US2898795A - Free-free type tone generating bar - Google Patents

Description

J. T. KuNz 2,898,795

FREE-FREE TYPE TONE GENERATING BAR 4 Sheets-Sheet 1 Aug. 1'1, 1959 Filed Aug. 19, 1955 Aug. 11, 1959 J, T, KUNZ 2,898,795

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' FREE-FREE TYPE TONE GENERATING BAR Filed Aug. 19. 1955 4 Sheets-Sheet 4 3 RD. PARTIAL 2 No. PARTIAL SCALE IS'T BRTIAL PMM @ma m United States Patent O l Jacob T. Kunz, Collegeville, Pa., assignor to Schulmerich Electronics, Incorporated, Sellersville, Pa., a corporation of Pennsylvania Application August 19, 19ss,seria1 No. 529,548 As claims. (c1. sti- 403) This invention relates to electric or electronic musical instruments and their tone generators, and particularly to one for producing cup-shaped or campaniform bell tones. y

Various types of tone generators have been used in music instruments, such as bars or rods, both solid and hollow, and other types of vibrating elements for the purpose of generating vibrations. Mechanical-electrical pick-ups or transducers for translating the vibrations have been employed, the electrical vibrations produced being amplified, modified as needed, and reproduced by a loudspeaker so as to obtain the desired bell note or tones. A campaniform or traditional bell has certain tonal patterns requiring specic vibrations or partials to be present in predetermined relationships in order to obtain a correct and desirable bell tone. It has been diiicult in many prior bell tone generators and instruments to produce the required partials in their correct relationship. The partials also must have the correct strength and duration relationship during the vibration in order to produce a pure bell tone in the loudspeaker. Another problem is to obtain the minor third required in a bell carillon and the hum, strike and iirst octave in octave relationship'.

One of the objects of the invention is to provide an improved tone generator arrangement having partials thereof in octave or desired relationship.

Another object of the invention is to provide a method of tuning a rod to bring various partials thereof into desired relationship.

A further object of the invention is to provide a tone generator means having the desired partials in a single rod.

The terms characteristic tone or note are used in this specification to mean the sound sensation identifying the pitch of the characteristic tone involved to the listener. Fundamental will be used herein to mean the lowest vibration or partial actually present in the vibrator or tone generator whether or not it is ernployed. In an instrument of the type concerned herein, when a vibrator is struck and set into vibration in a particular pattern, a person listening to the note produced as a result thereof, will select the characteristic tone identifying the pitch.

In the case of a campaniform or cup-shaped bell, the desired tones include a hum tone, the strike tone or characteristic tone which identifies the pitch of the bell to the listener, the iirst octave above the strike tone and the iifth tone above the iirst octave. The minor third above the strike tone also must be present, such being a required characteristic of a true bell note. In the Flemish type bell, the hum tone should be an octave below the strike tone. Thus, the hum tone, strike tone and the rst octave tone are in octave relationship. Such a bell also includes the minor third and a fth above the first octave. The normal rod does not provide these tones in their correct relationship. It has been found in the analysis of cast bells that the fth above the p 2,898,795; Piatented Aug. 11 1959l strike tone and major third above the rst octave contribute but little or nothing to overall tone color of a carillon bell.

In one form of the invention, a free-free rectangular rod or bar is used as the tone generator, the rod being set into vibration by a striker and vibrations picked-up by a mechanical-electrical transducer, amplified, and reproduced by a loud speaker. It was found after extensive work, that by forming grooves across the wide face of the bar at a speciiic distance from each end of the bar, that octave relationship would be obtained between the hum partial, strike partial and the partial an octave above the strike. The location of said grooves was found to be critical in that they should be between 0.195 and 0.205 times the length of the rod from each of its ends, the distance preferably being 0.2 times the length. The aforementioned location of the groove is particularly applicable to a bar of uniform cross section along the length, but if a bar of non-uniform cross section is used, the fgrooving location will change as a function of the configuration of the masses in the non-uniform bar. The hum, strike and octave partials then can be obtained from the plane of the face of the bar carrying the grooving. It was further ascertained that the minor third partial above the strike and fifth above the octave or third partial could be obtained if the rod in addition to said grooving was dimensioned to have a width to thickness ratio of 2:1, the grooving being across the Wide face. The rod then could be struck on a corner or in a direction angularly disposed relative to the planes of its wide and narrow faces so as to set the rod into vibration in both its wide and narrow directions. The minor third and octave vibrations are obtained from `the plane of the narrow face of the bar.

