United States Patent 3651242

A bass or other guitar has a transducer for each of its strings, and each transducer is connected to an octave jumping circuit which lowers the musical tone produced by the individual string, all without loss of either harmonics or amplitude variations. The wave form of the fundamental frequency of each musical tone is squared, divided by two and then amplitude modulated to follow the amplitude envelope of the original tone. The modulated square wave contains only odd harmonics of the lowered frequency fundamental. The missing even harmonics are restored by combining with the modulated square wave the original tone containing all of its harmonics.

Application Number:
Publication Date:
Filing Date:
Primary Class:
Other Classes:
84/736, 984/382
International Classes:
G10H5/07; (IPC1-7): G10H1/06; G10H3/00
Field of Search:
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Primary Examiner:
Kozma, Thomas J.
Assistant Examiner:
Witkowski, Stanley J.
I claim

1. Apparatus for lowering by one octave the frequency of an input signal having fundamental and harmonic frequencies, said apparatus comprising:

2. The apparatus of claim 1 wherein said second signal includes:

3. The apparatus of claim 2 wherein said lower fundamental frequency is one-half the fundamental frequency of said input signal, and

4. The apparatus of claim 1 wherein said first means includes:

5. The apparatus of claim 1 wherein said means for amplitude modulating comprises:

6. The apparatus of claim 4 wherein said amplitude modulating means comprises:

7. The apparatus of claim 1 wherein said first means comprises:

8. The method of generating a lower octave signal from an input signal of a higher octave comprising the steps of:

9. The method of lowering a varying amplitude tone by an octave comprising the steps of:

10. The method of claim 9 wherein said amplitude modulating step comprises:

11. Apparatus for lowering by one octave a musical tone produced by a tone generator, said apparatus comprising:

12. The apparatus of claim 11 wherein said modulator comprises a diode.

13. A circuit for musical instruments, comprising:

14. The apparatus of claim 13 wherein said means for generating a square wave signal comprises a divide by two circuit, said means for amplitude modulating said square wave signal comprising:

15. The apparatus of claim 13 wherein said means responsive to said first tone signal comprises a binary dividing circuit, said means for amplitude modulating said square wave signal comprising:

16. The apparatus of claim 13 wherein said circuit is combined with a musical instrument comprising:

17. The apparatus of claim 13 wherein said circuit is combined with a musical instrument comprising:

18. The apparatus of claim 17 including

19. The apparatus of claim 18 wherein said transducer is mounted directly to said bridge between the bridge and said string end portion.

20. The apparatus of claim 13 wherein said means for generating a square wave comprises:

21. The apparatus of claim 13 wherein said means for amplitude modulating comprises:

22. The apparatus of claim 21 wherein said circuit is combined with a musical instrument comprising:

23. The apparatus of claim 22 including a bridge, and wherein said string has an end portion supported on said bridge, and wherein said pickup is mounted closely adjacent said end portion of the string.

24. A bass guitar comprising

25. The bass guitar of claim 24 wherein said means for generating a first signal component comprises:

26. A bass guitar comprising:


1. Field of the Invention

The present invention relates to electrical tone generation and more particularly concerns selective frequency jumping of musical tones.

2. Description of Prior Art

Electric tone generation for various types of musical instruments has long employed octave jumping to provide broadened frequency range. Thus, an electric organ often employs a group of master oscillators, one for each of the 12 notes of the common scale. These highly stable LC tuned oscillators are precisely tuned to the notes of the highest octave to be available from the instrument. Then a first set of divide by two circuits yields notes of the second lower octave, a second set of divide by two circuits yields the third lower octave and so on for as many octaves as are required for the particular instrument. These tones have no amplitude variation as, for example, the decaying amplitude of a plucked string. Furthermore, such tones are initially lacking in even harmonics. The lack of even harmonics derives from the common use of binary circuits such as the bi-stable multi-vibrator or common flip-flop to provide the divide by two action. A symmetrical rectangular wave, having equal duration positive and negative going portions is commonly termed a square wave. Such a square wave is provided at the flip-flop output and embodies only odd harmonics of the fundamental frequency, as is well known. Commonly for octave jumping, one starts with a sinusoidal output of a stable master oscillator, feeds this sine wave signal into a suitable squaring circuit such as an overdriven amplifier, for example, and then employs the steep leading or trailing edge of the squared signal to trigger the flip-flop divide by two circuit. The latter provides its square wave output at half frequency, but without even harmonics. Even with the use of complex and sophisticated wave shaping circuitry, the various attempts to restore full harmonic content are not satisfactory. Other arrangements employing binary dividers for step by step frequency lowering are shown in the U.S. Pat. No. 3,490,327 to I. D. Volpe.

