JPH07506679A - percussion instrument - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention] Name of invention, percussion instrument Technical field The present invention relates to percussion instruments. In particular, the present invention provides a series of elongated, non-collinear, integral When 19A of said part is struck with a gavel, i.e., a drumstick, music is produced. This invention relates to a musical percussion instrument that produces a comfortable a. The quality of the sound generated depends on the nature of the gavel (soft). It varies depending on the percussion instrument (quality or hardness) and how the percussion instrument is played. Hard drumsticks In other words, when struck with a gavel, it produces a bell-shaped sound that includes partials that are roughly harmonic related. do.

Conventional technology The prior art closest to the present invention is usually an "orchestral triangle" or This is a musical instrument known as the ``battu triangle.'' traditional orchestral A triangle produces a characteristic "triangle" sound with an irregular pitch. Tiger The angle is not tuned to provide overtones. The scale circumference of the striking triangle The relationship between wave numbers is determined by changing the base angle and corner curvature of the triangle. Is it possible to change the degree? There are limits to such tuning. overall size The IIP nominal pitch is fixed by It is possible to design a triangle that brings about a harmonic relationship with Q. .

However, the remaining non-double in such a "tuned triangle" This limits the use of triangles to musicians, since the partials of a note are very noticeable. It is considered a degree.

Disclosure of invention It is an object of the present invention to have a series of elongated, non-collinear, integrally formed sections; is one of them, or a gavel, which provides a musically pleasant sound when struck with a bang. To provide a musical percussion instrument that is tuned to the uni.

This purpose is to form a shape with three or more parts, and when one part is struck, A sound of a certain length, i.e. a certain −, emitting a sound having a musically harmonious frequency range Music made of a piece of metal or a suitable material (e.g. ceramic material) This is achieved by providing percussion instruments. of said metal or other material; The part is formed into a generally flat shape, and the frequency range of the emitted sound is at least the first It is preferable that the five in-plane scales are generally harmonically related.

As described above, according to the present invention, the device is composed of a plurality of integrally formed elongated portions having three or more gates. , said parts being generally coplanar and non-collinear, and one of said parts being rigid at room temperature. A hammer formed from a material that produces a sound in harmony with the instrument when struck with a gavel. Instruments provided.

Preferably, the percussion instrument has five parts forming an irregularly symmetrical shape.

In particular, the shape of the The length of the middle part between the end part and the center part is also equal. Ru. The inventors of the present invention named this structure the "staff star" structure. [Staff star shape] structure In one embodiment of the construction, the length ratio of said portions is 1.00:1.95:0.92. Two groove angles are approximately 95 degrees, and the other two groove angles are approximately 93 degrees. child In another embodiment of the shape, the ratio of the lengths of the five-pointed star portions is 1.　00:1. aS: 0.97, and the groove angles are approximately 146 degrees and 10 degrees.

The invention also relates to an assembly or arrangement of the individual instruments described above, comprising a desired It also covers percussion instruments tuning said assembly to different pitches to provide musical scales. Ru. For example, it provides a two-octave scale (consisting of 25 individual instruments) and It can be played like a koto.

The musical instrument according to the present invention is provided with a sound radiator to improve sound generation efficiency. I can do it. Such radiators are too high for instruments consisting of a single staff star. Although it is preferable to use a non-resonant radiator in the band, even a resonant radiator may A resonant radiator may also be used. Known radiator structures that can be used include thin wire or A tunable pipe connected to a flexible diaphragm or instrument through a string. or a cavity (Helmholtz) resonator. Musical star shape with percussion instruments , a broadband non-resonant sounding plate in the cavity or back is preferred. present invention It is also possible to electronically amplify the sound produced by an instrument constructed by Ru.

These and other features of the invention can be found in the following description of embodiments of the invention. This will be explained in detail later. Provided by way of example only, and constructed in accordance with the present invention, In the following description containing details of the development of suitable shapes for integrally formed parts of the vessel. , see the accompanying drawings.

Brief description of the drawing Figure 4 is used as a starting point to mathematically model the preferred geometry of the present invention. A diagram showing a simplified five-line star shape.

Figure 2 shows the invention from a thin rod bent to form five parts. Graph showing the frequency variation of the first few in-plane modes of a more structured instrument.

FIG. 3 shows the solution of the three-dimensional shape mentioned in the explanation of the development of the shape suitable for the present invention. FIG.

FIG. 4 shows the (θ, Φ) sub-subs mentioned in the explanation of the expansion of the shape suitable for the present invention. A diagram showing the shape of a space.゛ FIGS. 5 and 6 are diagrams showing the star shapes of two musical instruments constructed according to the present invention. .

Section 7 represents a partial assembly of individual five-line star instruments constructed in accordance with the present invention. This is a schematic diagram.

Detailed description of the illustrated embodiments (i) Although the present invention can be used for various types of music, (ii)) Liangles are usually made of metal; (iii) The present invention also includes a metal rod. Since it is constructed by bending, the following detailed explanation will mainly focus on this. The direction shall be directed to structural technology. However, the integral part constituting the concept of the present invention The body part is made of metal or alloy casting, pressure forming, or firing of ceramic material. It should be recognized that it can also be formed by Casting technology and appropriate vibration characteristics using mechanically strong ceramic materials (e.g., certain oxide ceramics) that have Although the configuration by bending a metal rod is expensive compared to bending a metal rod, ( a) It is possible to eliminate problems related to the selection of the radius of curvature in loft bending, and (b) Top quality orchestral instruments don't come cheap.

If the percussion instrument according to the invention is to be made from ceramic material, any suitable ceramic It is possible to use block machining techniques. However, most ceramic bodies have the following steps. It is constructed using floors.

