JP2009053174A - Bow vibration measuring device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To grasp the basic performance of hair tension and ease of handling in a bow for a bowed string instrument with a quantitative numerical proof instead of a sensational judgment. <P>SOLUTION: While the hair of the bow of the bowed string instrument has been tensioned, the metal ring section of a frog is placed on a support that becomes the rotation center of the bow. While the hair of the bow is being placed on the other support, the rotational movement of the bow by the interaction between the elasticity of a rod-like member tensioning the hair and the mass of the bow is excited, thus allowing the bow to be subjected to pendulum vibration. By measuring the frequency of the pendulum at this time, the quality of the essential performance of the bow determined by the elastic strength of the stick of the bow, the tension of the hair, and the like can be grasped. Therefore, a performer can select a bow having appropriate performance with a numeric proof instead of a sensational judgment based on experience as before, and the manufacturer and seller of the bow can display appropriate performance of the bow. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

The invention according to the present application relates to a bow used to play a bowed instrument such as a violin or cello.

Increasing number of lovers enjoy music by playing their own musical instruments because of their leisure time. For such enthusiasts, it is desirable that even beginners who have acquired a musical instrument for the first time or training with a few exercises should be able to perform full-fledged performance with musical expressive power and rich musicality. It is even more important to be able to perform with a higher level of expression if further training is performed.

There are bowed instruments such as violins and cellos as instruments used by such enthusiasts. Such a stringed instrument is usually a string of four strings on the body of the instrument, with the stringed stick pressed against a stick made of wood or a resin material containing carbon fiber fibers with the tensioned hair pressed against the string. Is performed by vibrating.

In order to vibrate the strings, it is essential that the hair has sufficient tension. However, depending on the strength of the wood or carbon fiber fiber-containing resin material used for the stick-shaped stick, it may not be possible to ensure sufficient hair tension necessary for performance, and satisfactory performance may not be achieved.

A conventional bow structure and a method of applying tension to hair will be described with reference to FIG. The bow structure shown in this figure is the same for bowed instruments such as modern violins and cellos.

FIG. 1- (a) shows a state before the hair of the bow is stretched. A head 2 extending perpendicularly to the longitudinal direction of the stick 1 is formed at the tip of the stick 1 and one end of the bristles 3 is fixed. An adjuster 4 for adjusting the tension of the hair 3 is disposed at the other end of the stick 1, and the frog 5 to which the other end of the hair 3 is fixed can be moved by turning the adjuster 4.

FIG. 1B shows the internal structure of the adjuster 4. The adjuster 4 is inserted into a screw hole 6 formed in the stick 1 and is provided with a screw 7 that is partially configured as a male screw. On the other hand, an eyelet 8 with a female screw hole is attached to the frog 5 and is inserted into a groove 9 provided in the stick 1. The male screw of the screw 7 of the ajanta 4 is fitted in the female screw hole of the eyelet 8. When the adjuster 4 is rotated in this state, the frog 5 moves back and forth in the longitudinal direction of the stick 1.

FIG. 1- (c) shows a state where the hair of the bow is stretched. When the adjuster 4 is rotated in a direction in which the frog 5 moves away from the head 2, the hair 3 is pulled. At this time, the stick 1 is bent and tension is generated in the bow hair 3 according to the degree. The situation is as follows.

FIG. 2- (a) shows a state before the hair of the bow is stretched. The bow stick 1 is warped in advance so that when the adjuster 4 is rotated in a state where the tension of the bow hair 3 is almost zero, the distance between the center of the bow and the hair 3 is minimized. The distance between the stick 1 and the hair 3 at the center of the bow at this time is defined as d1.

FIG. 2- (b) shows a state in which the bow hair is stretched. By rotating the adjuster 4 and pulling the hair 3, the stick 1 is bent, and the distance between the stick 1 and the hair 3 is increased to d2. In this state, the center portion of the stick is bent by a dimension of dt = (d2−d1). Such bending is hereinafter referred to as “deflection”. According to the document ELEMENTS of STRENGTH of MATERIALS by Timoshenko, a formula for calculating the deflection of a rod-shaped member when a bending moment acts on both ends of the rod-shaped member is described. This formula is shown in Fig. 2- (c). When the bending moment acting on both ends of the rod-shaped member is M, the longitudinal elastic modulus of the material is E, and the cross-sectional secondary moment of the rod-shaped member is I, the deflection d at the center of the rod-shaped member is shown in FIG. It can be calculated by the calculation formula.

