US3866506A

US3866506A - Soundboard construction for stringed musical instruments

Info

Publication number: US3866506A
Application number: US407854A
Authority: US
Inventors: Jr Harold A Conklin
Original assignee: DH Baldwin Co
Current assignee: BPO ACQUISITION CORP; Baldwin Piano and Organ Co; DH Baldwin Co
Priority date: 1973-10-19
Filing date: 1973-10-19
Publication date: 1975-02-18
Anticipated expiration: 1992-02-18

Abstract

A soundboard for stringed musical instruments in which the soundboard is reinforced by a series of ribs spaced apart by a distance less than one-half the wave length of the vibration of the soundboard at the fundamental frequency of the highest note on the instrument scale.

Description

United States Patent 1 1 Conklin, Jr.

- 1 Feb. 18,1975

1 1 SOUNDBOARD CONSTRUCTION FOR STRINGED MUSICAL INSTRUMENTS [75] Inventor: Harold A. Conklin, Jr., Cincinnati,

Ohio

[73] Assignee: D. H. Baldwin Company, Cincinnati,

Ohio

[22] Filed: Oct. 19, 1973 {21] Appl. N0.: 407,854

3,086,420 4/1963 Yamumoto 84/195 3,443,464 5/1969 Akag' 84/195 FOREIGN PATENTS OR APPLICATIONS 27,771 11/1910 Great Britain 84/195 Primary E.raminerLawrence R. Franklin Attorney, Agent, or FirmMelvi11e, Strasser, Foster & Hoffman [57] ABSTRACT A ndboard for stringed music struments in all in wh' the soundboard is reinforced by a series of ribs spaced apart by a distance less than one-half the wave 1e of the vibration h undboard a fundam frequency of hi st note on instrument scale.

11 Claims, 2 Drawing Figures PATENTEI] FEB] 8l975 SOUNDBOARD CONSTRUCTION FOR STRINGED MUSICAL INSTRUMENTS BACKGROUND OF THE INVENTION This invention has to do with the soundboards for pianos and similar musical instruments, and relates more particularly to a soundboard construction having improved uniformity of frequency response, improved and extended high frequency response, higher efficiency at higher frequencies, and improved tone quality.

In a piano the soundboard is the major sound radiating element. Normally the soundboard is a thin wooden panel coupled mechanically to the strings in ways wellknown to those skilled in piano building, so that when the strings are struck by the hammers of the piano, the vibration of the strings is transmitted to the soundboard. Piano soundboards are customarily constructed of quarter sawn softwood, the usual practice being to fabricate the soundboard by gluing a number of relatively narrow quarter sawn strips together along their parallel edges with the grain of the wood running parallel to the length of the strips. As those familiar with industry practice will know, a perfectly quarter sawn strip of wood is one having the grain line running exactly perpendicular to the surface of the strip when viewed in cross-section. In practice, quarter sawn wood may be allowed to have some angular deviation of the grain from the perpendicular in order to minimize waste.

It is the usual practice to employ stiffening ribs fastened to the surface of the soundboard opposite from the strings, the ribs extending parallel to each other and positioned so as to have their longitudinal axes at right angles to the direction of the grain of the soundboard strips. The ribs themselves are usually made of quarter sawn softwood with the grain of the wood normally oriented in a direction lengthwise of the ribs and hence at right angles to the grain direction of the soundboard strip.

Soundboard ribs serve three basic purposes:

1. to stiffen the soundboard in a direction in which the soundboard itself (without the ribs) inherently lacks stiffness;

2. to add mechanical strength in a direction in which the soundboard is inherently weak; and

3. to help make soundboards more uniform in characteristics from one to the other.

In conventional pianos the number and size of the ribs and the spacing between the ribs varies from one design to another within well-known typical limits. Generally, the number of ribs depends upon the size of the soundboard; the longer the soundboard the more ribs required. The cross-sectional area of the ribs may vary, but generally will be in the range of between approximately 3.0 and 6.5 square centimeters along the mid-section of each rib, the ribs usually being of maximum thickness in their mid-section with their opposite ends tapered to be of lesser thickness. The spacing of the ribs, from centerline to centerline, normally varies moderately, both from rib to rib within a particular instrument and also from one design to another. Generally speaking, however, the spacing varies over no greater range than from approximately centimeters to approximately 18 centimeters. The foregoing parameters are so prevalent as to constitute standard industry practice; and while individual designs may depart slightly from the foregoing criteria, the amount of the deviation usually is so small that it can be ignored in considering the basic performance of the soundboard.

