it to thrust out to the side. Too little makes the bow lame, and causes an irregular bounce, although it can also make the tone nice and round. A full camber is especially good for the bounce, while less camber relaxes the sound and increases the bow's lateral stability.

If the bow has too much strength in the vertical direction, it gives way laterally, with a loss of energy. The same bow with less camber will be more stable, and therefore more powerful. How much camber is right for any given bow depends on the material, the player's taste, and the instrument. Bows where all conditions match one hundred percent are rare, but most players are so accustomed to their bows' "moods" that they compensate automatically by adjusting their technique to the bow. But occasionally the bowmaker can achieve a mini-miracle with a slight change in the camber. Sometimes remarkably little is needed to restore a bow's equilibrium, and it then sounds and works much better.

In the transfer of strength from the hair to the stick, the tip naturally is not the only important thing, the frog is just as important. In principle, the same considerations apply as to the tip, only the region of the frog is somewhat more complicated.

If the bow is tensed, then the frog sits securely on the stick. The only movement it still has to make is a slight turning towards the stick (or revolving in the direction of the hair, or around the brass nut). Even the smallest pressure given the bow by the musician while playing works itself out in this small turning movement.

A particularly tall frog creates greater leverage, and in this way, the situation is exactly the same as for the tip. But with the frog, the strength works itself out from the turning movement at the near end of its base. So the distance from the brass nut, which holds the frog firmly in place, to the near end of the base, also has a part to play. This length is also a lever, only the opposite way.

A long base lessens the strength of the leverage. A tall frog with a short base, therefore, makes for the strongest transference of the vibrations of the hair on to the stick.

How strong this transference should be, depends upon the opposing strength of the stick at this point. The opposing strength given by the stick depends again on the thickness of the wood and the curve in the region of the frog. A bow that is thinner at the end than in the middle is best matched to a low frog with a long foot. A bow whose thickest point, with much curve at the frog, needs a fairly high frog with a short foot. But very high frogs have another disadvantage, which is that they lose lateral stability.

Many of the old French bowmakers made the middle track on the underslide beneath the frog broader than the lateral tracks. The reason must be that the player's middle and ring fingers rest on the frog, and thereby exercise some lateral pressure. In addition, the bow seldom lies flat on the string, but is tipped a bit. This increases the lateral pressure on violins and violas, which tilt to the right. But in the case of cellos and basses, which tilt to the left, the pressure of the fingers on the bow and the pressure arising from the tilted bow cancel one another out.

The broader the middle track of the underslide, the more resistent is the frog to lateral pressure. But there is a bit of leverage here too. The breadth of the middle track of the underslide should therefore increase with the height of the frog.

Every detail and measurement of the bow is functionally related to every other detail. The smallest change affects the whole bow. Therefore, no two bows are exactly identical, irrespective of differences in the quality of the wood, and this is the basis of every concept.

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