When this formula is applied to the calculation of the tension of the bow hair 3, the tension of the hair can be calculated. In the case of a bow, the height of the head 2 and the height of the frog 5 are substantially equal, and the value is h. The thickness of the stick 5 is usually thin near the head 2 and the frog 5 is thick. However, in the state where the bow hair 3 is stretched, the central part of the bow is bent most greatly, so that the thickness of the cross section for calculating the secondary moment I of the cross section of the stick 1 when calculating the tension is the thickness of the central part of the bow. You may approximate. Therefore, let the moment of inertia of the cross section of the stick 1 be I. The length of the stick 1 is the length l on which the hair 3 is stretched. When the tension of the hair 3 is Th, the hair tension Th when the central portion of the stick is bent by dt = (d2−d1) can be calculated by the calculation formula shown in FIG.

That is, it can be seen that the hair tension Th is a value that can be calculated by the formula Th = 8 × E × I (d2−d1) / (h × l × l). Here, α = 8 × E × I / (h × l × l) is defined and named as a stick coefficient α. What is important when playing a bowed instrument such as a violin or cello is that the hair tension Th must be sufficiently secured. The magnitude of the hair tension varies depending on the value of the longitudinal elastic modulus E that determines the bending strength of the material. If the material used for the bow has a small value of the longitudinal elastic modulus E, the hair 3 and the stick 1 at the center of the stick when the hair 3 is stretched to secure a predetermined hair tension. It is necessary to increase the dimension of the distance d2 and increase the deflection of the stick 1.

When playing a stringed instrument such as a violin or cello, the performer performs the performance by rubbing the string while holding the stick 1 of the frog 5 with the right hand and pressing the hair 3 against the string to apply pressure. At this time, if the dimension of d2 which is the distance between the bristles 3 at the center of the stick and the stick 1 is large, the force of the stick 1 does not act perpendicularly to the bristles 3 and the stick 1 swings sideways, making it difficult to play extremely. turn into.

In order to prevent this phenomenon, wood or carbon fiber fiber-containing resin material having a large longitudinal elastic modulus E is used for the material of the bow stick 1 for playing a bowed instrument such as a violin or cello. In the case of wood, Fernanbuco wood having a value of the longitudinal elastic modulus E that is about twice that of normally hard materials such as “zelkova” and “oak” is used. However, in materials such as wood, there are large variations in the characteristic values of the materials, so the numerical values are not constant. Incidentally, the value of the longitudinal elastic modulus E of the Fernanbuco material is a value around 3,000 (Kg / mm × mm).

When the player chooses a bow, for example, there is no way of knowing how much the already-made bow is made of a material having a value of the longitudinal elastic modulus E, and the stick 1 is bent by hand or the frog 5 One of the difficulties is that there is no other way to judge it sensuously by holding the part and shaking the entire bow.

There is another problem due to the value of the longitudinal elastic modulus E of the bow material. Next, the phenomenon and problems are described.
FIG. 3A shows the posture of the bow in the playing state. The performer supports the bow with the right hand 11 and hits the hair 3 against the string 12. The thumb 13 of the right hand 12 is at the tip of the frog 5 and the index finger 14 is placed several centimeters ahead of it. The hair 3 applies pressure to the index finger 14 by applying the load P to the index finger 14 with the position of the thumb 12 as a fulcrum, and the string is vibrated to perform the performance by rubbing the string in this state.

When the length of the bow hair 3 is l, the distance to the position where the index finger 14 is placed is 12, and the position where the hair 3 hits the string 12 is the position x · l from the tip, the index finger 14 sticks. The following relationship is born between the load P for pressing 1 and the hair load Ph for pushing the hair 3 by the string 12. Here, x is a coefficient from the tip indicating the position where the string 12 hits against the length of the bow.
Ph = (P × l2) / (l × (1-x))

In this state, a moment of (P × 12) is applied to the stick 1, thereby causing the stick 1 itself to bend. According to the document ELEMENTS of STRENGTH of MATERIALS by Timoshenko, there is a formula for calculating the central deflection dp of a rod-shaped member when a moment is applied to a specific position of the supported rod-shaped member. This formula is shown in FIG. In this state, since the stick 1 is considered to have increased by dp in the center compared to the state in which the hair is initially stretched, the hair tension Th increases. Assuming that the increased hair tension at this time is Tp, the value can be obtained by the following equation.
Tp = Th + α × dp = α (d2−d1) + α × dp