Application of selective frequency jumping has been suggested for various types of stringed instruments such as, for example, the electric guitar. For this type of instrument, octave jumping will provide a greatly increased range of tone generation. A more specific problem exists in the bass guitar, where because of the low tones required of this instrument, string diameter and length introduce many problems. Instrument size begins to be unwieldy since the neck of the common bass guitar may be on the order of 32 inches, whereas the standard guitar neck need be but 25 to 26 inches. Juxtapositioning of the strings and the relatively large spacing between adjacent frets are other problem areas with the bass guitar. All of these problems can be considerably minimized through the use of electronic circuits for lowering frequency output of such an instrument.

For provision of a broadly varying tone generation system, J. C. Cookerly, et al., in U.S. Pat. No. Re26,533, employs for each string of an electric guitar, an amplifier, a wave shaper, and an amplitude modulator. The wave shaper may be one of several different types, including a frequency doubler and a binary dividing circuit. For each of these wave shapers, the square wave output is fed to a signal reproducing means that includes an amplifier. The output amplitude is varied by controlling the bias of the amplifier in a manner corresponding to the volume variation of the tone of the original instrument.

The system of Cookerly, et al., is complex, expensive, and at best, fails to adequately reproduce the original tone. It fails to produce a signal that includes all harmonics of the tone originally generated. As previously mentioned, a square wave contains only odd harmonics of its fundamental frequency. Cookerly, et al., show or suggest no way to overcome the lack of even harmonics in the output signal. Further, the volume control shown by Cookerly, et al., achieved through variable bias control of the amplifier, either introduces significant non-linearity into the output signal or requires a costly amplifier that exhibits high linearity over a wide frequency and amplitude range.

Accordingly, it is an object of the present invention to achieve frequency jumping of a generated tone without loss of either harmonics or amplitude modulation, and in a highly simple, practical, and inexpensive manner.


In carrying out principles of the present invention in accordance with a preferred embodiment thereof, the frequency of an input signal that has fundamental and harmonic frequencies is lowered by apparatus that comprises means responsive to the input signal for generating a first signal component having a lower fundamental frequency and odd harmonics. Second means responsive to the input signal combines a second signal component with the first signal component. The second signal component has even harmonics of the lower frequency. Stated otherwise, practice of one form of the present invention includes generation of a lower octave signal from an input signal of a higher octave by first dividing by two the frequency of the fundamental of the input signal, then combining the higher frequency input signal with the divided frequency fundamental. A feature of the invention is amplitude modulation of the divided frequency signal prior to its combination with the input signal. This is achieved by means of a simple low cost diode modulator.


FIG. 1 illustrates a preferred embodiment of the invention as applied for octave jumping of tones generated by a bass guitar,

FIGS. 2a and 2b illustrate harmonic content of signals of adjacent octaves,

FIG. 3 illustrates in detail a single octave jumper according to principles of this invention,

FIG. 4 shows an alternate modulator, and

FIG. 5 and 6 depict placement of pickups.


As illustrated in FIG. 1, the electrical bass guitar includes a body 10 fixedly carrying a neck or fingerboard 12 with a number of frets such as that indicated at 14 thereon. In the illustrated instrument, four strings generally designated S are each secured at one end thereof to a bridge device 16 carried at one end of the body. The strings extend over the frets of the guitar neck and are secured at the other ends thereof to individual ones of four tuning screws 18 carried at the guitar head. The body 10 also carries a pair of volume and tone control knobs 20, 22.

A plurality of transducers 24, of which there is one for each of the four strings of the instrument, is carried by the body 10 in close proximity to the individual strings. Each transducer has an independent electrical lead 26, 28, 30 and 32 which transmits a signal to an individual one of four octave jumpers 34, 36, 38 and 40.

Each of the octave jumpers 34 through 40, is identical to each of the others. For simplicity of illustration, basic elements of octave jumper 40 only are shown in this figure, it being understood that each other octave jumper incorporates the same basic elements.

The signal produced by any one of transducers 24, and provided on lead 32, for example, is an accurate reproduction of the sound of the plucked string, within the limits of transducer linearity. This includes the fundamental and all harmonics, all subject to the exponentially decaying amplitude that is characteristic of a string. The purpose of the octave jumper 40 is to lower the musical tone, appearing as an electrical signal on lead 32, by one full octave without any significant loss of its amplitude modulation or of any of its harmonics. The essential components of the octave jumper include a binary divider 42, a modulator 44, and a summing network 46, each of which will be described in further detail in connection with the description of FIG. 3.

