US3478631A

US3478631A - Curved finger boards for stringed musical instruments

Info

Publication number: US3478631A
Application number: US784536A
Authority: US
Inventors: Alan Robert Fisher
Original assignee: Individual
Current assignee: Individual
Priority date: 1968-12-05
Filing date: 1968-12-05
Publication date: 1969-11-18
Anticipated expiration: 1986-11-18

Description

Nov. 18, 1969. A. R. FISHER 3,478,631

CURVED FINGER BOARDS FOR STRINGED MUSICAL INSTRUMENTS Filed Dec. 5, 1968 2 Sheets-Sheet l F'lG.l

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F'IG.4 m5? A T TORNE Y Nov. 18, 1969 A. R. FISHER 3,478,631

CURVED FINGER BOARDS FOR STRINGED MUSICAL INSTRUMENTS United States Patent O US. Cl. 84-293 2 Claims ABSTRACT OF THE DISCLOSURE A finger board for stringed musical instruments which has a face longitudinally curved on a logarithmic spiral so that a string when pressed against the finger board at any point along its length will make the same angle with the finger board at each point.

REFERENCE TO RELATED APPLICATION This application is a continuation-in-part of my copending patent application which is now abandoned. Title: Curved Finger Board For Stringed Musical Instruments; Serial No.: 640,674; Filing Date: May 23, 1967.

GENERAL DESCRIPTION OF THE INVENTION This invention relates to finger boards for stringed musical instruments wherein the finger board has a longitudinally curved face portion so that it lies closer to the strings at the nut and bridge and allows greater amplitude of string vibration midway between the nut and bridge. This curvature is a logarithmic spiral originating at the point where the string crosses the bridge so that the active portion of a string pressed against said finger board at any point along its length makes the same angle with the finger board at each point.

Stringed musical instruments such as violins, violas, cellos, double basses, banjos, mandolins, guitars, etc. generally have longitudinally straight finger boards against which the strings are pressed by the musicians fingers l shorten the length of a vibrating string to raise the pitch of the emitted sound. These straight finger boards are set on an angle to the strings leading away from the strings as the finger board extends from the nut toward the bridge or anchor means. As they approach the bridge the straight finger boards are so far from the strings that the strings cannot be pressed against them and they are shortened to a usable length.

In the case of longitudinally straight finger boards, the strings are most diflicult to depress against the finger board adjacent their points of suspension at the nut and the bridge and least diflicult to depress against the finger board in the positions midway between the nut and the bridge because the midway positions are remote from the points of suspension of the strings. The diificulty of depressing the strings adjacent their points of suspension can make playing unnecessarily tiring and strenuous.

Also the strings vibrate with maximum amplitude at the positions midway between the points of suspension small magnitude and is unideal in shape so that the objections remain unsolved.

With the foregoing in view it is an object of the invention to provide a curved finger board which lies ideally close to the strings adjacent their points of suspension so that it is easier to depress the strings against the finger board adjacent their points of suspension. The fact that the strings are easier to depress to the finger board near the bridge increases the usable length of the finger board.

In this invention the constant angle between the string and the finger board at any point at which the string is pressed, establishes a proportionality between the maximum allowed amplitude of vibration and the active length of string. As a result, any active length of string, when plucked to vibrate at maximum amplitude, undergoes the same strain and hence the same stress. This ensures a constant plucking force for any active length of string plucked to vibrate at its maximum amplitude. The tendency to unexpectedly snap the string against the finger board is thereby minimized. The logarithmic spiral curve necessary to provide the constant angle between the string and finger board is therefore the ideal shape.

A constant plucking force applied to a string whose amplitude is proportional to its active length, will produce an energy input to the string that is inversely proportional to the frequency of emitted sound. As applied to the double bass, which produces low frequency sound, this feature results in a constant subjective loudness.

In another form of the invention the logarithmic spiral curve is applied directly to the neck portion of the instrument instead of to a separate finger board.

In another form of the invention frets are positioned on a logarithmic spiral curve so that the top contact surfaces of the frets describe the curve whether the supporting neck or board is curved or straight.

BRIEF DESCRIPTION OF THE FIGURES OF THE DRAWINGS FIG. 1 is a side elevational view of a stringed instrument equipped with a longitudinally curved finger board.

FIG. 2 is a side elevational view of the curved finger board seen in FIG. 1 separate from the instrument.

FIG. 3 is a face elevational view of the device seen in FIG. 2.