When a load P is applied to the stick 1 with the hair 3 applied to the string 12, the hair 3 is bent and the bow is rotated as shown in FIG. The balance of the moment maintaining the bow posture in this state is that the moment applied at the load P and the distance l2 to the load point, the force of the upward vector component of the increased hair tension Tp, and the hair 3 are the string 12 The moment multiplied by l (1-x), which is the distance to the position, is balanced. Considering the case where the value of the moment applied at the load P and the distance l2 to the load point is Mp and the rotation angle θ of the bow is small, the relationship between the moment and the rotation angle θ as shown in FIG. .
Mp = k (x) · θ
However, k (x) = Tp · l · (1-x) / x
Here, k (x) is defined as a “pendulum spring constant”. k (x) indicates a different value depending on the value of the position (x) where the hair 3 hits the string 12.

On the other hand, since the bow is heavy, there is a certain amount of moment of inertia Ib when the position of the thumb 13 of the right hand 11 is considered as the center of rotation. Therefore, in a state where the bow hair 3 is pressed against the string 12, a rotational vibration system is generated by the inertial moment Ib determined from the elasticity of the hair tension Tp and the weight of the bow.

This bow vibration system is both an advantage and a disadvantage when playing. By making good use of the elasticity of the bow due to the hair tension Tp, the hair 3 applied to the string 12 can be quickly separated from the string 12. In other words, when the hair 3 is applied to the string 12 for a very short time and the bounce 3 is used to release the hair 3 to release the string 12, and the “Spiccato” technique, that is, a technique of repeating the action, is performed continuously. Will take advantage of the rotational vibration system of the bow.

Conversely, when the rotational vibration system of the bow is disadvantageous, when the hair 3 is rubbed quickly on the string 12, the bow may vibrate in the middle and the sound may be shaken. This phenomenon is likely to occur especially when the performer is a beginner who is unfamiliar with the performance. In addition, the bow 12 may vibrate just by applying the bow hair 3 to the string 12, which may hinder the performance.

FIG. 4 shows the relationship of the natural frequency of the rotational vibration system of the bow. Here, the vibration generated from the rotational vibration system of the bow is named “bow pendulum vibration”. The natural frequency fo of the “pendulum vibration of the bow” was derived from the value of the frequency ratio C determined by the values of the hair tension Tp, the moment of inertia Ib, and the position (x) where the hair 3 hits the string 12. Here, C = 1.73 when x = 0.25, C = 1 when x = 0.5, C = 0.58 when x = 0.75, and the bow hair 3 hits the string 12 It is induced that the natural frequency fo of the “bow pendulum vibration” becomes higher as the position goes beyond the bow.

In the case of a bow whose natural frequency of “bow pendulum vibration” is low, there is a problem that it is difficult to perform extremely like the “spiccato performance” described above. This is mainly because the hair tension Tp that determines the natural frequency is small and it is difficult to use the elasticity of the bow. That is, this phenomenon is also made of a material having a small value of the longitudinal elastic modulus E necessary for securing the hair tension Tp. When the hair 3 is quickly rubbed on the string 12, the problem that the bow vibrates in the middle and the sound oscillates also tends to occur in a bow having a low natural frequency of “bow pendulum vibration”.

Thus, how much the bow is made of a material having a longitudinal elastic modulus E is to secure a basic hair tension Tp for a bow used to play a bowed instrument such as a violin or cello. In spite of being the most important numerical value, there is no way to know the value of the already-made bow. Therefore, there is a reality that a player cannot make an appropriate judgment when seeking an appropriate bow.
ELEMENTS of STRENGTH of MATERIALS by Timoshenko (published on September 20, 1957, Maruzen)

The invention according to the present application is to make it possible to easily know whether or not a bow can secure a hair tension Tp suitable for performance.

According to the document ELEMENTS of STRENGTH of MATERIALS by Timoshenko (published on September 20, 1957, Maruzen), the value of the longitudinal elastic modulus E of the material of the rod-shaped member is supported in the center. The value of the longitudinal elastic modulus E can be calculated from a general formula of material mechanics by placing a weight and measuring the deflection at that time. However, it is difficult to perform such a measurement method with a curved structure such as a bow.