The transducer output on lead 32 may have a fundamental frequency (f) of 80 Hz., for example. This becomes a square wave of 40 Hz. (f/ 2) at the output of the binary divider 42. The square wave, however, contains only odd harmonics and, in order to obtain a more faithful reproduction at the lower frequency, it is necessary to add the missing even harmonics into this 40 Hz. frequency. This is done by adding to the square wave signal of the lower frequency f/ 2, the original signal with all of its overtones and having the fundamental of the higher octave, namely f. Summing network 46 accomplishes the combination of the signals f and f/ 2. The combination of f with all harmonics and the odd harmonics of f/ 2 provides a signal having all harmonics of f/ 2 as illustrated in FIGS. 2a and 2b.

FIG. 2a illustrates harmonics of a normal 80 Hz. signal provided at the transducer on lead 32. This signal includes the harmonics H1, H2, H3, H4, etc., at the indicated frequencies respectively of 80, 160, 240 and 320 Hz.

Illustrated in FIG. 2b is harmonic content of the lower octave signal at the f/ 2 fundamental frequency of 40 Hz. Since this signal is a square wave containing only odd harmonics, it contains only harmonics indicated at h1, h3, h5, h7, namely harmonics at frequencies of 40, 120, 200, 280 Hz., etc.

Comparison of FIGS. 2a and 2b readily indicates that the harmonics of the higher octave signal at 80 Hz. respectively correspond to the missing even harmonics of the lower octave square wave signal. Thus H1, the fundamental of the 80 Hz. respectively correspond to the missing even harmonics of the lower octave square wave signal. Thus H1, the fundamental of the 80 Hz. signal, is the second harmonic of the lower octave. Similarly, H2, H3 and H4 are the fourth, sixth, and eighth harmonics of the lower octave square wave signal. Thus, by combining the signals and the several harmonics thereof, illustrated in FIGS. 2a and 2b, there is obtained a signal with the lower octave fundamental of 40 Hz. and all of its harmonics, both odd and even.

The relative amplitudes of the several odd harmonics (FIG. 2b ) are substantially the same as the relative amplitudes of the harmonics of the higher octave signal. Accordingly, the even harmonics of the lower octave signal, obtained from the full harmonic content of the higher octave signal, may be directly added to the lower octave signal having only odd harmonic content, and any resultant distortion will be substantially minimal. Nevertheless, for those situations where even such minimal difference in relative intensities of the several harmonics cannot be tolerated, a simple circuit that is nonlinear with frequency, such as, for example, the combination of a single resistor and capacitor, may be inserted into one of the inputs to the resistive summing network to conform the relative intensities of the two groups of harmonics.

As is well known, the standard flip-flop or binary divider operates to provide at its output a signal of either of two possible levels, whereby the half cycles of the signal f/ 2 are of unvarying amplitude. In order to achieve a decaying amplitude envelope, modulator 44 having a modulation control signal input thereto from the originally generated signal of frequency f, is interposed between the summing network 46 and the binary divider 42. Thus, the lower octave square wave having only odd harmonics is amplitude modulated before even harmonics are restored.

The output of summing network 46 on lead 48 is therefore a substantially accurate replica of the original input on lead 32, but one octave lower. It contains all of the original harmonics and also has a substantially identical amplitude envelope. If deemed necessary or desirable, the lower octave signal on lead 48 may, itself, be processed in a second octave jumper 50, identical to octave jumper 46, to provide at the output thereof, a signal having a fundamental frequency f/ 4 with all of its harmonics and having an amplitude envelope substantially duplicating the original amplitude envelope.

Each of octave jumpers 34, 36 and 38 is, as stated above, identical to octave jumper 40, except for the fact that it receives its input signal from a different transducer which, in turn, is responsive to vibrations of a different one of the four strings of this four string bass guitar. Accordingly, each of the octave jumpers 34, 36, and 38 provides at its output a signal including all harmonics and amplitude envelope, and having a fundamental that is one octave lower than the input thereto. Collectively, the four lower octave signals then appear at leads 52, 54, 56, and 58 of the several octave jumpers, when switches (described below) in the output circuits of octave jumpers 34, 36, 38 and 40 are in the positions illustrated.