In accordance with the present invention, it has been found that the normal spacing of the ribs employed in conventional pianos produces certain undesirable effects on the frequency response of the soundboard with the result that an important portion of the sound spectrum generated by the strings of the instrument is radiated with lower efficiency and with less uniform efficiency than the remainder of the spectrum. Specifically, it has been found that the frequency response of a conventional soundboard is deficient at high frequencies. In addition, the conventional rib construction re sults in non-uniformity in the instrument scale. Varitions of efficiency in soundboard radiation will cause some notes or groups of notes to be less loud than others.

RESUME OF THE INVENTION.

In accordance with the present invention, it has been found that altering the number, size and spacing of the reinforcing ribs produces a material improvement to the efficiency and uniformity of response of the soundboard, particularly at the higher audio frequencies.

It has been found that if a soundboard strip is driven at one point the sound pressure level at some other point, such as the far end of the strip, depends upon the transmission characteristics between the two points. In other words, if the sound radiating efficiency at a distant point of such a strip is to be uniform as the frequency is varied, then the transmission characteristic of the strip must be uniform. If the transmission response is first measured for a soundboard strip without ribs and then measured with conventional ribs added, i.e., ribs of conventional size and spacing, it has been found that an undesirable alteration of the transmission response characteristics of the strip occurs because of the addition of the ribs. The nature of this alteration has been found to be similar to the effect produced by a low pass mechanical filter in that attenuation of the higher frequencies occurs. The amount of such attenuation has been found to depend upon the number, spacing, and mass of the ribs. For rib arrays normally used on soundboards of conventional design the attenuation effect is significant at frequencies within the normal keyboard range of the instrument.

An important criterion for determining the lowest frequency at which severe attenuation or frequency distortion occurs is the spacing of the ribs. At the frequency at which the spacing of the ribs is equal to onehalf a vibrational wave length along the soundboard strip, a significant attenuation in the transmission efficiency of the strip has been found to occur. As the driving frequency is increased the attenuation also increases, although the response may increase temporarily after a maximum of attenuation at the half-wave length frequency has been passed.

In accordance with the invention, in order to'prevent undesirable attenuation of the higher frequencies, the spacing of the ribs (center-to-center distance between adjacent ribs) must be less than one-half the wave length of the vibration of the soundboard in the direction of the grain at the highest frequency of interest, which is usually the highest note on the instrument scale. In a conventional piano tuned to international standard pitch wherein the note A, the 49th note of a standard 88 note piano keyboard, has a frequency of 440 Hz., the highest fundamental scale frequency of interest is the 88th note on the keyboard, which has a nomial frequency of 4,186 Hz. As will be known to those familiar with piano design, inharmonicity and the resulting natural stretch in tuning of the instrument normally make the highest note slightly higher in frequency than 4,186 Hz., but, nevertheless, 4,186 Hz. may be regarded as the highest standard reference scale frequency.

In order to establish the proper rib spacing for a soundboard it is necessary first to measure or otherwise determine the length of a half-wave of vibration on a soundboard strip in relation to the vibration frequency. This relationship may be determined either empirically, by measurement of propagation on an acutal soundboard strip, or it may be calculated based on assumed or measured values for the parameters of the strip. For typical soundboard wood, a half-wave length in the direction of the grain at 4,186 Hz. will be about 6.35 centimeters for a soundboard 0.635 centimeter (A inch) thick and about 7.78 centimeters for a soundboard 0.953 centimeter inch) thick. Rib spacing must be significantly less than these values in order to have uniform transmission response of a soundboard strip up to the highest scale frequency. The ribs must thus be spaced much closer together than in a conventional soundboard construction.

Another factor affecting significantly the frequency response of the soundboard is the cross-sectional area or mass of the ribs. In general, increasing the weight of the ribs causes significant attenuation to being at a lower frequency and causes total attenuation at a particular frequency to be greater than for ribs of lesser mass. If additional ribs of standard size are used, the total weight of the soundboard and its total stiffness will be increased, and less than optimum performance obtained. Consequently, in accordance with the invention it is desirable to employ ribs having reduced crosssectional width, so that the total net effective stiffness and mass of the soundboard assembly will remain the same or nearly the same as for a well-designed soundboard of conventional construction. It should be noted in particular that it is perferable to reduce the crosssectional width of the rib, rather than its depth, when the number of ribs is increased. This is because the stiffness ofa rib is directly proportional to its width, but varies as the cube of its depth. In addition, the natural vibrational frequencies of a rib do not change if the width is reduced but, on the other hand, if the depth is varied, the vibrational frequencies are proportional to the depth. Therefore, if the rib cross-section were to be reduced by reducing the depth of the rib rather than its width, as the number of ribs is increased, then both the net stiffness and the modal resonant frequencies of the soundboard would be undesirably changed. Consequently, if the number of ribs is doubled as compared to a conventional soundboard construction, the width of each rib should be made approximately one-half that of the original.