The value of the longitudinal elastic modulus E of the material of the bow is a numerical value that determines the bristle tension Tp and at the same time determines the natural frequency of the “bow pendulum vibration”. Therefore, by measuring the natural frequency, the bow is measured. It can be determined whether or not the hair tension Tp suitable for performance can be secured. According to the invention of the present application, the natural frequency of the “bow pendulum vibration” can be easily measured, so that the suitability of the bow used for the performance can be easily determined.

Embodiments of the present invention will be described below with reference to the drawings. An example of the bow vibration measuring apparatus of the present invention is shown in FIG.
On the base 21, a block 22 having a convex upper surface perpendicular to the longitudinal direction of the base 21 is fixed. On the block 22, the metal ring part 23 which fastens the hair 3 to the frog 5 of the bow is placed, and the bow is placed parallel to the longitudinal direction of the base 21. At this time, the hair 3 of the bow is set to have a hair tension Th in a state of playing.

A block 24 having a convex upper surface is placed at right angles to the longitudinal direction of the bristles 3 and the bristles 3 are placed thereon. Block 24 allows the position to move. Since the natural frequency fo of the “pendulum vibration of the bow” varies depending on the value of the position (x) where the hair 3 hits the string 12, the position where the block 24 is placed is, for example, 0.25 of the length of the hair 3 from the head 2 at the bow tip. And the natural frequency fo of the “bow pendulum vibration” is measured. The position of 0.25 of the length of the hair 3 is x = 0.25, the position of 0.5 of the length of the hair 3 is x = 0.5, and the position of 0.75 of the length of the hair 3 is x = It is defined as 0.75. The position of the block 24 shown in FIG. 5- (a) is a position of x = 0.25. That is, the position where the hair 3 is placed on the block 24 corresponds to the position where the hair 3 hits the string 12 during actual performance.

Pins 26 are arranged on both sides 25-1 and 25-2 of the base, and rubber rings 27 are hung on the pins 25-1 and 25-2, and a load of about 150 g is applied to a position several centimeters ahead of the tip of the frog 5. This is for the purpose of preventing the hair 3 from floating from the block 22 or the block 24 at the time of measurement.

A hammer 33 is made by fixing a weight 32 made of rubber or resin to the tip of a thin rod 31. A felt 34 is attached to the striking surface of the hammer 33 so that the bow is not damaged when hit. When the hammer 33 is struck lightly on the upper surface of the stick 1, rotational vibration is generated around the position of the bow on the block 22. This vibration is “bow pendulum vibration”. In addition, as another method of exciting the “bow pendulum vibration” in the bow, the head 2 which is the tip of the bow is lifted by 2-3 mm by hand and the hair 3 is once lifted from the block 24 and then the hand is moved to the head 2. The “bow pendulum vibration” is also generated by dropping the hair 3 on the block 24 away from the head.
Next, measurement of the natural frequency fo will be described.

A diode housing 41 and a transistor housing 42 are arranged on both sides of the stick 1 on the base 21 in the vicinity of the center of the length of the stick 1. FIG. 5B shows a cross-sectional view of the stick 1, the diode housing 41, and the transistor housing. A hole 43 is formed in the diode housing 41 at a position where the upper surface of the stick 1 is the center, and the light emitting diode 44 is disposed so that the optical axis is directed in the direction of the stick 1. A hole 45 is formed in the transistor housing 42 at a position where the upper surface of the stick 1 is the center, and a phototransistor 46 is disposed in the hole 45 so that the optical axis is directed in the direction of the stick 1. With this arrangement, the light 47 emitted from the light emitting diode 44 is partially blocked by the stick 1 and reaches the phototransistor 46.

FIG. 6A shows an embodiment of the vibration measuring device for the stick 1. Power for driving the light emission of the light emitting diode 44 is supplied from the sensor amplifier 51. The sensor amplifier 51 is provided with an amplifier circuit for amplifying an electric signal from the phototransistor 46, and the signal can be output to the outside.

When the upper surface of the stick 1 is lightly struck with the hammer 33, a rotational vibration is generated around the position where the bow is placed on the block 22. At this time, the upper surface of the stick 1 vibrates up and down, and the light 47 coming out of the light emitting diode 44 and reaching the phototransistor 46 changes with time. Therefore, at this time, the sensor amplifier 51 outputs an electric signal 52 that changes with time.

In recent years, personal computers 53 are generally provided with a function of reproducing audio contents such as music and outputting them as audio, and a function of importing external audio signals into the personal computer 53 as digital signals. By incorporating audio editing software into the personal computer 53 having such a function, it is possible to display or edit the electric signal 52 that changes with time output from the sensor amplifier 51.