(a) a finely ground powder of at least one ceramic material is a temporary binder; mixed with (b) the mixture thus formed is shaped into the required shape and (e.g. isostatically processed); (using pressure techniques) to form what is known as a "green" body. , (C) The green body is then fired (sintered) to a temperature at which the ceramic material is sintered. During the initial stage of heating to the formation temperature, the temporary binder evaporates from the green body) , (d) the sintered ceramic body is free from major cracks in the body; cooled to room temperature at a cooling rate that guarantees

In the original form of the present invention (all having a five-line star structure), the inventor of the present invention The diameter is 12. L mm, the length of the rod in each five-line star shape is about 0.5 meters to 1 Mild steel rods varying up to 5 meters were mainly used. Mild steel rods are expensive easy to process and suitable as far as internal buffering and abrasion tolerance of the finished product are concerned. It has appropriate vibration characteristics. Other metals and alloys may also be used.

If musical instruments were to be made using metal casting techniques, bronze would be a particularly useful material. be.

Traditionally, musical instrument design has evolved without the use of more advanced mathematics.

A percussion instrument constructed according to the present invention can be used to experiment with various combinations of variables associated with the instrument. It can be designed by However, mathematical modeling and analysis This has enabled the inventors of the present invention to carry out the invention usefully in a relatively short period of time. number The details of the scientific analysis will be explained below.

Figure 1 shows a simplified form of a five-line star formed by bending a thin rod. show. The independent dimensional parameters are (i) the portion (al.

a, and aS) and (it) the included angle ( θ and Φ). The metal rods used to construct the original instrument were thin in size. This shows that the rod approximation formula is effective. (This is true for finite element packages. This is the same as the usual approximation for the beam behavior performed in the )Math The next assumption (simplification) made for modeling is the plane of the part forming the five-line star. that the instrument is played using a hammer blow that has a velocity only at It is. Such a shock excites only the modes located in the plane of the instrument. irrational In the hypothetical case, when other vibrational modes are excited, the amplitude of the in-plane mode becomes much larger than the amplitude of the out-of-plane mode.

Another simplification made to the initial mathematical analysis is that the five-pointed star structure has sharp corners. It is assumed that there is. This assumption eliminates one parameter, namely the corner curvature. and combine the analytical solution for the straight rod section with appropriate boundary conditions at the corners. can be done.

The propagation of a transverse elastic wave across a thin rod is expressed by the following equation.

y is the movement perpendicular to the rod, X is the measured length of the coordinate along the rod, ρ is the density, E is the Young's modulus of the rod material, and a is the diameter of the rod. Do the following The above equation, with appropriate correction for longitudinal motion, is It shows the behavior of a straight section and is simply defined as (i) a bend where two rods meet, and (ii) There remains an appropriate condition to be imposed at the free end of the stave. In this way, actually The analytical solution to this general representation of the problem is usually the mode frequency This can be achieved by simply and quickly calculating numbers.

Examining equation (1), we can see that its general solution can be written in the form of the following equation. It shows.

y, (x) = a, cos kx + β, cosh kx +7. sin kx+δ, 5inh kx (2) k is expressed in terms of angular frequency by the following formula: It is the wavenumber given by equations (1) and (2).

In equation (2) referring to the part of the rod with the subscript n, α1, β1, The quantities γ and δ are constant and their values are determined by the boundary conditions at .

However, equation (2) only describes movement perpendicular to the axis of the rod.

To complete the explanation of the vibrations, the possibility of movement parallel to the axis of the rod is also considered. I have to think about it. For the part n of the rod, the sign of ε is used to indicate the parallel movement. The number is used. Each ε, is considered constant over the length of the associated rod, This means that the ability of waves in the longitudinal direction of the rod material is denied. this This means that the frequency of the normal modes associated with longitudinal waves is higher than the frequency of the bending modes. much higher and therefore outside the frequency range in which the mode to be tuned is located. Physically justified.

Since the five-star-shaped rod has five straight parts, there are 25 unknown coefficients. Ru. However, the five-line star structure is a plane of symmetry indicated by the axis oC in Figure 1. It should be noted that the mode is symmetric with respect to this plane. This means that it should be either asymmetrical. By applying this condition This reduces the number of unknown coefficients to 15.

However, the above 15 coefficients are sufficient to describe the dynamics of the problem. Not. In particular, it is necessary to appropriately balance the forces and moments at the corners of the five-line star structure. be. The bending moment is determined by (i) the elastic modulus, (11) the radius of the rod, and the right angle is properly written in terms of the second derivative of the movement y. Similarly, the shear force also depends on the elastic modulus and and the third derivative of orthogonal movement. However, regarding the tensile force of the rod, The explanation requires the introduction of a tensile force T that varies over the length of each rod. follow Therefore, another five independent quantities are introduced for only the corner compatibility conditions. Figure 1 These are O used for corners (or for centers) Symbols used and "rl'l　rlAI　Tt',"r2'l　T You can also specify the rod number, such as s'. Ten at free end C tion will clearly disappear. Considering the symmetry, the tension for half of the musical star is It is only necessary to specify the

Adding the 5 tension amounts to the 15 independent movement parameters results in a simple A total of 20 unique elements are required to specify the dynamics of the purified thin rod model. Provide set parameters. Thus, the 20 linear equations for these quantities An independent expression is required for Once these are written out and resolved, the A nonlinear equation is provided for the number, or equivalently, at frequency ω, the solution is a five-ray star. An expression is provided that is the mode frequency for the shape.