It may be noted that conventional soundboards do not necessarily have all of the ribs equally spaced. Typically, spacing on a given soundboard may be 1 1.5 centimeters at the treble end, increasing to perhaps centimeters or so at the bass end of the soundboard. It is not necessary for a soundboard constructed according to the teachings of this invention to have constant rib spacing, but rather the rib spacing may vary over a percentage range similar to that of conventional soundboards, so long as the widest spacing is still less than one-half wave length at the highest frequency for which uniform response of the soundboard is desired.

DESCRIPTION OF THE DRAWINGS FIG. 1 is a bottom plan view of a soundboard constructed in accordance with the present invention.

FIG. 2 is a sectional view taken along the line 2-2 of FIG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT In order to determine the critical rib spacing for any given frequency it is necessary to first determine the length of a half-length of vibration on a soundboard strip in relation to the vibration frequency. Measurement on an actual soundboard strip can be readily made using a narrow longitudinal section of the soundboard strip which acts as a transmission line. While the vibration of the soundboard as a whole is much more complex that that of a narrow strip of the soundboard material, the vibrational behavior of a narrow strip is basically like that of the soundboard itself insofar as propagation of vibrational energy in the direction of the soundboard strips is concerned. Ignoring for the moment the effect of the ribs, the behavior of the soundboard strips is basically similar, once the strips are installed in the piano case, to that of a clampedclamped beam, because the ends of each strip are fixed solidly by adhesive to the massive sides of the piano case. As is well-known to those familiar with vibration technology, the natural frequencies of a clampedclamped beam are the same as those for a free-free beam, and are dependent upon the elastic modulus and density of the material of the beam and on its length and thickness, and may be computed according to formulas available from standard textbooks on sound and vibration. lfa narrow strip is driven in flexural or trans verse vibration at or near one end by a mechanical vibration generator and if the resulting vibration at or near the opposite end of the strip is picked up by a min iature accelerometer and recorded as the driving frequency is varied through the audio frequency range, frequency response data .for the transmission characteristic of the soundboard strip can be obtained. Standing waves are present on the strip and may be recognized as alternate maxima and minima in the vibration intensity measured at successive points on the strip. The distance between two adjacent points of minimum intensity at any particular transmission frequency represents a distance of one-half wave length at that particular frequency. As the driving frequency increases, the wave length or distance between sucessive minima decreases.

Alternatively, if the distance of one-half wave length is to be calculated, it is necessary to know the thickness, elastic modulus, and density of the strip material. It is not necessary to know the width of the strip because propagation of flexural vibrations lengthwise on such a strip is basically independent of width.

The basic equation is:

The equation applies to an homogeneous strip of rectangular cross-section where h is the thickenss of the strip in centimeters,fis the frequency in Hz., V is the velocity of propagation of longitudinal waves in the material in centimeters per second, and M2 is the halfwave length in centimeters.

In order to obtain values of )\/2 versus f, it is necessary to obtain the correct value for V,, The equation for longitudinal velocity of propagation is:

VL /p)1l2 where E is the Youngs or elastic modulus of the mate rial in dynes per square centimeter, and p is the density of the material in grams per cubic centimeter.

If typical valves of E and p are known, the value for V may be readily obtained. If E and p are not known for the wood being used, they may be determined by known methods. However, dynamic methods of obtaining E should be used rather the the method of static loading because the two methods do not give the same answer, and because the vibrational method gives the result that is applicable to pinao soundboards, since soundboard performance under vibration rather than under static loading is the thing of interest. p may be readily determined by dividing the weight of a typical sample of the material in grams by its volume in cubic centimeters.

Piano soundboards normally are fabricated of spruce or a similar wood which is relatively light in weight, a typical value for the density of suitable wood being about 0.4 grams per cubic centimeter. A typical soundboard may have a thickness in the range of about 0.6 to 1.0 centimeters, exclusive of the ribs, and may have a length and width almost as great as the length and width of the piano case itself. For a large grand piano the length of the soundboard may be as much as 210 centimeters and the width 150 centimeters.