As an example of the audio editing software, there is Adobe Audition 2.0 manufactured by Adobe. Adobe Audition 2.0 manufactured by Adobe has a function of displaying the input electric signal 52 in a waveform on the display screen 54. By using this function, the electric signal 52 output from the sensor amplifier 51 is displayed on the display screen 54 as a damped vibration waveform. The natural frequency fo of “bow pendulum vibration” can be obtained by counting the number of peaks of the waveform per unit time on the display screen 54 of this damped vibration waveform.

Adobe Audition 2.0 manufactured by Adobe also has a function of analyzing the frequency of the input electrical signal 52 inside the personal computer 53 and displaying the frequency component contained in the electrical signal 52. Therefore, the natural frequency fo of the “pendulum vibration of the bow” can also be found by reading the frequency included in the electrical signal 52 using this function.

FIG. 6B shows another embodiment of the vibration measuring device for the stick 1.
The frequency counter device 55 is a frequency counter having a function of automatically measuring the number of peak of the waveform of unit time with respect to the electric signal 52 output from the sensor amplifier 51 and displaying the value on the display. By using this device, the natural frequency fo of the “pendulum vibration of the bow” is automatically displayed on the display, so that it can be easily measured.

The natural frequency fo of “pendulum vibration of the bow” is measured for 13 actual cello bows shown in Table 1 with the vibration measuring device of the stick 1 shown in FIGS. 5 (a) and 6 (b). The results are shown in Table 2. Test bows range from low-priced popular products and advanced products made by specialized bow maker, including various types of materials and shapes. In the material column of Table 1, Pe is Fernanbuco material, CFRP is a resin material containing carbon fiber, Hw is a material generally called hardwood, and Bw is Brazil wood material.

The bow weight / dimension column in Table 1 shows the results of measuring the outer shape and weight of the bow. The measurement result of the natural frequency fo of the “pendulum vibration of the bow” is shown in the frequency fo column of the pendulum vibration in Table 2. The position where the block 24 is placed is the natural frequency fo of the “bow pendulum vibration” at the three positions of the head 2 at the bow tip, the position of 0.25, the position of 0.5, and the position of 0.75. Was measured. According to the result, at the position of 0.25 from the tip, the lowest natural frequency fo is 20.3 Hz, and the highest natural frequency fo is 29.8 Hz.

The natural frequency fo of the “pendulum vibration of the bow” is C = 1.73 when x = 0.25 and C = 1.0 when x = 0.5 according to the value of the position (x) where the hair 3 hits the string 12. Since it is known that the frequency ratio C is C = 0.58 when x = 0.75, the value of the frequency ratio C of the natural frequency fo actually measured is shown in the frequency ratio C actual measurement value column. It was described in. According to this, it can be seen that the frequency ratio of the natural frequency fo of the actually measured “bow pendulum vibration” almost coincides with the theoretical value, and accordingly, FIGS. It is considered that the natural frequency fo of the “bow pendulum vibration” measured by the vibration measuring device of the stick 1 shown in FIG. The numerical values are displayed in a graph in FIG.

As shown in FIG. 4, the natural frequency fo of the “bow pendulum vibration” is derived from the value of the frequency ratio C determined by the values of the hair tension Tp, the moment of inertia Ib, and the position (x) where the hair 3 hits the string 12. It was. Since the natural frequency fo is measured, the value of the hair tension Tp can be known if the inertia moment Ib of the bow is known. FIG. 8 shows a method for measuring the inertia moment Ib of the bow. The center of rotation of the “bow pendulum vibration” is the tip of the frog 5, and a rod 61 with less friction is placed at that position, and the head 2 at the tip of the bow is swung left and right by hanging vertically with the bow hair stretched. Pendulum movement of the bow.

This state is generally called a rigid pendulum. If the period T of the vibration of the rigid pendulum is known, the moment of inertia of the rigid pendulum can be calculated by the calculation formula shown in FIG. The period T of the vibration of the rigid pendulum was obtained by measuring the time of 10 cycles twice to obtain an average value and obtaining the period T of 1 cycle. The results are shown in the period column of Table 2. The moment of inertia Ib was calculated from that value and listed in the column of moment of inertia.