When the rod is arranged so that the vibrations from both the wide and narrow faces are utilized, the pickup can be placed at an appropriate place adjacent a corner of the rod.

These and other objects, features and advantages of the invention will become apparent from the following description and the accompanying drawings which are merely exemplary.

In the drawings:

Fig. 1 is a side view of one of the vibrators or tone genera-tors of the invention.

Fig. 2 is a section taken along the line 2-2 of Fig. 1, a striker being included.

Fig. 3 is a perspective schematic view of one manner in which the invention can be carried out, the striker being omitted.

Fig. 4 is a representation of the desired tones in a bell.

Fig. 5 is a table showing relation of partials in an unnotched bar.

Fig. 6 is a graph showing the relation of the groove location to a function obtained by use of the curves of Figs. 7, 8 and 9, the latter curves having as their base, a determination of the effect of changing groove location.

Fig. l0 is a graph showing note or frequency relation to change of groove position for three partials of a notched rod.

The invention may be used with various type musical instruments but will be described specifically in conjunction with a bell tone generator for a traditional carillon wherein the hum and strike tone are in octave relationship. As can be seen in Fig. 4, the tones or partials for a bell having the pitch C include the hum, strike and rst octave all in octave relationship and a minor third above the strike and a lifth above the iirst octave. InV an untuned bar, the nodal points are indicated in Pig. 5, these not -being in the proper relation to each other to produce the desired tones.

A musical instrument embodying the invention may include one or more notes selectively strikable by actuation of keys from a keyboard. Where one vibrator is employed for each note it may take the form illustrated in Figs. l, 2 and 3 wherein rectangular bar 20 may have a wide face or width W which is twice the width, within narrow limits (5%), of the thickness or narrow face N of the bar. Vibration in the W direction means in the plane of the wide face and in the N direction, in the plane of the narrow face. The required octave relationship between hum, strike and octave above strike partials occurs only when the grooves are cut as described herein with the center of each groove substantially at a distance 0.2L from each end of the rod.

As mentioned above, a bell tone also must have a minor third above the strike and a fifth above the first octave. It was found that these vibrations could be obtained from the same rod by using those from the narrow face when the W and N dimensons of the rod have the correct dimensional relation to each other.

Grooves 2l, 21 are cut or formed in rod 20 at a location described in detail hereafter. The rod may be supported, for example, by stretched threads or strands 22, said support strands being fastened to frame 23 in any suitable manner. In the illustrated form wherein vibrations from both the W and N faces are to be used, the striker 24 is arranged so that plunger 25 (Fig. 2) will strike a corner of the rod 20 or will strike the rod in an angular direction relative to the planes of faces W and N. If the partials from the W face only are to be used, the striker can be arranged to strike the rod in a direction perpendicular to face W. lf there are a plurality of rods as in a carillon, each striker can be selectively actuated from a keyboard 27.

A mechanical-electrical pick-up of any suitable type can be located adjacent a corner of the rod so as to pick-up vibrations. The pick-up is illustrated as of the magnetic type but may be a capacitive arrangement. The pick-up is connected through an amplifier 29 to a loud speaker means 30 in the usual manner, the amplifier and speaker being chosen to attenuate partials as needed.

As a result of the discovery, studies were made and it can be theorized that each point on a rod vibrates with simple harmonic motion or y=arnplitude cos 2 fr ft.

where f=frequency and t=time. Substituting, we obtain y=A sin 2TTXcos 2nft.

where l=length These relations are quite complex for a bar such as a free-free rod and can be expressed by the equation:

wherein X is the amplitude function, x the coordinate along the rod, and f the frequency.