In a typical example in which the soundboard strip has a thickness of 0.953 centimeter, a density of 0.4 grams per cubic centimeter, and an elastic modulus of (1.38) l0 dynes per square centimeter, the value of one-half wave length at a frequency of 4,186 I-Iz; would be 7.78 centimeters (about 3.06 inches). In a soundboard strip having the same physical properties except being only 0.635 centimeter thick, the half-wave length value would be 6.35 centimeters (about 2.5 inches). These strip thicknesses represent approximately the extreme values of soundboard thickness encountered in conventional panios. It should be pointed out in connection with soundboard thickness that it is a common practice to taper the edges of the soundboard, the tapered portion usually being confined to a peripheral band around the outside edges of the soundboard which may be on the order of to 18 centimeters wide. As used therein, the soundboard thickness is the value applying to the central portion of the soundboard and it is the thickness which is used to calculate the spacing of all of the ribs.

It follows from the principles taught herein that in order to avoid significant distortion and non-uniformity of frequency response of the soundboard within the frequency range of the basic scale tones, it is necessary to have the distance from the centerline of one rib to the centerline of the next rib less than about 7.78 centimeters for a soundboard 0.953 centimeter thick, and less than about 6.35 centimeters for a soundboard 0.635 centimeter thick. Even smaller rib spacing may be desirable in order to avoid response perturbations within the entire high frequency audio range, which extends above the highest piano fundamental scale frequency. It may be noted from the half wave length formula that the critical rib spacing varies in inverse proportion to the square root of frequency. It follows, therefore, that to double the frequency would require the rib spacing to be reduced by a factor of l/ VTMinimum rib spacing is governed primarily by practical design considerations. Excessive reduction in rib spacing would only increase the cost and complexity of constructing the soundboard without a significant improvement in the tonal result.

As to the width of the ribs themselves, if it is desired to employ a large number of narrower ribs, keeping the same rib depth, and if it is desired to keep the net resulting stiffness of the soundboard essentially the same, the numerical ratio between the width of the ribs (W) and the spacing from the center of one rib to the center of the next rib (D) should be kept constant. This ratio may be expressed by the fraction W/D. By way of example, if it is desired to redesign a conventional soundboard using ribs 2.5 centimeters wide and spaced 14 centimeters on centers so as to have a new spacing of 5 centimeters center-to-center, while maintaining the same net stiffness per unit length of the soundboard, the new value of rib width would be selected to retain the same value of W/D as in the old soundboard. For the old soundboard W/D 2.5/14 0.1786; therefore the new rib width would be W= (5) (0.1786) 0.892 centimeter.

It is not necessary for a soundboard in accordance with the present invention to have constant rib spacing, as long as the widest spacing is less than one-half wave length at the highest frequency for which uniform response of the soundboard is desired. Generally speaking, the spacing may vary over a percentage range comparable to that of conventional soundboards, which may vary in spacing from about 1 1.5 centimeters at the treble end to about 15 centimeters at the bass end of the soundboard.

FIG. 1 illustrates a soundboard, indicated generally at 1, designed according to the principles of the invention. The soundboard is composed of a plurality of strips 2 formed from quarter sawn lumber having the grain direction extending lengthwise of the strips. This is a soundboard for a concert grand piano having thirty nine ribs 3 extending at right angles to the length of the strips 2, the ribs being spaced apart from 5.08 to 6.02 centimeters. The thickness of the soundboard is between 0.874 and 0.953 centimeter. The nominal elastic modulus of the soundboard strips is (1.38) 10 dynes per square centimeter and the density is 0.4 grams per cubic centimeter. Each rib is approximately 1.12 centimeters in width. The soundboard was designed to replace a conventional soundboard having 17 ribs each of which is 2.54 centimeters wide.

While the foregoing example is exemplary of a soundboard constructed in accordance with the invention, it is possible to vary the width of the ribs and their number consistent with good design practice, including varying the width of the ribs from rib to rib. A salient consideration is the maintenance of the desired tonal characteristics of the instrument, including improved efficiency and uniformity of response of the soundboard at higher audio frequencies.

It has been found that piano soundboards constructed in accordance with the principles disclosed herein, namely, soundboards having the ribs spaced and sized according to the criteria given, have improved uniformity of frequency response, improved and extended high frequency response, higher efficiency at higher frequencies, and improved tone quality. Such instruments may employ softer hammers than conventional pianos, while .still radiating sufficient sound energy at high frequencies. Soft hammers are advantageous because such hammers allow improved quality of tone and improved tone-to-noise ratio.

Modifications may be made in the invention without departing from its spirit and purpose. Numerous variations in the design criteria have already been discussed, and others will undoubtedly occur to the skilled worker in the art upon reading this specification. For example, while the soundboard strips may be formed from quarter sawn lightweight wood, the principles of the invention are applicable to other materials capable of forming a suitable soundboard, such as a laminated soundboard structure. While the invention is directed primarily to standard pianos having 88 notes in the scale, the principles are also applicable to instruments having a greater or lesser number of notes, within practical limits of sound piano design.