FIG. 4 is an end elevational view of the device seen in FIG. 2 taken on the line 4-4 thereof showing a transversely curving face on the finger board.

FIG. 5 is a side elevational view of a curved finger board equipped with frets.

FIG. 6 is an end elevational view of the device seen in FIG. 5 taken on the line 66 thereof showing a transversely flat face on the finger board.

FIGS. 7 and 8 are side elevational views of the device seen in FIG. 1 with the string pressed to the finger board at different points showing that the same angle a is formed at every point.

FIG. 9 is a graph illustrating an assumed relationship of plucking force to vibration amplitude.

FIG. 10 is a graph of standard loudness level contours for the human ear, incorporating a field of lines showing constancy of loudness for a double bass incorporating the invention.

PARTICULAR DESCRIPTION OF THE INVENTION Referring now to the drawings wherein like numerals refer to like and corresponding parts throughout the several views, the longitudinally curved finger board shown therein to illustrate the invention, FIGS. 1-4, comprises a finger board 10 mounted to the neck portion of a musical instrument 11 having strings 12, a nut 13, and a bridge 17. The strings are suspended over the nut 13 and bridge 17. The finger board 10 has

opposite ends

14 and 15 and a face 16 curving inwardly lengthwise from the

opposite ends

14 and 15. The face 16 at the

ends

14 and 15 is closer to the strings 12 adjacent the nut 13 and bridge 17 respectively relative to a straight finger board. The face 16 intermediate the

ends

14 and 15 is farther away from the strings 12 due to the face 16 curving lengthwise inwardly relative to a straight finger board. The broken line 18 of FIG. 2 may be regarded as the plane of the face of a straight .finger board for comparison. The

broken lines

19 and 20 of FIG. 1 may be regarded as the maximum amplitude of string vibration with a straight finger board whereas the dotted line 21 illustrates the increased amplitude of vibration possible with the curved finger board 10. It is to be noted that the end 15 extends to a point closely adjacent the bridge 17 and also closely adjacent the strings 12. This is only possible with the curved finger board.

It will be apparent that the strings 12 adjacent the nut 13 and bridge 17 may be more easily pressed against the face 16 of the curved finger board 10 as the face 16 lies closer to the strings 12 adjacent the nut 13 and bridge 17 compared to a straight finger board.

The face 16a of the finger board 10a may be equipped with frets 22, FIGS. and 6. Also the face 16 may be transversely curved as seen in FIG. 4 or the face 16w may be transversely straight as seen in FIG. 6. Also the top contact surfaces of the frets 22 may lie on a curve without the supporting board lying on a curve. By top contact surface is meant the edge of the fret that the string is pressed against.

Throughout this disclosure the terms active portion and active length refer to that portion of the spring capable of vibrating to produce sound. In FIG. 7 these terms refer to the length of string between point A at which the hand presses it, and the bridge 17. In FIG. 8 the terms refer to the length of string between point B and the bridge 17. The terms vibrating portion and vibrating length, as sometimes used for clarity, refer to the identical part of the string that the aforesaid terms refer to. A string is said to be open when it is not pressed to the finger board at any point, so that its active portion is the length of string between the end 14 of the finger board, and the bridge 17.

FIGS. 7 and 8 illustrate how the magnitude of angle formed between the string and the finger board is the same at every point at which said string is pressed to said finger board. The magnitude of the angle it formed between the active portion of the string 12a and a line 26 tangent to the finger board at the point A at which said string is pressed to said finger board is the same as the magnitude of the angle or for-med between the active portion of the string 12b.and a line 28 tangent to said finger board at any other point B at which said string is pressed to said finger board. The open string 12 shown in FIG. 1 also forms the same magnitude of angle with said finger board at the end 14.

It is a property of a logarithmic spiral curve that a straight line drawn from the origin of said curve to a point on said curve will form an angle with a line tangent to said curve at said point, this angle being equal to that formed between any other straight line drawn from said origin of said curve and the tangent to said curve at the point where said other straight line intersects said curve.

The constant angle at between the string and the line tangent to the finger board at the point where said string is pressed to said finger board is therefore achieved by incorporating a logarithmic spiral curvature to the face 16. The origin of said spiral is at the point 23 at which the string 12 crosses the bridge 17. The logarithmic spiral proceeds from the point 23 along the imaginary line 24 to the end of the finger board 10 and then forms the longitudinal curvature of the face 16 of said finger board. The angle a between the active portion of the string and a line tangent to the finger board at the point where said string is pressed to said finger board will hereinafter be referred to as the angle between the string and the finger board.