The value of the hair tension Tp was determined using the calculated values of the inertia moment Ib, the natural frequency fo of the “bow pendulum vibration”, and the frequency ratio C. The results are shown in the Tp hair tension column of Table 3. Further, using this value, the stick coefficient α was obtained from the relationship of Tp = Th + α × dp = α (d2−d1) + α × dp. However, the load applied to the bow when measuring the natural frequency fo of the “bow pendulum vibration” is as small as about 150 g, and the value of the deflection dp of the stick is negligible, so Tp = α (d2−d1) It was. The numerical value of the calculated stick coefficient α is shown in the estimated stick coefficient α column of Table 3.

According to the above method, the natural frequency fo and the moment of inertia Ib of the “bow pendulum vibration” are measured, so that it is not possible to know how long the bow is made of the material having the value of the elastic modulus E. The numerical value of the hair tension Tp can be known. Looking at the numerical values of the hair tension Tp shown in Table 3, some bows show a value of 12 Kg or more for large bows, but small ones are as small as 5-8 Kg. It can be judged as a bow that is difficult to play.

Also, the value of the stick coefficient α can be known without knowing how much the bow is made of the material of the longitudinal elastic modulus E. Therefore, the value of the distance d2 between the stick 1 and the hair 3 is considered as the limit. It is possible to know the hair tension when the hair 3 is stretched up to 12 mm. The value is shown in the limit d2 hair tension column of Table 3. Even in such a case, a bow whose bristle tension is as small as 5-8 kg can be reliably determined as a bow that is difficult to play due to lack of bristle tension.

The natural frequency fo of the “bow pendulum vibration” was measured, and it was found that the appropriateness of the hair tension, which is the basic performance of the bow, can be determined by the magnitude of the value. Next, the validity of the 13 test bows will be further verified. FIG. 9 shows an example in which the electrical signal 52 output from the sensor amplifier 51 is displayed on the display screen 54 as a damped vibration waveform. Among the test bows, the natural frequency fo of the “bow pendulum vibration” showed a relatively high value of 28.6 Hz at a position of 0.25 from the tip. B. The damped vibration waveform of AC-30 which showed the lowest value with Gabriel G-30 and 20.3 Hz is shown.

In the damped vibration, the damping ratio obtained from the natural logarithm of the ratio between the values of two adjacent peaks is defined as a numerical value indicating the magnitude of the damping capacity of the vibration. The induction formula is shown in FIG. Table 3 shows the results of calculating the attenuation ratio of each bow from the damped vibration waveform displayed on the display screen 54 when the natural frequency fo of the “pendulum vibration of the bow” was measured for the 13 cello test bows. Actual measurement value) Shown in the Damping vibration damping ratio column.

FIG. 10 illustrates the relationship between the natural frequency fo and the damping ratio of the “bow pendulum vibration”. A bow with a high natural frequency fo of “bow pendulum vibration” tends to have a proportionally large damping ratio value, and even if “bow pendulum vibration” occurs, the vibration is attenuated quickly and the operation of the bow is stabilized. It is done. The three evaluations entered in FIG. 10 indicate the level of ease of handling when the 13 bows were actually played.

One of the techniques related to bow operation when playing bowed instruments such as violins and cellos using the bow is the aforementioned “Spikkato technique”. This technique is a performance technique in which the bow hair is pushed down to the string. In this case, it is inevitable that a vibration phenomenon will inevitably occur in the bow that is down. In such a case, it is desirable for the vibration to settle quickly. The three evaluations entered in FIG. 10 are the results of classifying the degree of “runout” generated in the bow when the 13 test bows are downed under the same conditions into three stages. According to this, it has been found from actual performance that the bow having a high natural frequency fo and a large damping ratio of the “bow pendulum vibration” has a smaller “shake” generated in the bow and is easy to play.

FIG. 11 shows the relationship between the natural frequency fo of the “bow pendulum vibration” measured for 13 cello test bows and the stick coefficient α calculated from the value of the inertia moment Ib obtained separately. Comparing this result with the evaluation of an easy-to-play bow shown in FIG. 10, for example, if the bow has a natural frequency fo of 28 Hz or higher, the stick coefficient α is large, so that the hair tension can be sufficiently secured, and “ You can see that it is a bow that can be used without problems even in advanced performance techniques such as "Spiccato". If the bow has a natural frequency fo of 25 Hz or more, advanced performance techniques such as “Spikkato” may require some training and habituation. Is considered a well tolerated bow. On the other hand, when the natural frequency fo is less than 25 Hz, there is a bow in which sufficient bristle tension cannot be secured, and since the inertia moment Ib is large although the bristle tension can be secured, the bow is easy to swing. There are cases where the damage is impaired.

