JP6803062B2 - Clavichord - Google Patents

Description

The present invention relates to a clavichord.

The Clavichord was born around the 14th century and was a favorite keyboard instrument mainly in the German-speaking world from the 16th century to the 18th century. It plays a distinctive tone that is different from other keyboard instruments such as the piano. There are still many enthusiasts.

The characteristic tone of the clavichord depends on its sounding mechanism. On the piano, it is pronounced by striking the strings with a hammer linked to the keys, while on the clavichord, it is pronounced by striking the strings with a rod-shaped part called a tangent linked to the keys. And unlike a piano where the hammer separates from the strings immediately after pronunciation, in the Clavichord, the pitch (pitch) is changed by pressing a key during pronunciation in order for the tangent to maintain contact with the strings during pronunciation. be able to.

However, the conventional clavichord did not have a mechanism to control the amount of pitch fluctuation due to key pressing, so the pitch variable mechanism is used exclusively for playing vibrato-like sound expressions. It did not stay and was not used for active musical expression.

JP-A-2002-221960

The present invention has been made in view of the above, and an object of the present invention is to provide a clavichord in which the amount of pitch fluctuation due to key pressing is controlled.

As a result of diligent studies on the configuration of the clavichord in which the amount of pitch fluctuation due to key pressing is controlled, the present inventor has come up with the following configuration and arrived at the present invention.

That is, according to the present invention, in a clavichord sounded by striking a tangent fixed to a key in conjunction with the key pressing, the pitch fluctuation rate with respect to the key pressing amount is designed to be a predetermined value. A clavichord is provided, which is characterized by being.

As described above, according to the present invention, there is provided a clavichord in which the amount of pitch fluctuation due to key pressing is controlled.

Schematic diagram showing the internal structure of the clavichord. Diagram to illustrate the basic formula used to design the clavichord. The figure which shows the mechanism which controls the pressing amount of a key. The figure which shows the result of the verification experiment.

Hereinafter, the present invention will be described with reference to the embodiments shown in the drawings, but the present invention is not limited to the embodiments shown in the drawings. In each of the figures referred to below, the same reference numerals are used for common elements, and the description thereof will be omitted as appropriate.

The present embodiment discloses a method of controlling the amount of pitch fluctuation accompanying key pressing in a clavichord. Specifically, in the Clavichord, a method of designing a pitch fluctuation rate with respect to a key pressing amount to a predetermined value will be disclosed.

The present embodiment discloses a method of designing a clavichord so that the volatility of the pitch with respect to the amount of key pressing is equal for all keys.

The present embodiment also discloses a method of designing a clavichord so that the feeling of pressing a key feels the same for all keys.

Further, the present embodiment discloses a limiting means for controlling the amount of key pressing in the clavichord.

Here, before starting the explanation of the clavichord of the present embodiment, the basic structure of a general clavichord will be described as a premise.

A typical clavichord has a rectangular box-shaped structure, with keyboards arranged side by side along one long side of the rectangle, and strings stretched almost parallel to the long side. FIG. 1 schematically shows the internal structure of the clavichord. As shown in FIG. 1, in the clavichord, when the key is pressed down, a metal rod called a tangent, which is fixed to the tip of the key and interlocked with the key, rises and is a string stretched horizontally directly above the key. Strike the strings as if piercing. At this time, string vibration occurs with the contact point between the tangent and the string as a node, leading to pronunciation. On the other hand, the felt for mute is wrapped around the part of the string located on the opposite side of the bridge (piece) when viewed from the string striking point, and when you release the key, the tangent that was a node of string vibration As a result of the string being separated from the string, the string vibration reaches the felt and the sound stops.

Since the basic structure of the clavichord has been described above, the explanation of the clavichord of the present embodiment will be started.

Here, first, three basic equations used in the design of the clavichord of the present embodiment will be described. In the following description, FIG. 2 will be referred to as appropriate.

<Basic formula (1): Basic formula for string dimensions and fundamental frequency>
The basic equation (1) relating to the string size and the fundamental frequency is derived as follows.

The relationship between the fundamental frequency f of the string and the tension T is expressed by the following equation (1-1). In the following equation (1-1), L indicates the total length of the string, a indicates the distance from the fixed end of the string to the striking point (contact point between the string and the tangent), and La indicates the pronunciation of the string. It indicates the length of the part, and μ indicates the linear density of the string. (The same applies to the other formulas listed below.)