The set of functions resulting therefrom defining the shape of a vibrating free-free rod is called the set of normal functions for the rod. In ascertaining frequency the potential and kinetic energy relationships can be considered as the rod vibrates. Inertia enters into the problem as Well as the modulus of elasticity of the rod material. in a cycle of vibration of a rod, the total energy is at one time all kinetic and at another time all potential. If the shapes of the characteristic functions are known, frequencies can be determined.

If the grooves are made close to the ends of a freefree rod Where the displacement is relatively large and curvature small, the tendency would be to increase frequency. If the notches are located where the curvature is large but displacement small, then frequency will decrease. The displacements and curvatures of the bar are different for each of the first three partials.

The expressions for frequency contained in the quantity p for each of the first three partials for a notched rod can be written:

where P01, P02, P03 relates to the frequency factor of an unnotched rod. AX is the width of the groove; A0 is the area of the unnotched bar; and A is the area of the web section; I0 is the moment of inertia of the unnotched section; and I is the moment of inertia of the notched so dividing and solving the following may be written:

The subscripts indicate the partial involved; I is the inertia factor, is a second derivative function, is

a function, a g is a function of the notched dimension and inertia concerned.

The curves of Figs. 7, 8 and 9 were calculated from the above formula utilizing the shape of the curves experimentally determined, such as illustrated in Fig. l0. Fig. 10 shows the effect of changing the groove locations relative to the ends of the rod. It is to be noted that for the grooves used in Fig. l0, the first three partials are in octave relationship when the grooves are at a position 0.2L, the distances X and Y being substantially equal. The curves were obtained by plotting results obtained from a stroboscope.

Equation 7 can not be solved numerically but cank be determined graphically as is plotted in Fig. 6, the crossing of the 0 axis being the value of x where satisfied.

In Fig. 6 several curves are plotted for slightly varying groove characteristics in rods found to be satisfactory and it can be seen that octave relationship is obtained when the grooves are located from the end of the bar in the range of .195 and .205 of the length thereof. The notch factors used were chosen to represent various web thickness, these representing relative variation in bar thickness (N) to the thickness of the bar at the notch (a, Fig. 2).

The rods involved were madey of steel inasmuch as a magnetic pick-up or transducer was employed but other materials can be used in accordance with the pick-up arrangement.

It is to be understood that the invention can be used in conjunction with picking up vibrations from. only the wide face as well as the combination ofvibrations. Also, it should be obvious that variations may be made. in

g details of construction and procedure without departing from the spirit of the invention except as defined in the appended claims.

What is claimed is:

1. A free-free vibrating elongated bar for use in electric tone producing instruments having transverse grooves spaced from each end thereof between about .195 to .205 of the length of the bar.

2. A rectangular free-free vibrating elongated bar for electric music instruments having transverse grooves spaced from each end thereof between about .195 and .205 of the length of the bar, said bar having a width to thickness ratio of abouttwo to one.

3. In a bell tone producing instrument, an elongated bar having transverse grooves spaced from each end thereof at a distance in the range of .195 and .205 of the length of the bar, said bar having a width to thickness relation of two to one, the grooves being across the wide face, means selectively setting said bar into vibration in both transverse directions, mechanical-electrical transducer means for picking up vibrations, amplier means, and loud speaker means connected to said amplier means for reproducing tones.

4. A rectangular free-free vibrating elongated bar for use in electric tone producing instruments and adapted to provide at least three partials in octave relation when struck, said bar having Itransverse grooves of substantially equal depths and widths spaced from each end thereof between about .195 to .205 of the length of the bar.

5. In a bell tone producing instrument, a rectangular elongated free-free bar having transverse grooves spaced from each end thereof at a distance in the range of .195 to .205 of the length of the bar, means flexibly supporting said bar in free-free relation, means for selectively setting said bar into vibration, mechanical-electrical trans-- ducer rneans for picking-up said vibrations, including at least three partials in octave relation, amplifier means, and loud speaker means connected to said amplifier means for reproducing tones.

References Cited in the le of this patent UNITED STATES PATENTS

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