Bow

• The mass of the bow determines its dynamic qualities when playing the instrument. It is necessary to take into account the ratio of the weight of the bow to the responsiveness of the instrument, the stiffness of the strings and other points. So, the responsiveness of the violin is much more than viola , and viola - than cello , cello - than double bass. The mass and stiffness of the bow for the cello is much larger than the violin, due to the slightly smaller size and significantly larger thickness of the shaft.
• The position of the center of gravity of the bow and its own mass affect the speed of rotation of the bow when moving from one string to another. When approaching the center of gravity of the bow to the block (and to the hand) to reduce the moment of inertia (sensation of a lighter bow weight), we must not forget about the influence of the mass of the bow on the convenience of extracting uniform sound in any part of it. This remark is more relevant for bows with a lightened end, when for a full sound in the upper part of the bow you will need excessive pressure from the right hand.
• The correctness of the ratio of the bend and the thickness of the shaft is determined by pulling the hair; in the bow, it should take a straight form, without waves and bends.
• The stiffness and uniformity of the shaft is determined by hitting the convex part on the palm edge when taking it at a certain distance from the bow block. For a 4/4 violin, the bow is taken at 15 cm and emits a note of fa (43-44Hz) for at least 1 second.

Adjustable parameters include:

• The elasticity of the hair depends on its tension, mass, uniformity of styling during the installation of the bow and the elasticity of the bow cane itself.
  • The tension of the hair in the bow is regulated by turning the screw in the bow block by the violinist;
  • The weight (quantity and type) and uniformity of hair styling is regulated by the master, depending on the stiffness of the bow;
  • The elasticity of the cane is regulated by the replacement thereof.
• The stiffness of the bow (the amount of hair that it is not designed for is inserted into the bow):
  • If the stiffness is less than required, then the fracture of the hair at the point of contact with the string forms an angle greater than required, which leads to grazing when playing adjacent strings. An increase in hair tension leads to a bend to the other side of the bow. For correction, it is necessary to reduce the amount of hair in the bow.
  • If the stiffness is greater than required, then when playing, there is a practically absent angle of inflection of the hair at the point of contact with the string, which noticeably affects the quality of sound extraction, especially when playing the piano . For correction, it is necessary to increase the amount of hair in the bow. ^[3]

Treble bow

It has sizes: 1/16, 1/8, 1/4, 1/2, 3/4, 4/4

• 4/4 - 55-65 g., Length about 730 mm, center of gravity ~ 18 cm from the block.

Viola Bow

• 4/4 - 68-74 g., The length and center of gravity are the same as in the violin bow.

Cello Bow

Sizes: 1/8, 1/4, 1/2, 3/4, 4/4

• 4/4 - 78-88 g.

Bass Bow

It has dimensions: 3/4 and 4/4 and is distinguished by two types:

• French system
• German system
• 4/4 - 130-170 g.

The complete bow theory was developed by the French mathematician Duhamel .

The location of the bow on the string, its pressure and speed

The point of contact of the string with the hair of the bow is called the game point . Depending on the speed of movement, pressure force and the playing point on the string determines the nature of the sound: volume and timbre . The table shows the main dependencies ^[3] :

Designations in the table:

• The first column indicates the strength of the sound ( pianissimo , piano , mezzo-piano , mezzo-forte , fort , fortissimo , fort-fortissimo ).
• In the first line, the numbers of game points, if we mark the string into 14 equal parts, from the 1st, which corresponds to the closest point to the stand, to 13th, the farthest, located at the top of the nut with the string open, or at the finger when it is clamped.
• The second row shows the ratios v and p , which mean the ratios of the bow speed and its pressure on the string, respectively. The ratios depicted in black correspond to the highest quality sound, and gray correspond to sound with a completely or partially lost tone quality; sul ponticello (for the left side of the table) or sul tasto (for the right side of the table) is indicated in the musical notation. The parameters v and p are presented according to a 7-point system, as follows:
  • p = 1 and p = 7 correspond to the minimum and maximum pressure at which the musician can produce a steady sound;
  • v = 1 and v = 7 corresponds to the minimum and maximum speed at which the musician can maintain constant pressure and speed.
• The second column shows the pressure according to the seven-point system at which the corresponding sound power is obtained.
• The cells filled with numbers indicate at such a game point at which pressure and speed high-quality sound is produced.
• The last line indicates the possible timbre characteristics proposed by C. Flash ^{[to clarify ]} . This is due to the fact that the timbre changes depending on the location of the game point:
  • The closer to the center of the string (game point No. 7, highlighted in gray), the more energy is transferred to the main tone (higher harmonics), and the less energy is given to overtones (1st and higher harmonics);
  • The farther from the tool stand, the greater the resonant frequency of the instrument at a given point. This is due to the fact that the neck , tapering, increases the frequency of natural free vibrations that can resonate with forced vibrations of the string.

Using strings

In the above table, the values ​​are relative, and you need to make corrections depending on:

• string stiffness
• string thickness
• playing space strings.

String stiffness

Harder string

• It makes it possible to extract harmonious notes farther from the stand , as it provides sufficient resistance to the bow and does not constrain to hoarseness and creak.
• Reduces the ability to extract gentle and quiet sounds, contribute to the disruption of sound production, which limits the artist’s artistic palette.

Bow Tilt

Tilt the bow towards the neck for:

• Changes in the width of the hair ribbon, which contributes to the manifestation of higher harmonics; It is most often used when playing closer to the fretboard on the nuance of the piano or when playing flageolets .
• Adjusting the direction of the spring force of the cane of the bow, which is necessary for various articulation effects, for example: mitigating the attack of sound, reducing the jumping ability of the bow, etc.

Two cases are possible:

• If the plane of the bow spring is perpendicular to the plane of the string, then the elastic properties of the bow are used to the maximum extent (sin (90) = 100%). The direction of arm strength is always perpendicular. Hence the geometric effect of the elastic qualities of the bow relative to the pressure on the string of the hand is Sin (bow ^ strings) / Sin (hands ^ strings) = Sin (90) / Sin (90) = 100% / 100% = 100%.
• When the bow is tilted to the bar, these two planes make up an acute angle between themselves, then the sine of this angle is less than 100%. Then the elastic qualities of the bow are realized to a lesser extent with constant pressure on the string by hand. This balances the tension in the string on either side of the bow (used when playing in the fort).

• The price of unique bows can reach several hundred thousand US dollars .

• Secrets of a high quality bow. Sergey Muratov. Musicians about classical music and jazz. Jazz and classics.
• Bow and articulation. Muratov Sergey Vitalievich.

• Violin
• Passport on a bow