The following equation establishes the logarithmic spiral shape of the face of the finger board:

d=distance of face of finger board from the open string 12 at any point along said string.

r=distance along the string, from the point where d is measured, to the point 23 where said string crosses the bridge.

a=desired angle to be formed between the string and the finger board at every point on said finger board to which said string is pressed.

ln=natural logarithm.

t=length of the open string.

The constant angle a formed between the string 12 and the finger board 10 at every point of depression establishes a fixed proportionality between the vibrating length of said string and the maximum amplitude of vibration of said string without said string hitting said finger board. The vibrating length of the string 12a divided by its maximum amplitude of vibration C equals any other vibrating length of the string 12b divided by its maximum amplitude of vibration D. The same applies to the open string so that the locus 21 of the string 12 vibrating at its maximum amplitude contains a total included angle of 2X0; at each end. Similarly the locus 30 of the string 12a vibrating at its maximum amplitude contains a total included angle of 2 a at each end. Similarly any other locus 32 of the string 12b vibrating at its maximum amplitude contains a total included angle of 2X0: at each end. Therefore all loci of maximum amplitudes are geometrically similar.

The foregoing establishes that for any string on the instrument 11 the unit strain of the string when vibrating at maximum amplitude is the same for any vibrating length of said string. The unit strain in the vibrating portion 21 of the open string 12 is the same magnitude as the unit strain in the vibrating portion 30 of the string 12a and is the same magnitude as the unit strain in any other vibrating portion 32 of the string 12b when said string is vibrating at maximum amplitude in each case.

It is essential for producing accurate pitches that a string be constructed of homogeneous material and that it be constant in cross section along its length. This also ensures that a constant unit strain of one value will have associated with it a unit stress of only one value for the entire length of the string. Therefore, the unit stress in the vibrating portion 21 of the open string 12 is the same magnitude as the unit stress in the vibrating portion 30 of the string 12a, and is the same magnitude as the unit stress in any other vibrating portion 32 of the string 12b when said string is vibrating at maximum amplitude in each case.

It has been established that the string cross section is constant, and that for any active length of string vibrating at maximum amplitude the unit stress and angle a are constant, Therefore the longitudinal force present in the string when said string is in the position of maximum amplitude is the same for any vibrating length of string. For simplicity it will be assumed that the string is always plucked at the longitudinal mid-point of its active portion. From the foregoing it can be deduced that the force requred from the plucking hand to pluck the string to produce a vibration at maximum amplitude is the same magnitude for any active length of string. The plucking force required to vibrate the open string '12 at its maximum amplitude 21 is the same magnitude as the plucking force required to vibrate the active portion of the string at its maximum amplitude 30, and is the same magnitude as the plucking force required to vibrate any other active portion of the string 12b at its maximum amplitude 32. When the musician has learned what this constant maximum plucking force is for each string, he will less often snap the string against the finger board unexpectedly because of plucking too hard. 7

As the plucking hand deflects the string in the act of plucking, the rate of rise 34 of force in the string 12a is not necessarily a straight line function but may be related to string amplitude in any complex manner as shown by the curved line 34. The properties of the string and the geometric similarity of the loci of maximum vibration amplitudes of any active length of said string having been established, it logically follows that the rate of rise 36 of plucking force in any other active length of the string 12b will occur in a manner similar to the rate of rise 34 of plucking force in the active length of the string 12a, but that the rate of rise must be inversely proportional to the active length of the string. This is equivalent to stating that the distances of

curves

34 and 36 from the vertical 0-line in FIG. 9, as measured along any horizontal line, are proportional to the amplitudes C and D respectively and therefore are proportional to the active lengths of

string

12a and 12b respectively. Therefore, for the constant maximum plucking force established to occur for all active lengths of string vibrating at maximum amplitude, the areas under the curves are proportional to the active lengths of string. The active length of the string 12a divided by the .area under the curve 34 equals any other active length of the string 12b divided by the area under its curve 36.

Since:

Energy=j (forcexds) where s=distance the areas under the curves of FIG. 9 are proportional to the energy imparted to the string in the act of plucking. In summary, when the string is plucked to vibrate at its maximum amplitude allowed by the logarithmic spiral curvature of the finger board, the energy imparted to said string is proportional to the active length of said string.

The science of acoustics has been proven that the frequency of vibration of a string is inversely proportional to its vibrating length. Therefore when the string is plucked to vibrate at its maximum amplitude allowed by the logarithmic spiral curvature of the finger board, the energy imparted to said string is inversely proportional to the frequency produced by the vibrating length of said string. The frequency is the pitch of the emitted sound. Dilferent pitches are heard by the ear as different notes.