Now, for each of the two bent parts A1 and B (see Figure 1), is that the parts of the rod are continuously (in the case of two formulas) joined to each other, and that Their slopes θy/δX are matched (in the case of one equation), so the bending angle is distorted. (as the distortion in the bending angle gets an indeterminate moment around the junction point) ) is necessary. Additionally, consider small elements of the rod in bends. For example, the bending motion of two rods at the joint if their motion or growth remains must be equal, θ8y/θx! It means the continuity of (1 formula).

Finally, the forces exerted on the element by the two rods are balanced diagonally across the plane. (provide two equations including θ"y/&x", T and bending angle).

Therefore, there are 6 equations in A and another 6 equations in B, for a total of 12 equations. Provide a formula.

At the free end C, both the bending moment and shear force should disappear, and a2y /δx"=0 and a"y/θX"=0 (two further equations) are provided.

The tensile force − is already set equal to 0 by not including it in the unknowns. It is.

The length of each rod or section due to the effect of the difference between the tensions at the two ends The motion in the direction will be considered below. This difference in tension is equal to the mass of the rod times its acceleration. Therefore, the travel distance (ε), rod length, cross section and density, and frequency It is proportional to the power (3 equations).

Therefore, a total of 17 linearly independent equations are provided. Thin rod model da The remaining three equations required to determine the parameters necessary to define the dynamics is derived with respect to point 0 on the plane of symmetry, and is different for symmetric and asymmetric models. Ru. For a symmetric model, clearly ay/ax=0 and θ”y/ax’= It is 0. On the other hand, the need for a fixed center of mass requires T1°20. antisymmetric model For the case, the symmetry is y=o, a”y/F3x寞=0 and Fj’y/δx ’=0. In each case, three separate equations are provided.

Since no external forces are involved, the 20 equations are homogeneous and there is no actual solution. A necessary and sufficient condition for this is that the determinant of these coefficients be zero. This determinant From formula (2), it can be seen that the coefficient is, for example, cos ka'F'cosh ka. It is complex, as you can see that it involves quantities. The inventors of the present invention believe that once the elements Given the mathematical form of , to evaluate the determinant by choosing the quantity k (Cambridge University Press, New York, 1986) Published by University Press, New York) “Quantity A double book called “Numerical Recipes” Ichi Breath (llf HPress), Bibi Flaneri (BPFlan) Nery), Varnish Nietoikolsky (SA Teukolsky), and Books by W.T. Vetterling One of the computer programs published on page 39 of . Selection U< Using this program, we calculated the value of k to make the determinant zero. Next, formula (3) Using , the values of the elastic constants were inserted and these k values were converted into frequencies. This operation Wrote a separate computer program to run. Microsoft Using Quick Basic (Microsof tQuickBasic) The first 6 to It provided frequencies of seven tones. The speed of this part of the analysis can be improved by first using algebraic operations. Further improvement could be achieved by lowering the rank of the determinant. The corresponding I[limit lx calculation Requires extra constraints and rigid body modes that exist in some implementations There were no problems with exclusion.

The results calculated using this analysis method are shown in Figure 2, which shows a diameter of 12°. A 7mm and 1m long steel rod is gradually bent into a rectangle and then bent in the opposite direction. This shows the fluctuation of the first hexatone frequency when it is bent back. In Figure 2, θ and Φ The angle of is defined in Figure 1, and the length of the part is as shown in the formula below. It is selected as follows.

It is clear that there are large changes in the relative frequencies of scales, and that there are significant changes in the relative frequencies of scales. A shape that provides approximately harmonic relationships between wavenumbers or a possible effect on the strength of the peaks achieved. It suggests that. By using such analytical approximation methods and the tuning principles described below, Once a suitable shape is determined more primarily, the shape can be modified by including distinct curvatures at the corners. Refining the shape is a relatively simple task using a finite-wire package.

As mentioned above, the musical instrument according to the present invention is limited to a symmetrical shape, and the curvature at the bending part is changed. By avoiding the possibility of Five parameters (al + at + ax l θ and Φ) can be used That is clear. This means that you can tune the pentatonic scale, and even more usefully, you can tune the basic pitch. This shows that it is possible to tune the pitch and the ratio of the frequency of the four-tone scale to it. this Basically, it is clearly tuned in the church bell or in the carolon. is the number of scales.

In the five-line star shown in Figure 1, the basic pitch is the combined part (a, +2 at+2as). Parameters to tune this instrument It is convenient to set the set to (R21t Rs++ θ, Φ). However, R41 =at/a, and R41=at/at.

For bell or gong-type percussion instruments, there is a technique known as global listening or analytical listening. You can listen to sounds in two ways. In global hearing, the objects of perception are sufficient. A defined musical pitch and a characteristic musical or timbral quality. analytical In listening, the object of perception is the set of individual partials that make up a sound. Accepted product For these instruments, the relationships between the partials are such that they activate global listening. This means that the most prominent partials are integral (harmonic) in frequency. This is most easily achieved when there is a substantially uniform frequency relationship.

Such a relationship can be written as a product of prime signs, where n, ml 8 is small is a positive or negative integer. The required tuning accuracy is: (i.e. the tuning produces pronounced partials in the octave) ). 2 and 3 occur (i.e., significant partials 5th and 6th intervals) fairly severe, but major and monotonous thirds It becomes less severe as it occurs, including second, third and fifth notes. Seven degrees or more The adjustment of the pitch including the tonic is not really a problem as far as consonance is concerned. part in sound The exact order of the articulations and their relative strengths are important analytically, as they are not commonly listened to. The higher the tuning, the stronger the partials and the general frequency distribution as well as the tonal quality. It has a strong influence.