The output of each of the octave jumpers 34, 36, and 38, like the output of octave jumper 40, may be fed to a second octave jumper respectively indicated at 60, 62, and 64. The lower frequency output on output leads 52, 54, 56 and 58 is either lowered by one or two octaves depending upon the position of the several switches 66, 68, 70 and 72. These switches may be moved individually or in unison from the illustrated position thereof, wherein the frequency is lowered by a single octave to the other positions thereof wherein the frequency is lowered two octaves. Still further octave jumping employing additional groups of the described circuits may be provided.

Each octave jumper, as illustrated in detail in FIG. 3, responds to its individual pickup 82 from which a signal is sent through a pre-amplifier 84, there being one such pre-amplifier for each pickup. This provides on lead 132 the normal harmonic content signal of the individual string. This signal is then fed through a low pass filter 134 that is designed with a pass band for the fundamental of the signal on lead 132 whereby all (or substantially all) harmonics are blocked. The fundamental at the higher octave frequency is then fed to a squaring circuit 136 which may be of any convenient type such as, for example, an overdriven amplifier. The squaring circuit 136 provides a signal having steeply rising and falling leading and trailing edges one of which is conveniently used for triggering the standard bi-stable multi-vibrator or binary divider 142. The latter changes its state once for each full cycle of the square wave output of circuit 136 whereby the square wave output of the divide by two circuit 142 is at half frequency, that is, one octave lower.

In order to derive a suitable amplitude modulation control signal, the original signal at the higher octave on line 132 is fed to a full wave rectifier 138, thence through a smoothing circuit or filter 140 at the output of which is provided the amplitude modulation control signal. This modulation signal is fed via a resistor 141 to control the bias on a diode 144 that comprises the amplitude modulator 44 employed in the illustrated embodiment of this invention.

Diode 144 is a linear clipping diode having its anode connected to the junction of series resistors 143, 145, and its cathode connected to the resistor 141. The resistor 143 and 145 are series connected in the output of divider 142. Accordingly, the diode effectively provides a shunt path to the internal ground connections of filter 140 and rectifier 138. When the cathode of diode 144 is high, the diode is back biased and all of the square wave is passed to the summing network. AS the control signal at the diode cathode goes more negative (or less positive) some of the square wave is shunted. Thus, more or less of the square wave output of divider 142 is shunted in accordance with the amplitude modulation control signal provided at the diode cathode by filter 140.

It is emphasized that linearity of the modulator 144 is no problem in the described arrangement since the modulation is imposed upon the square wave output of the binary divider. A modulator of this type could not be used without introducing serious distortion if employed for modulation of a sawtooth or a sine wave or for modulation of other complex wave shapes. Thus, it will be seen that the amplitude modulation of the square wave itself by a clipping diode before any further wave shaping is attempted, greatly simplifies the required circuitry.

The amplitude modulated square wave is fed through resistor 145 and is combined with the original higher octave signal, with its amplitude variation and all of its harmonics. This is achieved via a resistor 146 to provide at output lead 148 the lower octave signal of desired harmonic content and amplitude envelope.

Resistors 145 and 146 are summing network input resistors. Together with an output resistor 147, connected between ground and a common junction of the three resistors, they form the summing network 46 of FIG. 1.

Thus, the described circuit receives the 80 Hz. signal on lead 132 and divides this signal by two by means of filter 134, squarer 136, and divider 142 to obtain the 40 Hz. square wave having only odd harmonics. The square wave is amplitude modulated with the envelope of the original 80 Hz. signal by means of rectifier 138, filter 140 and clipping diode 144. The 80 Hz. signal on lead 132 and the modulated 40 Hz. square are then combined in resistive summing network 145, 146, and 147. On output lead 148 appears the lower octave signal with all harmonics and proper modulation. It is fed either directly or through a second octave jumper 50 to a system output (power) amplifier 150 that is arranged to be connected to a standard speaker system (not shown).

As previously indicated, the fact that amplitude modulation is imposed upon a square wave, greatly simplifies the circuitry required for such modulation. Actually, all that is required is an impedance at the output of the binary divider 142, either in shunt or in series with the output of this circuit, that can be varied in accordance with the amplitude envelope of the higher octave tone signal. Thus, a variable potentiometer or a gain controlled amplifier could be employed. Nevertheless, fully satisfactory results are obtained by the much simpler and inexpensive clipping diode illustrated, whereby the latter, of course, is preferred.

The preferred simplified form of clipping gate can be applied in several different circuit arrangements. A shunt arrangement is illustrated in FIG. 3 operating to decrease the reverse bias applied to the diode cathode as the control or modulating signal decreases. Accordingly, as the normal input tone decays in amplitude, greater proportions of the output of the divide by two circuit 142 are fed through the shunt diode 144, whereby the output signal fed to the summing network is similarly caused to decay.