Here, the linear density μ of the string is expressed by the following equation (1-2). In the following equation (1-2), ρ _c indicates the volume density of the core wire of the string, and ρ _w indicates the volume density of the thin wire (hereinafter referred to as the thin wire) wound around the core wire when the string is a winding. shown, a _c represents the cross-sectional area of the core wire, a _w represents a cross-sectional area of a portion occupied by the thin line of the total cross-sectional area of the winding. (The same applies to the other formulas listed below.)

Then, by rearranging the above equations (1-1) and (1-2), the following equations (1-3) can be obtained.

Here, the relationship between the tension T, the stress σ _{c of} the core wire, and the stress σ _{w of the} thin wire is expressed by the following equation (1-4).

The ratio q of the cross-sectional area _{A w} of the thin line portion to the cross-sectional area _{A c} of the core is represented by the following formula (1-5).

Then, by modifying the above equation (1-3) based on the above equations (1-4) and (1-5), the basic equation (1) relating to the string size and the fundamental frequency f becomes as follows. Derived.

Here, in the above basic equation (1), s means the ratio of the thin wire stress σ _w to the core wire stress σ _c (σ _w / σ _c ), and u is the volume density of the thin wire with respect to the core wire volume density ρ _c. means [rho _w ratio of (ρ _w / ρ _c) (also in another type listed below). Further, the cross-sectional area A _c of the core wire in the basic formula (1) is represented by the following formula using the diameter d of the core wire (1-6).

Also, the basic equation (1) the effective cross-sectional area A _w of the thin line in can be expressed by the following equation using the diameter d and fine wire diameter t of the core wire (1-7). Here, the total cross-sectional area of the winding is approximated by the area of a circle having a diameter of d + 2t.

Since the basic equation (1) relating to the string dimensions and the fundamental frequency has been described above, the basic equation (2) will be described next.

<Basic formula (2): Basic formula for lateral rigidity of strings>
In this embodiment, the spring constants divided by the vertical displacement load in a direction perpendicular to the axial direction of the chord (the lateral load) in Datsuruten (load application point) is defined as the lateral stiffness k _cp strings. In the present embodiment, the clavichord is designed by using the lateral rigidity _kcp of the string as an index of the key pressing comfort corresponding to the string.

The basic equation (2) relating to the lateral rigidity _kcp of the string is derived as follows.

The following equation (2-1) holds from the balance between the concentration force F acting on the string and the tension T of the string at the striking point (load action point) where the tangent contacts the string.

Here, since θ ₁ and θ ₂ in the above equation (2-1) are minute quantities, if the vertical displacement at the string striking point is δ, the concentration force F acting on the string is given by the following equation (2-2). Can be approximated.

On the other hand, the concentration force F acting on the string is expressed as the product of the lateral rigidity _{kcp of the} string and the displacement δ as shown in the following equation (2-3).

Therefore, by substituting the above equation (2-3) into the above equation (2-2) and rearranging it, the following equation (2-4) can be obtained.

Further, when the above equation (2-4) is modified based on the equations (1-4) and (1-6) mentioned above, the basic equation (2) relating to the lateral rigidity _kcp of the string is as follows. Derived.

Since the basic equation (2) relating to the lateral rigidity and displacement of the string has been described above, the basic equation (3) will be described next.

<Basic formula (3): Basic formula for displacement and pitch volatility at the striking point>
The basic equation (3) relating to the displacement at the striking point and the pitch volatility is derived as follows.

The amount of increase in tensile strain Δε due to pushing at the string striking point where the tangent contacts is expressed by the following equation (3-1). In the following equation (3-1), δ indicates the displacement at the chord striking point.

Here, the two terms in parentheses of the first molecular item of the above formula (3-1) can be approximated by the following formulas (3-2) and (3-3).

Therefore, the parentheses of the first molecular item of the above formula (3-1) can be expressed as the following formula (3-4).

Therefore, when the above formula (3-4) is substituted into the first item of the molecule of the above formula (3-1) and arranged, the amount of increase in tensile strain Δε is expressed by the following formula (3-5).

Then, assuming that the amount of increase in the tensile stress of the core wire due to pushing at the string striking point is Δσ _c , the following equation (3-6) is derived from the relationship between Δσ _c and Δε. In the following formula (3-6), E _c represents the Young's modulus of the core wire. (The same applies to the other formulas listed below.)