Table 1 shows the overtones for the musical pitch when tuning the five-line star-shaped instrument shown in Figure 1. (i.e., “legitimate”) frequency ratios are listed.

Table 1 Overtones or “legal” pitch ratios (The first line is about C3, the second line is about C3) C+ E+ F+ G+ C*Es GI C4E4G4CI EbiEsGsI 5/4 4/3 3 /2 4 5 6 8 101216 96152024.25. 3125 ．． 3333. 375 1 1.25 1.5 2 2.5 3 4 4.8 5.6 In Table 1, the subscripts for the pitch signs indicate where they occur. Indicates the octave, C4 is the "middle C" on the piano keyboard, and C1 is the lowest This is C. For example, notes on a keyboard instrument like the piano are tuned to [well-tempered J]. , and all fifths are about 0. It is lowered (tuned) by 1% by a semitone. , all 12 notes of the scale have the same frequency ratio to their neighbors 21/l! exists are doing. This result differs from the double power ratio 5/4 and 615 by about l percent. Generates major and minor thirds.

In order to generate a satisfying bell-like sound using the five-line star instrument according to the present invention, The use of a particular partial, typically the strongest lower partial, that is considered the bell's nominal pitch. and tune at least four prominent partials to small integer ratios. What if it's a purpose? If the purpose is to generate a sound like the bell of a church, a minor third pitch is used for this nominal pitch. It is highly desirable to include a degree interval (6:5 or one in an octave) .

For a straight rod with radius a and length and free end, the nth scale The frequency of is given by the equation below.

A is a constant that varies depending on the density of the rod material and its Young's modulus. This way Uni, the scale frequency is 0.36:1.00:1.96:2.56:3.24:- --- has a ratio close to the order that can most usefully be written as one. lowest Frequencies are well removed from other frequencies and are radiated very efficiently. Therefore, the frequency of the second scale should be considered as defining the nominal pitch. is logical. From Figure 2, the lowest scale of the bent rod is similarly the upper scale. , and therefore the same designation assignment for the musical instrument of the present invention. Find out if it can be adopted. The second scale is also the same as that which defines the pitch of church bells. It is also worth noting that this can be considered generally.

Therefore, the next step in selecting the tuned form of the stave is to consider the four-dimensional parameters. data space lR*+, R□, θ, Φ), and use the second scale as a standard. The goal is to find a form that has the frequency ratio or the required simple form. this work is potentially extremely wide-ranging in quantity, but as shown below, it is possible to progress one note at a time. and can be greatly simplified by adding one parameter at a time.

The sound resonator (radiator) connected to the instrument can be tuned to the second scale, and can be tuned on the spot. In this case, there is almost no dissipation at this lower frequency, so the secondary name The 1g-order frequency is of little importance. Therefore, this secondary nominal frequency can be ignored. , and only the higher scale frequencies need to be considered for the fourth scale. 2 pieces Assuming reasonable values for parameters, e.g. side length ratio, R21 and R11 By calculating the scale frequency over the grid of about 5 x 5 points by 81, And the required times ffJ,! By drawing a shape (θ, Φ) that fits the four wave number relationships, , which enables quantitative exploration of a two-parameter (θ, Φ) shape space. Shown in Figure 3 The basic plane of the three-dimensional shape space is, for example, 2:l or 3:l for the second scale. This is an example of the outline for the third and fourth scales at such an allowable frequency ratio. tuning If there is a solution to the problem, then these two contours are accessible (θ, Φ) Is it necessary to intersect at a point in space?

Acceptance of a similar set for another value of one of the remaining parameters, e.g. R11 It is possible to expand the phase space to three dimensions by calculating 51 of the Tsuru (θ, Φ) shapes. You can do something like that. Therefore, the plane in the three-dimensional (θ, Φ, R1+) space is shown in Figure 3. The corresponding frequency ratio tolerances for scales 3 and 4 can be drawn as shown below. Ru.

If a solution actually exists, these two surfaces intersect at curve AB. Insert.

Draw the third plane in the space of Figure 3 corresponding to the appropriate ratio to the frequency of scale 5. I can write something. This surface is, for example, the solution for ditone scales 3 and 4 at point S. If we were to cut line AB, this point would be for scales 3, 4 and 5 for scale 2. We show a satisfactory solution. Next, repeat this process to include the remaining parameters and place point S into the curve. , and search for the intersection with the plane for scale 6 at the allowable frequency ratio. It can be continued by doing so.

The advantage of this procedure is that the amount of shape space that needs to be explored at each stage is set in advance. This greatly reduces the required calculation time. It is to let it go down. In fact, the orthogonal (θ, Φ) and (Rt+, Rs+) Searching for a solution by sequentially iterating through the shape space means that the solution points in the shape space can be roughly This is an effective method if the location of the In this way, Figure 4 shows the correct solution. (θ, Φ) empty for Rz+=2, Rs+=1, which is close to the ratio but does not match Indicates the part in between. This subspace is marked S++S++ and Sl, . There are three regions marked with Close to many intersection points of the solution surface. The search for solutions is then carried out directly in these regions. Vine limited to nearby areas.

Using the methods described above, these solutions address the problem of tuning ideal sharp corners. It was elaborated against. The search has not been completed completely, so there are some very different edges. Other solutions for length ratios are also possible. Only solutions related to region S1 are basically accurate There was. In the case of region S I 1 and Sl, 1, the solution surface passes through all the solution points. rather than simply approaching it. Details of the initial solution are listed in Tables 2 and 3. enumerate.