A series connected clipping diode modulator is illustrated in FIG. 4 for use with a square wave provided at the output of divide by two circuit 142. This series modulator comprises a pair of series connected diodes 152, 154, poled as illustrated and having the junction therebetween grounded through a resistor 156. The modulating or control signal provided from the filter 140 provides a positive forward bias at the anode of diode 154 that decreases as the original tone input decays. As this forward bias decays, decreasing proportions of the square wave are passed through the diodes whereby the output of the modulator diodes decays in accordance with decay of the input tone signal.

As illustrated in FIG. 1, the pickups for the several strings are preferably placed on or immediately adjacent the bridge device 16 in order to enable the octave jumper to properly discriminate against second harmonics. A common placement of electrical pickups for a stringed instrument is at a considerable distance from the bridge structure. Components of vibration of the string due to the first harmonic or fundamental have maximum excursions at the midpoint of the string. Those vibrations of the string due to the second harmonic have maxima at a point one-quarter of the distance from the string end or, more specifically, one-quarter of the distance from the point at which the string passes over the bridge. Of course, the effective length of the string varies as different frets of the fingerboard are employed. Thus, where the transducers or pickups are placed a considerable distance from the bridge, the quarter-length point of the several strings for at least some of the notes that are played will be considerably closer to the particular pickup position than will be the half-length point. In such a situation, the filter of the octave jumper may select a second harmonic, instead of the fundamental, since the former may appear to be of considerably greater magnitude. The low pass filter of the octave jumper has a band pass width of approximately one octave in order to accommodate the different fret positions of a given string and further, does not and cannot have an ideally sharp cutoff. Accordingly, in situations where magnitude of the second harmonic as detected by the pickup is substantially equal to or greater than the magnitude of the first harmonic, the octave jumper filter may respond to the second harmonic instead of to the first. This undesirable result is prevented by the pickup location as set forth at the beginning of this paragraph.

As the location of the pickup becomes closer to the bridge, excursions of all harmonics become less whereby greater sensitivity and increased preamplification of pickup output are required. Nevertheless, as the pickup is positioned closer to the bridge, the second harmonic amplitude, as sensed by the pickup, drops considerably more rapidly than the decrease in magnitude of the sensed fundamental. Accordingly, with the pickup at or closely adjacent the bridge, the second harmonic amplitude sensed by the pickup will be less than the fundamental amplitude. Thus the system will always discriminate against the second harmonic and the multivibrator divide by two circuit will always be controlled by the fundamental and not by the second harmonic. In such an arrangement, where pickups are to be placed directly on the bridge, it is most convenient to employ piezoelectric type pickups of a construction well known to those skilled in the art. For pickups placed immediately adjacent the bridge, other types of transducers such as conventional magnetic devices may be employed.

Schematically illustrated in FIG. 5 is a preferred location of ceramic piezoelectric transducers. String 158 is secured at its opposite ends to mounting pins 160, 162 that are carried by the instrument structure schematically depicted at 164. Tension holds one end of the string against the final fret or "nut" 166. The other end of the string is held against a piezoelectric pickup 168 that is fixed to and carried upon a bridge device 170. This is a preferred arrangement.

For use with magnetic pickups or other devices wherein it is not feasible to mount the pickup directly upon the bridge, the arrangement of FIG. 6 may be employed. In this configuration, string 172, mounting pins 174, 176, instrument structure 178, and nut 180 are all constructed and arranged just like the corresponding elements illustrated in FIG. 5. In the configuration of FIG. 6, however, the string is held directly against the bridge 184 which carries no transducer. The magnetic pickup 182 is mounted directly upon or within the instrument structure 178, but positioned closely adjacent bridge 184 for reasons described above.

Although the octave jumper of the present invention has been described specifically in connection with an electric bass guitar, it will be readily appreciated that principles described herein may equally well be applied to a variety of other types of stringed instruments and, further, to a variety of other types of instruments, including percussion, reed, etc.

There has been described an octave jumping circuit and method that are simple and inexpensive and yet provide a faithful reproduction of the input, including harmonic content and amplitude envelope. Although the apparatus and method of the invention have been specifically described in an application that enables decrease in size of various elements and components of an electric bass guitar, the invention will be widely applicable in a variety of systems and devices wherever faithful reproduction of an electrical signal at a lower octave is desired.

The foregoing detailed description is to be clearly understood as given by way of illustration and example only, the spirit and scope of this invention being limited solely by the appended claims.