Here, since the same equation as the above equation (3-6) holds for the thin wire, if the amount of increase in tension T due to pushing at the chord striking point is ΔT, ΔT is the amount of increase in strain of the core wire and thin wire Δε. Under the assumption that they are equal, the amount of increase in tensile stress of the core wire Δσ _c , the cross-sectional area of the core wire A _c , the amount of increase in the tensile stress of the thin wire Δσ _w , and the cross-sectional area A _w of the thin wire portion are used as follows. It can be expressed by the formula (3-7). However, E (_) _w is the equivalent Young's modulus of the thin line, and E (_) _w = sE _c by s = (σ _w / σ _c ).

Here, assuming that the amount of increase in the fundamental frequency due to pushing at the string striking point is Δf, the following equation (3) is based on the above equation (1-1) showing the relationship between the fundamental frequency f of the string and the tension T. -8) holds.

Further, the rate of change (f + Δf) / f of the fundamental frequency due to pushing at the string striking point is determined by the following equation (3) using equations (1-1), (3-7), and (3-8). It is represented by -9).

Then, by rearranging the above equation (3-9), the pitch volatility r (= Δf / f) is expressed by the following equation (3-10).

Further, by modifying the above equation (3-10) based on the equation (1-4) mentioned above, the basic equation (3) regarding the displacement δ and the pitch volatility r at the chord striking point is as follows. Derived.

Since the derivation process of the basic equations (1) to (3) has been described above, the design method of the sounding mechanism of the clavichord using the basic equations (1) to (3) will be described next.

Table 1 below summarizes the 13 variables (3 material constants, 5 shape parameters, 5 characteristic parameters) appearing in the above-mentioned basic equations (1) to (3).

Here, in designing the sounding mechanism of the clavichord, the values of five variables (f, k _cp , δ, r, s) among the 13 variables listed in Table 1 above can be given as follows. it can.

First, the fundamental frequency f gives a value corresponding to the pitch of each string (key). For example, the pitch of the string (key) of interest is set to "center la (A)", and "440 Hz" is given as the value of f.

Next, the lateral rigidity _{kcp of the} string gives an appropriate value according to the pressing comfort of the key to be realized. In this embodiment, in consideration of playability, the lateral rigidity _kcp of the strings is set with respect to all the strings (keys) so that the feeling of pressing the keys feels the same for all the keys. Give a common value.

Similarly, the displacement δ at the striking point and the pitch volatility r are given common values for all strings (keys) so that the pitch volatility with respect to the key pressing amount is equal for all keys. .. Since the displacement δ is a value directly proportional to the amount of pressing the key, the displacement δ (for example, 10 mm) proportional to the design value of the amount of pressing the key is calculated and given. Further, for the pitch fluctuation rate r, the pitch fluctuation c (for example, a semitone: 100 cents) to be realized with respect to the design value of the key pressing amount (that is, the value set in the displacement δ) is substituted into the following equation (4). Give the calculated value obtained.

Further, when the string is not a winding, or when the string is a winding but tension does not act on the thin wire, s = 0 is set. On the other hand, when the string is a winding and tension acts on the thin wire, the ratio of the equivalent Young's modulus of the thin wire to the Young's modulus of the core wire is given as s.

In designing the sounding mechanism of the clavi chord, 5 variables (5 variables) out of the 13 variables listed in Table 1 above, depending on the specifications to be realized (pitch fluctuation rate with respect to the key pressing amount, key pressing comfort). Since the values of f, k _cp , δ, r, s) can be given in advance, the remaining eight variables (E _c , ρ _c , ρ _w , L, a, d, t, σ _c ) can be given in advance. If five variables are arbitrarily selected from the variables and their values are determined, the values of the remaining three variables can be derived using the above-mentioned basic equations (1) to (3). .. In designing the sounding mechanism of the clavichord, which of the eight variables (E _c , ρ _c , ρ _w , L, a, d, t, σ _c ) is given a value in advance and which one It is up to you to derive the variables using the above-mentioned basic equations (1) to (3), and various modes can be assumed. However, two cases will be described below as specific examples of the design. ..

(Case 1)
In Case 1, of the eight variables described above, the values of E _c , ρ _c , ρ _w , L, and a are given in advance, and then d, t, and σ _c are given in the basic equations (1) to (3). Is derived using.

First, σ _c is derived by substituting the values given to δ, r, E _c , L, a, and s in the following formula (5) obtained by modifying the above basic formula (3). ..

Subsequently, in the following equation (6) obtained by modifying the above-mentioned basic equation (1), the values given to f, ρ _c , ρ _w , L, and a are substituted, and the above equation (5) is assigned to σ _c. ) Is substituted to derive q.

Subsequently, in the following equation (7) obtained by modifying the above-mentioned basic equation (2), the values given to k _cp , L, a, and s are substituted, and σ _c is derived by the above equation (5). D is derived by substituting the obtained value.