Table 2 initial shape R,, R□　θ　Φ Solution T 1.95 0.92 96° 93° Solution 11 2.20 1.07 13 5° 46° Solution III 1.85 0.97 146° 106 Table 3 initial scale frequency ratio Solution! (0,35) 1.002.003.004.806.00 pitch (F #,) C, C, G, Eb, G.

Solution 11 (0,32) 1.00 1.5 dishes 1.98 2.99 4.80 Pitzchi (E+-F+) Cs G-C4G4 2b@Solution Ill (0,31) 1.00 1.25 1.462.494.04 pitch (E,) C, E, According to G, E, CI solution ■ (see Table 2), the two free ends of the five-line star structure are The top angle is closed to the extent that they overlap. This can be seen from the five-line star structure plane. The free ends should be sufficiently separated by bending with a slight offset. Scale 2? up to 6 can be tuned accurately by the sharp corner approximation method, and at scale 5. Provides a well-expanded set of scales, including a minor third. the call of these notes As for the nominal pitch, the entire nominal pitch of the five-line star structure is tenor C (C1). more directed. Unfortunately, the subnominal scale l has a dissonant pitch close to F#, However, it cannot be ignored for the reasons mentioned above.

Solution] ■ indicates a [coat hanger] shaped instrument, and as can be seen from Table 3, the instrument has the following shapes: There is a well-distributed set of scale frequencies. In this case, the secondary name is overtone frequency. It is located sufficiently close to the wave number. Again, a minor third (in this case at scale 6) There is a scale 3 with a frequency ratio of 1. 5, so the frequency ratio is 0.5, and the spirit For physical reasons, there is an implied fundamental pitch one octave below the nominal pitch.

In solution I11, which has an extremely flat shape due to the small value of Φ, the scale frequency is 1. Densely concentrated within the range of 0 to 2.5, with 3 or more for the nominal pitch. Contains the upper major third. Because the intervals of these scale frequency ratios are close, The main pitch is again below the nominal pitch. However, this five-line star shape , which is unsatisfactory for practical reasons, especially when rounded corners are considered. Not a spider. For this reason, solution III was not pursued by the inventors of the present invention.

Not necessary if the percussion instrument is cast or molded with sharp corners. The final step in the mathematical modeling method is to modify solutions l and 11 to round the corners. It is to include the effect of having . For this part of the design implementation ( - Strariya, N5W2007, Ultimo, Smale Street 3, Suite 3 07 G&D Computing, 5unit 307, 3 Sm1l 5treet, UItiox+, N 5W2007. Finite element pack (manufactured by Au5tralia) The cage "Strand 5" was used in an AT compatible microcomputer.

This package has access to all files and executables by its structure. Therefore, the necessary exploration of the shape space in the immediate vicinity of the initial solutions ■ and II This calculation is used because it is relatively easy to write a batch program to execute is particularly appropriate. It is not necessary to include external constraints on the stave. this method to optimize the staff shape for the effect of rounding the corners. For type A, it simply takes several hours.

If the effect of rounded corners should be included in the mathematical modeling, the curvature should be It is necessary to define what to measure. The selection is (f) between the centers of curvature, (ii) between the between the intersections of the axes of cut cut 11, and (iii) from any other method. be exposed.

The selection will affect the result if the corner radius is large or the bend angle is large. Is there a noticeable impact?

For steel rods, the smallest reasonably achievable heel bend radius is The bending radius of the middle part corresponds to bending around the body and is approximately equal to the diameter of the rod. Fix the straight edge-to-length ratio for at least this magnitude by providing It's about correcting. Since the bending radius is concerned with the absolute first order, the total length of the rod is specified. It was determined that it was necessary to set a value of 100 mm. 12.7mm diameter rod If the bending radius is set to 15 mm, there is almost no need to change the shape of the five-line star shape. do not have.

However, for this reason, it is not possible to curve a small five-line star by simply matching the scale. There is no flexibility in the radius. Therefore, the bending radius γ of the neutral part is (20 mm inner bending 26 mm for a rod of 100 mm (corresponding to the radius), so the same rod The bending of the smaller staves made from scratch became severe. Based on these assumptions Solutions I and 11 were then refined as shown above. 26mm radius adopted required significant changes in both the length and bending angle of the rod segments. the final solution Table 4 shows the length of the straight section or the curvature of the corner along with the bending angle. Provides the distance between the centers.

Table 4 The last practical design Dimensions a+(an) at(nn) as(mm) θ Φ r(an) Design solution 1 1t13 258 109 90° 90° 26 Design Solution II 113 250 100 13G° 19° 26 For solution I, use a straight line to round the corner. Adjust the side lengths very slightly and reduce the interior angles to achieve better accuracy than 2%. Is it necessary to bring the designed scale frequencies closer together? The results are shown in Figure 5. Ru. It's basically a rectangle, with the larger sides overlapping. Solution] Adjustment of I The resulting shape is shown in Figure 6. In this case, by rounding the bottom corner, 'iU? L significantly changes the distribution of This significantly reduces the corner Φ relative to the shape of the sharp corner. need to be reduced. Nevertheless, the original calculated scale frequency is 1 part It has been well restored over cents. However, depending on the degree of this angle change, The five-line star shape corresponding to solution I11 cannot be produced by simply bending the rod. supports the view that it is not possible.

By relaxing the flatness constraint applied to the finite element method, the practical importance is reduced to Calculating the frequency of the out-of-plane vibration mode by adding it to the plane scale is limited. It is possible. These non-harmonic out-of-plane scales allow the performer to understand the quality of the instrument to a certain degree. be able to control the degree. The reason is that these This is because it is possible to strike to minimize or maximize the amplitude of the scale.

