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Secrets Of The High Quality Violin Bow

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   Like a violin, the bow came first in a very imperfect form, and has undergone a number of improvements.
  Final improvement of a bow (fig. 1) was made by François Xavier Tourte (1747-1835).
  fig. 1
   Here are improvements of the bow made by Tourte:
  - bending of a stick to inside;
  - spreading of the hair in the form of a ribbon;
  - establishment and standardization of material (Pernambuco tree);
  - use of the metal screw for a hair tension;
  - standardization of the length (74-75 cm) and weight (About 60 grams) of the bow;
  - establishment of the center of gravity for the violin bow at a distance of about 18 cm from the frog;
   The position of the center of gravity was established by smooth thinning of the top part of a bow and weighting of the frog and the tension screw with metal plates.
   By bending of a stick to inside Tourte gave a bow the two essential qualities:
   - retained the same elasticity over its entire length;
   - increased static stability of the bow on the string when playing.
   If the definition of the total weight of the bow and the position of the center of gravity is not difficult, and do not need comments, then the definition of the compliance of curvature of a stick to its changing diameter demands some explanation.
  Correctly executed elasticity loss compensation due to thickening of the stick by the end of its bending is defined as follows:
   Correctly executed compensation of loss of elasticity because of thinning of a stick by the end by means of her bend is defined as follows:
   - Stretch the hair of the bow by the screw to full straightening of a stick;
   - If the stick has taken the straight shape, the bow spring is properly developed (figure 2);
   - If the stick has not taken the straight shape, and its curvature resembles the letter S, then we can see where compliance between the diameter and the curvature is broken (fig. 3 and 4);
   - the sector of the stick, which is aspiring to bend in the opposite direction, is considered to be weak;
   - the sector of the stick, which keeps the bend inside at the general straightened stick, is rigid.
  fig. 2
  fig. 3. The bow with a weak stick in the top half.
   fig. 4. The bow with a weak stick in the lower half.
  Strengthening or weakening of the sectors of the stick is made by both changing of the diameter and character of the bend.
   Various mistakes in making of a stick of a bow arise as at its cutting out with the set curvature at once, and when bending a stick after its cutting out in a straight form. The question of whether to bend a straight stick or to cut with the predetermined curvature is solved unambiguously: the stick should be cut out along the wood fibers. Therefore with straight-grained wood we have to bend a straight stick, and in the presence of the fiber bends, repeating (at least approximately) the profile of the future bow, it is possible to cut the stick at once with a predetermined curvature.
   One of the most important moments in the making of a bow is the correct distribution of thickness along the stick. If you have not a good bow for copying, it is possible to take the Jean-Baptiste Vuillaume's advice. He determined the average length of a bow to a head = 700 mm.
  fig. 5. Reconstruction of the drawing of Jean-Baptiste Vuillaume.
  AB = 700 mm
  AC = 110 mm
  DB = 22 mm
   Implementation of such a drawing requires special accuracy. To avoid mistakes I have solved this geometrical task to operate with precise numbers, but not approximate drawing constructions. Calculations show that adjacent segments are in the ratio 7/8:
  AE = 110 mm
   EG = 96,25 mm
   GI = 84,22 mm
   IK = 73,7 mm
   КМ = 64,5 mm
   МО = 56,42 mm
   OQ = 49,37 mm
   QS = 43,2 mm
   SU = 37,8 mm
   UW = 33,1 mm
   WY = 28,9 mm
   YB = 25,3 mm
   BD = 22,14 mm
   Besides, if we take the starting segment = 110 mm, the total length of the bow is not that of 700 mm, but 702.76 mm, which corresponds to the accepted standards of the modern bow. Placement of thickness of a violin bow is as follows:
  А - 8,6 мм;
  Е - 8,6 мм;
  G - 8,3 мм;
  I - 8,0 мм;
  K - 7,7 мм;
  М - 7,4 мм;
  О - 7,1 мм;
  Q - 6,8 мм;
  S - 6,5 мм;
  U - 6,2 мм;
  W - 5,9 мм;
  Y - 5,6 мм;
  В - 5,3 мм.
  On the basis of these data we can draw also a curve of a stick (fig. 6).
  fig. 6
  On the y-axis is 12 points, using the dimensions above and transferring a comma one character to the left:
  11,0 mm
   9,625 mm
   8,422 mm
  7,37 mm
   6,45 mm
  5,642 mm
  4,937 mm
   4,32 mm
  3,78 mm
   3,31 mm
  2,89 mm
  2,53 mm
  2,214 mm
   The sum of all segments will be equal to 70,3 mm, that is ten times less than the length of the stick to the head.
   On the horizontal axis we represents the 12 segments on 53 mm, which sum is equal to 636 mm that is length of a projection of the curved part of a bow from a frog to a head.
   1 - 53 mm
   2 - 106 mm
   3 - 159 mm
   4 - 212 mm
   5 - 265 mm
   6 - 318 mm
   7 - 371 mm
   8 - 424 mm
   9 - 477 mm
   10 - 530 mm
   11 - 583 mm
   12 - 636 mm
   The difficulty in making of the bow is in the correct development of deflection of a stick, which precisely would offset loss of elasticity at its thinning. When bending a stick it is necessary to consider not only settlement change of diameter, but also an anisotropism of the wood which is defined also by distribution of density in the mass of wood and the direction of fibers. Below I will show three ways to make the right deflection of the stick.
  The way of controlling of the correct development of the deflection is shown in Fig. 2.
  The first way.
  This method requires the use of wood with straight fibers. The stick must be sawed exactly along the fiber.
  After careful finishing of a stick with the correct distribution of thickness we start its bending. With any method of bending (e.g., holding a stick in hands over a fire) all possible errors can be gradually eliminated by using the known method of the control. But this way is long and irrational. To install the proper bending for this stick at one time, it is possible to use the special holder-lever. Figure 7 shows a method of mounting these levers to the stick.
  Fig. 7
   The distance between the levers corresponds to the length of the hair and, therefore, the bend starts from the place where the frog is attached. The upper ends of the levers are pulled together by a flexible wire to give the stick the desired bend.The distance between the edge of the circular hole and the lower end of the right lever should match the height of the frog. With this method of bending a stick even slight variations in its elasticity, due to the anisotropy of wood, compensated by a corresponding change in the bending line of the bow. If you pull the wire at the dotted line, it is possible to control the correctness of the bending of the bow similar to the method shown in Fig.2.
  The second way.
   In those rare cases, when the nature of the bending of the fibers of the wood almost coincides with the right arrow stick deflection, it can be cutted out at once with a predetermined curvature. The distribution of the thickness of the bow is made in the second turn.
  The third way.
   If the fibers of wood are slightly curved in the direction of the deflection of the bow, the stick (cutted out along the fibers) is bending by the first method, and the control is carried out more often.
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