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. In a musical instrument having a plurality of strings defining the scale of the instrument, a soundboard having a series of spaced apart reinforcing ribs secured thereto, adjacent ribs throughout said series of ribs being spaced apart by a distance between their centerlines which is less than one-half the vibrational wave length of the soundboard at the fundamental scale frequency of the highest note on the scale of the instrument, the numerical ratio between the cross-sectional widths of the ribs and the distance between the centerlines of adjacent ribs being maintained essentially constant irrespective of the number of ribs employed.

2. The musical instrument claimed in claim 1 wherein said soundboard comprises a plurality of elongated strips juxtaposed in side-by-side relation, and wherein said ribs extend in a direction at right angles to the lengths of said strips.

3. The musical instrument claimed in claim 2 wherein said soundboard strips comprise quarter sawn wood with the grain direction extending lengthwise of the strips and at substantially right angles to the surfaces of the strips.

4. The musical instrument claimed in claim 3 wherein said ribs are formed of quarter sawn wood having the grain extending lengthwise of the ribs and at substantially right angles to the surfaces of the strips.

5. The musical instrument claimed in claim 1 wherein said soundboard has a thickness of from 0.635 centimeter to 0.953 centimeter.

6. The musical instrument claimed in claim 5 wherein said adjacent ribs are spaced apart by a distance of less than 7.78 centimeters when said soundboard has a thickness of 0.953 centimeter, and a distance of less than 6.35 centimeters when the soundboard has a thickness of 0.635 centimeter.

7. The musical instrument claimed in claim 6 wherein the fundamental scale frequency of the highest note on the scale of the instrument is nominally 4,186 Hz.

8. A soundboard for use in a piano having a plurality of strings defining the scale of the instrument, said soundboard having a series of spaced apart reinforcing ribs secured thereto, adjacent ribs being spaced apart by a distance between their respective centerlines which is less than one-half the vibrational wave length of the soundboard material in accordance with the equation x 2 =(1rh VA V3 wherein h is the thickness of the soundboard in centimeters,fis the frequency in Hz. of the highest note on the scale of the instrument, V is the velocity of propagation of longitudinal waves in the soundboard material in centimeters per second, computed in accordance with the equation Vt (ta/p) wherein E is the Youngs or elastic modulus of the soundboard material in a direction at right angles to the longitudinal axes of the reinforcing ribs in dynes per square centimeter, and p is the density of the material in grams per cubic centimeter, and wherein M2 is the half-wave length in centimeters, the ratio of rib width to rib spacing being maintained essentially constant irrespective of the number of ribs employed.

9. The piano soundboard claimed in claim 8 wherein h is from 0.635 centimeter to 0.953 centimeter.

10. The piano soundboard claimed in claim 9 wherein M2 is less than 7.78 centimeters when h equals 0.953 centimeter, and M2 is less than 6.35 centimeters when h equals 0.635 centimeter.

11. The piano soundboard claimed in claim 10 whereinf is nominally 4,186 Hz.

Claims

5. The muscial instrument claimed in claim 1 wherein said soundboard has a thickness of from 0.635 centimeter to 0.953 centimeter.

8. A soundboard for use in a piano having a plurality of strings defining the scale of the instrument, said soundboard having a series of spaced apart reinforcing ribs secured thereto, adjacent ribs being spaced apart by a distance between their respective centerlines which is less than one-half the vibrational wave length of the soundboard material in accordance with the equation lambda /2 ( pi h VL4 Square Root 3f)1/2 wherein h is the thickness of the soundboard in centimeters, f is the frequency in Hz. of the highest note on the scale of the instrument, VL is the velocity of propagation of longitudinal waves in the soundboard material in centimeters per second, computed in accordance with the equation VL (e/ Rho )1/2 wherein E is the Young''s or elastic modulus of the soundboard material in a direction at right angles to the longitudinal axes of the reinforcing ribs in dynes per square centimeter, and Rho is the density of the material in grams per cubic centimeter, and wherein lambda /2 is the half-wave length in centimeters, the ratio of rib width to rib spacing being maintained essentially constant irrespective of the number of ribs employed.

10. The piano soundboard claimed in claim 9 wherein lambda /2 is less than 7.78 centimeters when h equals 0.953 centimeter, and lambda /2 is less than 6.35 centimeters when h equals 0.635 centimeter.

11. The piano soundboard claimed in claim 10 wherein f is nominally 4,186 Hz.