The five-line star instrument designed as described above does not require manual tuning; The floor frequencies are defined by their basic shape. Same thing or some tradition The same can be said for traditional church bells, but fine tuning of the scale frequency of church bells is done by turning the bells on a lathe. Generally, a small amount of metal is removed from the inner surface of the This is a helpful method. Tuning the first hexatonic deviation and possibly higher notes A certain procedure for tuning scales is also used for five-line star instruments. is clear.

A practical approach to the above-mentioned tuning problem in the case of bells is Developed by Noei Mills (RG J Mills) and released in the United States in 1989. Acoustical Society;! (Journal of the Acoustical 5o Society of America) Volume 85, pages 2630-2633. [Bell tuning using the δ1 stroke method] 1lsby a Linear Programming Method” ) in his paper entitled.

This approach removes a small amount of metal from each of a number of bands across the inner surface of the iron. This includes evaluating the effect of tuning on all scales. Then the linear meter A drawing method is used to define a metal removal plan that provides optimal tuning. such a method used a finite element package to remove metal from a rod at various locations. By detecting the effect of can be executed immediately. Cast metal or molded ceramic five-line star music In the case of vessels, the cross-section 11 method and shape of the five-line star-shaped part may be changed, or certain parts may be changed. Fine tuning can be achieved by including a "weight" with a wide cross section at an appropriate position. Wear. Finely tuning a metal five-line star-shaped instrument by welding [weights] It is also possible. However, the inventor of the present invention believes that in fact generally does not require fine tuning.

Once a suitable design has been achieved for a staff-star instrument of a given size, the sound Scale this design up to the size required to provide the required set of nominal pitches for the floors. You can also mix it with kale. There are three possible ways.

Conceptually, the simplest method is to include all dimensions of the musical star (lot length, diameter and The aim is to evenly scale the bending radius and bending radius. From formula (4), the musical scale It can be seen that the frequency varies inversely with the scale factor. Practical difficulties with this method The stiffness is due to the fact that each stave star requires a different rod diameter and bending radius. be.

On the other hand, at the extreme, both the rod diameter and bending radius are kept constant, and the length of the rod section is You may adjust the scale only. In this case, for each different member of the set, It is necessary to perform a separate finite element optimization to include the roundness of the curve. The restriction imposed by fixing the radius is that the resulting stave radius This means that the overtone structure of the instrument must be changed at a certain nominal pitch; It is not very successful.

The most practically attractive scaling dimension is therefore for all five-star instruments. Using rods with the same diameter, scale the rod length and bending radius, and If , the scale frequency is inversely proportional to the square of the scale factor. -Ring's law equation (4) is used again. For each size of five-line star instrument Although it requires making different bending dies, this method has economic advantages.

Table 5 shows the initial structure constructed by the inventor of the present invention based on the calculated image corner design. Figure 2 shows the measured scale frequency ratios for two five-line star instruments. calculated frequency The measured deviation from the number is due to the fact that the rod was bent by hand with a simple jig. Line star shape thick (due to small deviations from the desired shape of the instrument. Check the design principles That alone is enough.

As shown in Table 5, the out-of-plane scale forms a series of non-overtone scales that intermingle with those of the plane scale. The fifth floor frequency is shown. In fact, the necessity due to overlapping the edges in solution I is Despite the natural lack of flatness of the five-line star instrument shown in Figure 5, almost exclusively It is easily possible to strike an instrument in such a way as to excite in-plane or out-of-plane scales. . The large inharmonicity of out-of-plane scales generates extreme abnormal sounds, which can be of some interest to the performer. Get the effect you want.

Table 5 Five line star shaped instrument 1 0.35 1.00 2.01 3.05 4.79 5. 93 (measured) Off-plane scale 0.39 1.43 2.40? 4.97 9.57 (measured ) Five-line star-shaped instrument II O, 331,001,491,963,054,75 (measured fixed) Before out-of-plane # 0.83 1.06 1.42 2.57 4.03 5.17 (I l11 set) When evaluating musical actuation, a simulation of the sound of a traditional Western church bell can be used. It's just a matter of subjective judgment, whether you want to try it out or just want the sound to be enjoyable. This is a problem.

For traditional church bells, the I & first pentatonic scale is (i) frequency relative to the second scale. When 1=2, it is a hum sound, that is, a low tone, (ii) the fundamental tone, which is the reference frequency, and (iii) the th 3 tones, i.e. minor third (6: 5), (iv) 5th interval, i.e. perfect 5th degree and (V) vocative, or octave (2:l). Invention of the present invention Both of the first two five-line star instruments constructed by Not even close. Solution I is for the second scale of 2, including the minor third, except for the first scale. contains the correct frequency ratios up to the power, but they are not concentrated but rather distributed over several octaves. Solution■ focuses the scale frequencies more tightly This also has a minor third tone. Solution III is scale frequency or church bell. , or as mentioned above, this design is not practically implemented. Not yet. Therefore, the musical actuation of the present invention is not subject to accurate simulation. cannot, and must depend on the generation of an appropriate subjective bell-like sound.

In summary, the first few scales form a series of scales with harmonically related frequencies. We have explained how to optimize the shape of the framework of a five-line star-shaped musical instrument. This person The method is relatively simple and given that more instrument parts are used, the target parameters Although the meter rapidly increases, tuning various sets of scales for the five-line star instrument. either tune a set of scales within a framework of different shapes. can be generalized to.