Subsequently, d derived from the above equation (7) and q derived from the above equation (6) are substituted into the relational expression shown in the following equation (8) to obtain A _w .

Finally, t is derived by substituting d derived by the above equation (7) and A _w derived by the above equation (8) into the relational expression shown in the following equation (9).

In Case 1 described above, by designing the diameter of the core wire and the diameter of the thin wire of the string based on the d and t obtained for each string (key), the volatility of the pitch with respect to the amount of key depression and the key can be obtained. A clavichord is provided that has the same pressing comfort for all keys. If the solutions of d and t do not exist, it is necessary to change the preset values.

(Case 2)
In case 2, on the premise that no winding is used for the strings, E _c , ρ _c , ρ _w (= 0), t (= 0), s (= 0), and σ _c are given in advance, and then the basic equation is given. L, a, and d are derived using (1) to (3). In this case, the stress σ _c of the core wire is given an appropriate value so that the string does not break when the key is pressed in light of the breaking stress of the string.

First, in the following equation (10) obtained by modifying the above-mentioned basic equation (1), La is derived by substituting the values given to f, ρ _c , and σ _c .

Next, in the following equation (11) obtained by modifying the above-mentioned basic equation (3), the values given to E _c , δ, r, and σ _c are substituted, and the above equation (10) is assigned to La. A is derived by substituting the value derived in.

As a result, the length L of the chord is derived as the sum of La derived by the above equation (10) and a derived by the above equation (11).

Finally, in the following equation (12) obtained by modifying the above-mentioned basic equation (2), the value given to _kcp is substituted, and the previously derived value is substituted for L and a to d. Is derived.

In the above-mentioned case 2, the diameter of the core wire of the string, the length of the string, and the fixed position of the tangent are designed based on the L, a, and d obtained for each string (key), so that the key is pressed down. A clavichord is provided in which the fluctuation rate of the pitch and the feeling of pressing the keys are the same for all keys.

Now that the design method of the sounding mechanism of the clavichord has been described, the limiting means for controlling the amount of key pressing will be described next.

FIG. 3 shows an example of limiting means for controlling the amount of key pressing. The limiting means 10 shown in FIG. 3 includes a lever 12 and a tapered wedge 16 connected to the lever 12 via a link 14. In the limiting means 10, the wedge 16 is inserted between the pedestal 19 and the key 18 on which a slope is formed toward the tip of the key 18, so that the pressing amount of all the keys 18 is equally limited. There is. As a result, the performer can immerse himself in the performance without worrying about the strings breaking due to excessive key pressing, which improves playability. In addition to this, if the pressing amount limited by the limiting means 10 is a pressing amount corresponding to a desired pitch fluctuation (semitone, whole tone), the performer can perform two types of pressing operations by pressing one key to the limit. You will be able to express the pitch.

Further, in the limiting means 10, as shown in FIG. 3A, when the lever 12 is lifted, the wedge 16 rises on the slope of the pedestal 19 and limits the pressing depth of the key 18 to D1. ), When the lever 12 is pushed down, the wedge 16 goes down the slope of the pedestal 19 and limits the pressing depth of the key 18 to D2. By moving the lever 12 up and down, the key 18 is pushed down. The limit value of the amount of pushing down is variably controlled. As a result, the performer can change the fluctuation range of the pitch of the strings by operating the lever 12 during the performance, so that various performances are possible.

As described above, according to the present embodiment, the fluctuation rate of the pitch with respect to the amount of pressing the key is equal for all the keys, and the feeling of pressing the key is felt to be the same for all the keys. Code is provided.

In the above-described embodiment, a design method for giving a common value to the three parameters ( _kcp , δ, r) of all the strings (keys) has been described, but in other embodiments, the three parameters have been described. At least one of (k _cp , δ, r) may be designed to be different for each string. For example, the pitch fluctuation rate r with respect to the amount of key pressing may be designed so as to change gently in the key arrangement direction, or the lateral rigidity _{kcp of the} string corresponding to the key changes gently in the key arrangement direction. It may be designed to do so.

Although the present invention has been described above with embodiments, the present invention is not limited to the above-described embodiments, and the actions and effects of the present invention can be exhibited within the scope of other embodiments that can be conceived by those skilled in the art. As long as it works, it is included in the scope of the present invention.

In order to verify the validity of the basic equation (3) regarding the displacement δ of the strings and the pitch volatility γ, a verification experiment was conducted using an actual clavichord.