As described above, by measuring the natural frequency fo of the “pendulum vibration of the bow”, the performer can easily know whether or not the bow can secure the proper hair tension Tp for performance and is easy to handle. it can. Bow manufacturers and sellers can also grade bow performance. For example, bows of 28 Hz or higher are “superlative products”, bows of 25 Hz or higher are “advanced products”, bows of less than 25 Hz are “popular products”, and the like.

In the case of a general audio product, the reproducible range of the audio frequency of the device is usually displayed as a frequency characteristic value and sold. However, in the past, musical instruments and accessories such as bows were not sold with quantitative display of performance and grade. In recent years, catalog mail-order sales that require purchases without directly looking at or touching the actual product have become widespread due to the spread of the Internet and the like. In such a case, the performance of the instrument body and its accessories, such as a bow, is displayed and sold, which is a great advantage for consumers when selecting goods, and the manufacturer and sales Consumers can increase their trust in that they can sell products with appropriate performance at an appropriate price.

According to the present invention, it becomes possible for a player of a bowed instrument such as a violin or cello to select a bow having sufficient hair tension necessary for performance with quantitative data support. In addition, the manufacturers and sellers can increase consumer confidence in that they can sell bows with the right performance at the right price.

Structure diagram of bow for bowed instruments Illustration to calculate bow hair tension Illustration of pressure applied to the bow Illustration of bow pendulum movement Embodiment of bow vibration measuring apparatus of the present invention Embodiment of the vibration frequency measuring method of the bow vibration measuring device of the present invention Example of measurement results of bow pendulum frequency Example of measuring the moment of inertia of a bow Example of bow pendulum frequency damping ratio Example of bow pendulum frequency and damping ratio Example of bow stick coefficient and pendulum frequency

Explanation of symbols

1 Stick 2 Head 3 Hair 4 Adjuster 5 Frog 6 Screw hole 7 Screw 8 Eyelet 9 Groove 11 Right hand 12 String 13 Thumb 14 Index finger 21 Base 22 Block 23 Ring part 24 Block 25-1, 25-2 Base both sides 26 Pin 27 Rubber Wheel 31 Thin rod 32 Weight 33 Hammer 34 Felt 41 Diode housing 42 Transistor housing 43 Hole 44 Light emitting diode 45 Hole 46 Phototransistor 51 Sensor amplifier 52 Electric signal 53 Personal computer 54 Display screen 55 Frequency counter device

Claims (4)

  A bowed instrument player has a first fulcrum provided at a position supporting the bow and a movable second fulcrum provided at a position where the bow hair hits the string. The first fulcrum and the second fulcrum Between the fulcrums, disposed near the first fulcrum and having a pressing means for pressing the hair of the bow on the second fulcrum, the bow in a state where the hair is stretched on the first fulcrum and the second fulcrum is disposed, Rotation vibration of the bow can be generated by the interaction between the elastic force of the rod-like member that applies tension to the hair and the mass of the bow in a state where the hair of the bow is pressed against the first fulcrum and the second fulcrum by the pressing means. Bow vibration measuring device.   The bow vibration measuring apparatus according to claim 1 has vibration detecting means for detecting vibration of a rod-shaped member of the bow, and a bow having a hair stretched on the first fulcrum and the second fulcrum is arranged and pressed. A state in which rotational vibration of the bow is generated by the interaction between the elastic force of the rod-like member that applies tension to the hair and the mass of the bow while the bow hair is pressed against the first fulcrum and the second fulcrum by the means The bow vibration measuring apparatus according to claim 1, wherein the vibration of the rod-shaped member can be detected by the step.   3. The bow vibration measuring apparatus according to claim 2, wherein the vibration detecting means according to claim 2 can detect the vibration of the rod-shaped member without contacting the rod-shaped member.   The bow vibration measuring device according to claim 2 has a frequency measuring means for measuring the vibration frequency of the detected vibration of the rod-shaped member and displaying the value, and the bow hair is defined as the first fulcrum by the pressing means. The frequency of the rod-like member can be measured in a state where the rotational vibration of the bow is generated by the interaction between the elastic force of the rod-like member that gives tension to the hair and the mass of the bow while being pressed against the second fulcrum. The bow vibration measuring device according to claim 2.

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