Since creating the first two "staff star" instruments, the inventor of the present invention has shown a schematic diagram in FIG. As shown, a percussion instrument was constructed with 13 "staff-star" instruments. Each five-ray star The musical instrument is constructed in the form shown in Figure 6, and is suspended from a frame 6K using nylon thread. It has been lowered. The five-line star instrument is also connected to a broadband non-resonant sounding plate 62. A cavity, that is, a resonance chamber 63 is provided at the back to improve the sound propagation of the instrument. resonance Both the board and the resonance chamber are sloped from the bass end to the treble end (along the non-center line). connected to a five-line star instrument by an elastic string (attached to the soundboard at the point) There is. The soundboard, like a guitar or harpsichord, has a glued backing. It is supported by The distribution of these ribs and the cavity behind them, that is, the resonance chamber, The volume should have a suitably shaped sound dissipation response over the playing range of the instrument. It is something that This five-line star-shaped instrument has 13 steps, and this instrument has a diatonic scale. The instrument was ``tuned'' so that it could be played over a period of time.

This musical instrument is soft and beautiful when struck with a hard mallet to excite the five-line star-shaped instrument. Generates a harmonious sound. When the performer uses a soft mallet, the instrument has a warm tone. Makes a buzzing sound. The sound produced by increasing the hardness of the drumstick, i.e. the gavel. By increasing the higher frequencies of When it hits, a bell-like sound is produced. If a five-line star instrument is struck on one side, then A shocking sound is generated. The fact that the out-of-plane vibratory scale is not adjusted to harmonic relationships means that To the extent that it is useful to the performer, the total degree of freedom is Providing increased possibilities by building from rectangular steel bars instead of from rods It turns out that it does.

A large number of microphones were installed in the resonance chamber of the musical instrument shown in FIG. These my The Crophon is a musical instrument that uses an acoustic resonator, electronic amplifier, or It allows for use with both electronic and electronic amplification.

In order to complete this discussion (in order to test the scaling method that will be adopted later), An example of the scaling of the five-line star instrument (used by the Ming Dynasty inventor) is Below is information regarding using a sound radiator with a "line star" instrument.

Scaling example The purpose of this scaling example is E+ = 41. Shape of solution ■ for 2Hz note (See Figure 5) Select solution I for the shape of the five-line star-shaped instrument The reason is that it is more compact than the shape shown in Figure 6 (Solution 11) and has a smaller lock. This was because the amount of wood used was small. The five-line star instrument is quite large, so 14 mm diameter steel rods were used to provide weight and stiffness.

The five-line star-shaped instrument of the original solution (2) had a rectangular shape with θ = Φ = 90 degrees. of the rod The total length is 813 mm. The length of the part measured against the straight part is a+ = 85 mm. ri, at=212 mm, as=89 mm. Each corner has a bending radius of 26mm There was a neutral part. When made from a rod with a diameter of 12.6 mm, this five-pointed star The shaped instrument provided an internal bending radius of approximately 20 mm. Stave star instruments are reasonably good It was in tune and a frequency of approximately 185 tlz was measured. This five-line star-shaped instrument is the note E. The scale was adjusted to generate the necessary lower pitch for 1.

Assuming that the original instrument had a rod length of 11, a bar diameter of d8, and a frequency of f, The new instrument has a bar diameter of d2 and a design frequency of 1. If so, for a new instrument Rod length 1. is given by the following scaling algorithm.

Using this relationship for rod length, an equivalent inner bend radius of 38 mm A new five-line star-shaped instrument has been successfully constructed that remains with a 90-degree internal bend angle. .

In order to improve the propagation of sound, the percussion instrument of the present invention includes one of a number of different sound radiators. Either one can be adapted, but experience shows that the instrument in question is For shaped instruments, resonant structures are preferred over broadband radiators. most A simple resonant structure is a diaphragm-coupled pipe resonator. However, A tube-loaded cavity resonator or an air-loaded resonant diaphragm may also be used. these We will consider alternatives below.

At 41.2 Hz, the nominal sound wave length is approximately 8.25 meters, so the high A quarter-wave pipe resonator excited as an impedance has a sound wave of 2060 mm. have a long life. Although this length is long enough to require bending, it is still practical. Both Assuming that the sounder is made from a pipe of internal diameter d, its physical length L is L=2060-0.3d　m Also, d is expressed in millimeters. If the pipe is folded back using two right angle bends, If the pipe is piped, its length is measured approximately along the centerline of the pipe. The pipe is probably 3° Extend the length by O millimeter and cut the strip about 1/3 of the diameter over the length of the extra section. It is best to cut the lot. This slot is then gradually coated ( (similar to the pipes in some types of organs) can be tuned. Alternatively, the Attach a tuning sleeve to the outside of the pipe so that it slides over the pipe and increases its length. That's fine. The diaphragm covering the driven end of the pipe is The wavenumber should be very low and moderately strained. Diaphragm thickness and It is necessary to experiment to determine the optimal combination with the options.

Although it has a relatively large volume, its shape is not important and it can be connected to the air and excited by the membrane at its base or side wall. To design a Helmholtz cavity resonator, the volume of the cavity must be V (cubic meters). ), and the connection is carried out with length L and diameter d, both in meters. Assume something. At a selected frequency of 41.2 Hz, the resonator's pi The loop length is given by the following relationship:

The volume is approximately 0. Required pipes for a cavity with a length of 6m and a pipe diameter of 100mm The length is approximately 270 mm. Some part of this length protrudes into the interior of the cavity. .

It would also be advantageous to provide a means to tune the length of the pipe.

Another type of resonant radiator used with single-staff instruments is the timpani system. membrane and cerator, or in its simpler form, the bass drum member. Similar to Bren. The membrane is the regular pitch of a five-line star instrument, similar to the timpani. It is tuned to the pitch. The installation of a five-line star-shaped musical instrument selects the strings to strike the timpani. around the edge, i.e. from the edge to the center of the membrane. Is it necessary to encounter membranes in other places?