(1) Experimental method A4 string with a fundamental frequency of f = 440Hz was used as the target string, and the displacement δ of the target string due to the pressing of the key was measured with a dial gauge, and the change in the fundamental frequency was measured with a tuner. The shape parameters of the target string are as follows.
Overall length of the string L: 532mm
Distance from the fixed end to the contact point between the string and the tangent a: 70mm
Diameter of the core wire of the string d: 0.33mm
Diameter of thin wire in winding t: 0mm

(2) Experimental results Fig. 4 shows the relationship between the displacement δ (mm) of the target string and the pitch fluctuation c (cents) by combining the measured value and the theoretical value based on the basic formula (3) (pitch fluctuation c and pitch). For the relationship of the volatility r, refer to the above equation (4)). The theoretical values were calculated assuming that the volume density of the core wire ρ _c = 7.8 × 10 ³ kg / m ³ , the Young's modulus of the string E = 2.0 × 10 ¹¹ Pa, and the tension T of the string T = 110.2 N. As shown in FIG. 4, the measured value and the theoretical value are almost the same, and the validity of the basic equation (3) is confirmed.

10 ... limiting means, 12 ... lever, 14 ... link, 16 ... wedge, 18 ... key, 19 ... pedestal

Claims (9)

In the clavichord, which is pronounced by striking the tangent fixed to the key in conjunction with the pressing of the key.
It is characterized in that the fluctuation rate of the pitch with respect to the amount of pressing of each key is designed to be substantially equal for all keys.
Clavichord. In the clavichord, which is pronounced by striking the tangent fixed to the key in conjunction with the pressing of the key.
It is characterized in that the volatility of the pitch with respect to the amount of key pressing is designed to change gently in the key arrangement direction.
Clavichord. The lateral rigidity of the strings corresponding to each key is designed to a predetermined value.
The clavichord according to claim 1 or 2. It is characterized in that the lateral stiffness of the strings corresponding to the keys is designed to be approximately equal for all keys.
The clavichord according to claim 3. It is characterized in that the lateral stiffness of the strings corresponding to the keys is designed to change gently in the key arrangement direction.
The clavichord according to claim 3. Includes limiting measures that limit the amount of key presses approximately equally,
The clavichord according to any one of claims 1 to 5. The limiting means is characterized in that the limit value of the pushing down amount is variably limited.
The clavichord according to claim 6. Any one of claims 1 to 7, characterized in that the diameter d of the core wire of the string corresponding to each key and the diameter t of the thin wire are designed to satisfy the following equations (1) to (5). Clavichord described in.
(In the above formulas, T is indicated string tension, E _c represents the longitudinal elastic modulus of the core wire, [rho _c represents the volume density of the core, A _c represents the cross-sectional area of the core wire, d is the diameter of the core wire Indicated, ρ _w indicates the volume density of the thin wire, A _w indicates the cross-sectional area of the thin wire portion, t indicates the diameter of the thin wire, L indicates the total length of the string, and a indicates the string striking point from the fixed end of the string. Σ _c indicates the core wire stress, s indicates the ratio of the thin wire stress to the core wire stress σ _c , and u indicates the ratio of the thin wire volume density ρ _{w to} the core wire volume density ρ _c . q is the ratio of cross-sectional area a _w of the thin line portion to the cross-sectional area a _c of the core, f is shown the fundamental frequency of the string, k _cp denotes the lateral stiffness of the string, [delta] represents the displacement in the string striking point, r indicates the pitch fluctuation rate.) Claims 1 to 1, characterized in that the total length L of the string corresponding to each key and the distance a from the fixed end of the string to the striking point are designed to satisfy the following equations (1) to (3). The clavichord described in any one of 7.
(In the above formulas, T is indicated string tension, E _c represents the longitudinal elastic modulus of the core wire, [rho _c represents the volume density of the core, A _c represents the cross-sectional area of the core wire, d is the diameter of the core wire Indicated, ρ _w indicates the volume density of the thin line, A _w indicates the cross-sectional area of the thin line portion, L indicates the total length of the string, a indicates the distance from the fixed end of the string to the striking point, and σ _c indicates. shows the stress of the core wire, s is the ratio of fine wire stress to stress sigma _c of the core wire, u is the ratio of fine line volume density [rho _w to the volume density [rho _c of the core, q is the core of the cross-sectional area a _c The ratio of the cross-sectional volume A _w of the thin line portion to to is indicated, f indicates the basic frequency of the string, _kcp indicates the lateral rigidity of the string, δ indicates the displacement at the striking point, and r indicates the pitch fluctuation rate. )