In any well-constructed musical instrument any two notes of different pitch, but plucked with the same amount of force, will have approximately the same duration of sound. The conversion of plucking energy into sound energy after the plucking hand releases the string will occur in about the same time interval for all pitches. Therefore, when the string is plucked to vibrate at its maximum amplitude allowed by the logarithmic spiral curvature of the finger board, the sound energy imparted to the air per unit time is inversely proportional to the frequency produced by the vibrating length of said sting.

Energy per unit of time is power, which can be expressed in many kinds of units including microwatts. With reference to the scale on its right hand side, FIG. 10 shows the relationship of sound power to frequency for subjective loudness levels of the human ear. The curved lines from 0 to 120 sones indicate subjective loudness. The maximum amplitude of a vibrating string produces its maximum loudness. Therefore, when a string is plucked to vibrate at its maximum loudness allowed by the logarithmic spiral curvature of the finger board, the sound power imparted to the air is inversely proportional to the frequency produced by the vibrating length of said string.

Line 38 of FIG. 10 represents the sound power of a double bass with the logarithmic spiral finger board, plucked at maximum loudness for all notes. Said line is drawn at a slope that represents the established inverse proportionality of sound power to frequency. 'It is straight because of thelog-log scales of the graph. Lines 40 show sound power of said double base when its strings are plucked to amplitudes less than maximum. The ends of these lines terminate at the usual high and low limits of pitch that can be produced on the instrument. Line 38 closely follows the constant subjective loudness line of sones, providing that a stringed instrument with the logarithmic spiral finger board not only possesses a constant maximum plucking force but can produce a sound of constant subjective loudness associated with said plucking force.

The logarithmic finger board as disclosed and described makes it easier to depress the strings adjacent their points of suspension, allows increased amplitude of vibration of the strings intermediate their points of suspension, facilitates increased usable length of the finger board adjacent the bridge, and provides a constant maximum plucking force for all active lengths of a string. As applied to a double bass, the finger board also limits the maximum subjective loudness to the same value for all active lengths of the string.

I claim:

. 1. In a stringed musical instrument having a nut at its top end, a bridge or tail piece at its bottom end, and strings crossing and suspended over said nut and said bridge;

a curved finger board having a top end, a bottom end, and a longitudinally inwardly curving intermediate face portion between said top and bottom ends;

said curved finger board being adapted to lie adjacent the strings with its top end at said nut, and its bottom end adjacent said bridge;

the longitudinal curvature of said face portion being a logarithmic spiral originating at the point where said strings cross said bridge;

said logarithmic spiral forming the face curvature of said finger board under each string so that at every point along its length at which said string is pressed to said finger board, the same angle will be formed between said string and said finger board.

2. In a stringed musical instrument having a nut at its top end, a bridge or tail piece at its bottom end, and strings crossing and suspended over said nut and said bridge;

a finger board having a top end, a bottom end, and an intermediate face portion between said top and bottom ends, said intermediate face portion containing frets whose top contact surfaces lie on a longitudinally inward curve;

said finger board being adapted to lie adjacent the strings with its top end at said nut, and its bottom end adjacent said bridge;

the longitudinal curve described by the top contact surfaces of said frets being a logarithmic spiral originating at the point where said strings cross said bridge;

said logarithmic spiral forming said curve under each string so that on every fret to which said string is pressed, the same angle will be formed between said string and said curve.

References Cited UNITED STATES PATENTS 73,569 l/1868 Bishop 84274 1,290,177 l/19l9 GrimsOn 843 14 2,853,911 9/ 1958 Plants 84274 3,143,028 8/1964 Fender 84-293 RICHARD B. WILKINSON, Primary Examiner I. F. GONZALES, Assistant Examiner US. Cl. X.R. 84314 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3 ,478 ,631 November 18 1969 Alan Robert Fisher It is certified that error appears in the above identified patent and that said Letters Patent are hereby corrected as shown below:

Column 3, line 32, "spring" should read string Column 4, line 66, "requred" Should read required line 72, "1241" should read 12a Column 5, line 39, cancel "been". Column 6, line 3, "base" should read bass line 8, "providing" should read proving Signed and sealed this 3rd day of March 1970.

(SEAL) Attest:

Edward M. Fletcher, Jr. WILLIAM E. SCHUYLER, JR.

Attesting Officer Commissioner of Patents