The same goes for the bass drum resonator. However, the tuning is not so strict, and the installation is difficult. is not offset to one side, but rather in the center of the membrane. however, Generally speaking, the resonant sound it provides is inferior to that of a timpani-type resonator, which has several scales related to overtones.

For experts in the technical fields of musical instrument manufacturing and mathematical modeling, there is a term known as the "staff star". The adoption of the term means that the structure has the shape shown in Figure 6 and that the fifth Since the angle of is not immediately obvious to non-mathematicians, they will probably agree that it is inappropriate.

However, the inventors of the present invention are aware of (a) the mathematical modeling method used, and (b) ) Considering the relationship of the present invention to the orchestral triangle, the use of this dn is I like business. Further, the present invention described above is not particularly described or illustrated in this specification. It is recognized that other changes and modifications may be made, and that the invention covers all that come within the scope of the claims. It should be understood that this includes any changes or modifications. These changes or modifications shall be made in accordance with the applicable the use of hard plastics or modified materials in the formation of parts of musical instruments; the use of one or more arcs; Providing shaped or curved sections, tubular structures, multi-stage casting techniques several connected musical stars (or other multi-part instruments) and, in the case of an instrument of the type shown in Figure 7, a or include a mechanical drum separate from it. More than Listing doesn't mean everything.

FIG. 1 ('IJ $ too FIG. 7 Procedural amendment (voluntary) November 15, 1994 Eyelid transfer

Claims (18)

[Claims] 1. Contains three or more parts, and the parts are generally coplanar and non-collinear. The part is integrally formed from a material that is rigid and has vibration characteristics at room temperature, and A percussion instrument that emits a musically harmonious sound when one piece is struck with a gavel. A percussion instrument according to claim 1, having 2.5 parts. 3. The length of said parts and the angle included in adjacent parts are such that one of said parts is struck struck by a tool to excite a vibratory scale located in the plane of said part of said instrument and the sound emitted by said instrument has a series of harmonically related frequencies. The percussion instrument according to claim 1 or 2, which is a percussion instrument. 4. Each part has a generally uniform cross-section, and each part of the instrument has basically the same cross-sectional shape and size. The percussion instrument according to any one of claims 1 to 3, which has a vessel. 5. The said part is a part consisting of a metal or alloy rod or bar, and the front A recording instrument is formed by bending a metal or alloy rod or bar. The percussion instrument according to claim 4. 6. 6. A percussion instrument according to claim 5, wherein the metal is mild steel. 7. Claim 1, wherein the portion is formed by casting molten metal. The percussion instrument according to any one of paragraphs 2, 3, and 4. 8. 8. A percussion instrument according to claim 7, wherein the metal is bronze. 9. The musical instrument comprises (a) granules of at least one ceramic material and a temporary binder; (b) press-molding the mixture to form a green body having the required shape of the musical instrument; The green body is fired at a high temperature, and then (c) large cracks are formed in the fired body. The sintered body may be cooled to room temperature at a rate sufficient to prevent the sintered body from forming. It is formed by mechanically forming a strong ceramic material percussion instrument. A percussion instrument according to claim 1, 2, 3, or 4. 10. The instrument is made by bending a steel rod with a radius of 26 mm, and It has several parts, (a) the five parts form a symmetrical shape about the center point of the central part; (b) the central portion has a length a1; (c) each portion adjacent to said central portion has a length a2; and (d) each portion adjacent to said central portion has a length a2; (e) said central portion and each adjacent portion; The groove angle between them is θ, and (f) the groove between the parts whose lengths are a2 and a3. The angle is Φ, and (g) the ratio of a1:a2:a3 is approximately 1.00:2.50:1. 06, and (h) θ and Φ are approximately 90 degrees Percussion music according to any one of claims 1 to 9, characterized in that: vessel. 11. the instrument is made by bending a steel rod with a diameter of 26 mm, and It has several parts, (a) The five parts form a shape that is symmetrical to the center point of the central part, and (b ) the length of the central portion is a1; (c) the length of each portion adjacent to the central portion; (d) the length of each part far from the central part is a3; and (e ) The groove angle between the central portion and each adjacent portion is θ, and (f) the length is a2 or The groove angle between the parts called and a2 is Φ, and (g) the ratio of a1:a2:a3 is It is approximately 1.00:2.21:0.88, (h) θ is approximately 136 degrees, and Φ is approximately 19 degrees. The percussion instrument described in item 1 above. 12. Claims 1 to 11 include means for supporting said plurality of parts. The percussion instrument described in any one of the above. 13. The said part is acoustically connected to the sound radiator to increase the efficiency of sound generation by the musical instrument. Claims 1 to 12, which are combined percussion instruments. 14. 14. The sound radiator according to claim 13, wherein the sound radiator is a resonant radiator. Percussion instruments. 15. 14. A sound radiator according to claim 13, wherein the sound radiator comprises electronic amplification means. musical instrument. 16. A plurality of percussion instruments according to any one of claims 1 to 11. each percussion instrument in said assembly has a characteristic of each other percussion instrument in said assembly. Each percussion instrument has a characteristic pitch that is different from the normal pitch, and each percussion instrument has a mechanical or is acoustically coupled to an acoustic radiator or to an individual acoustic radiator. musical instrument. 17. Claim 16 including electronic amplification means associated with each acoustic radiator. Percussion instruments listed. 18. Claims 1 or 16 generally as hereinbefore described with reference to the accompanying drawings. Percussion instruments listed in.