Abstract: An apparatus for producing a signal indicative of the direction of bowing of a musical instrument by analyzing the signal from a transducer monitoring the displacements of a bowed vibrating element in the plane of bowing. The indicative signal is stored for the entire duration of a played note or musical passage.

Abstract: A pickup is disclosed for a stringed musical instrument having a plurality of strings. The pickup includes a bridge member having a surface which supports the strings at predefined positions along the surface, a plurality of bimorphic piezoelectric elements embedded in the bridge member at locations corresponding to the predefined positions along the surface of the bridge member, and connection wires for conveying the electric signals generated by said bimorphic piezoelectric element. Each bimorphic piezoelectric element has two oppositely polarized piezoelectric layers, separated by a metallic layer. The bimorphic piezoelectric elements are embedded in the bridge member so that the principal direction of vibrations of the corresponding string is normal to the metallic layer which separates the two piezoelectric layers of the bimorphic element.

Abstract: An electric musical string instrument, particularly an electric guitar, has a body structure carrying fret assemblies and at least one string extending lengthwise over the fret assemblies. Each fret assembly includes at least one resistive element which is associated with a string contact surface of that fret assembly. The effective resistance of the resistive element changes in dependence upon transverse deflection of the string, when in contact with the string contact surface, to effect bending of the note being played. Preferably the string contact surface is formed by the resistive element.

Abstract: A device to produce sub-harmonic tone signals in response to a tone signal from a transducer having preferably maximum sensitivity in the plane of bowing of a bowed musical instrument by passing selected cycles of the transducer signal through signal gates which are controlled jointly by sub-harmonic control signals at sub-multiples of the fundamental frequency of the transducer signal and by a signal indicative of the detection of a fundamental frequency. Each sub-harmonic tone signal thus produced has a tone color which approximates that of the corresponding bowed musical instrument of the same frequency range and which is independent of the direction of bowing.

Abstract: A detachable electric stringed instrument pickup system for an electrical stringed instrument of the type including a body, a neck having a head, a bridge assembly connected to the body, and a plurality of strings positioned between the head and the bridge assembly includes a mounting fixture having an opening attached to the front of the body of the electrical stringed instrument under the strings, a base plate attached by height adjustment screws to the mounting fixture, and a height adjustment spring biasing the base plate away from the mounting fixture and also includes a first connector for elecrical connection mounted on the base plate and a second connector for electrical connection mounted on an assembly mount and detachably plugged into the first connector through the opening in the mounting fixture and wherein an electromagnetic pickup is mounted on the assembly mount and electrically connected to the second connector.

Abstract: A transducer for a musical instrument through which vibrations can be fed back to the instrument so that notes played on the instrument can be sustained. The transducer comprises a bracket for mounting the transducer to the instrument. First and second opposited permanent magnetic poles project away from the bracket. A first surface of a sheet of non-magnetic, non-electromagnetic resilient material is attached to the projecting first and second magnetic poles. An electromagnetic core has a spine and first and second legs originating at, and extending away from, the spine and terminating at first and second end faces, respectively. The first and second end faces are attached to a surface of the sheet opposite the surface of the sheet to which the permanent magnetic poles are attached, with the first face adjacent the first permanent magnetic pole and the second face adjacent the second permanent magnetic pole. A conductor is wound on the core.

Abstract: An electrical detector attachment to the sound post of a stringed instrument is connected by an electric conductor to a coupling device adapted to receive at the exterior of the instrument the coupling member of an electronic device such as a sound amplifier.

Abstract: An input waveform signal is converted into a digital peak value signal by an A/D converter, and the digital peak value signal is input to one input terminal A of a comparator. The other input terminal B of the comparator receives a preset digital peak value signal from a memory. These input signals are compared by the comparator. The content of the memory is reduced at a predetermined rate. If the comparator detects that the currently input waveform level is larger than the continuously reduced level of the memory, i.e., if A>B, a new waveform level is loaded in the memory. As a result, the output from the comparator is inverted. That is, condition A>B is changed into condition A<B. The timing of this change in condition serves as a peak timing of the input waveform signal.

Abstract: An electric guitar having a vibrato function includes first and second operation elements and an operating unit. The first operation element can designate a pitch width to be changed by setting a first pitch width as a unit. The second operation element can designate a pitch width to be changed by setting a pitch width smaller than the first pitch width as a unit. The operating unit performs an operation of the pitch width to be changed, which has been designated by the first operation element, and of the pitch width to be changed, which has been designated by the second operation element. The operating unit forms the control information representing a width of pitch change of a vibrato to be imparted on the basis of the operation result, thereby imparting the vibrato effect on a musical tone to be produced in accordance with the control information.

Abstract: Apparatus is disclosed whereby an electronic musical tone generator is controlled in response to a musical instrument using mechanically vibrated strings. A bank of digital note filters is associated with each string to find the closest true musical note frequency corresponding to the vibration frequency of the string. The filters operate by computing the autocorrelation function of the string's vibration waveshape and then performing a Fourier transform to obtain the identification of the closest true musical note. An efficient and simple implementation is disclosed for an analog-to-digital signal conversion, the computation of the autocorrelation, and the Fourier transform. Provision is made for introducing frequency changes corresponding to a pitch bend in the vibration frequencies of the string.

Abstract: For electronically reproducing the total sound produced by a musical instrument, the musical instrument comprises a plurality of components each of which produces one aspect of the total sound, an electronic acoustic reproduction system comprises vibration transducer means mounted on the instrument for receiving the one aspect of the total sound from one of the components and transforming the one aspect to an electrical signal, and electronic filter means for processing the electrical signal to produce a total electrical signal representative of the total sound of the musical instrument.

Abstract: An electronic stringed instrument includes a mode selecting section for selectively setting a normal play mode and at least one other selection mode. When picking of a string under a pitch designation operation status is performed after the normal play mode is selected by the mode selecting section, generation of a musical tone with the designated pitch can be started. When picking of a string also under the pitch designation operation status is performed after another selection mode is selected by the mode selecting section, a desired musical tone parameter such as a timbre corresponding to the designated pitch or a rhythm pattern can be easily set. The content of the set musical tone parameter can be confirmed by a sound.

Abstract: A system for the selection and recall of individual phase, pickup selection, tone, overdrive and volume control for each of a plurality of pickup coils in electric guitars. These various controls for the humbucking pickup coils in the guitar are initially set by either rotary or toggle switches to achieve a particular combination of switch settings. Additional controls then allow the musician to write the states of these various controls into digital memory contained within the guitar. Several such combinations may be memorized and then recalled at a later time by actuation of a memory address selection switch which then reads the contents of the memory for a particular combination of settings and internally causes the various controls to reset themselves to this particular combination of settings.

Abstract: A photoelectric transducer is provided for musical instruments to pick up musical tones so that they may be amplified, transcribed, resynthesized, or recorded. A light source, such as a light emitting diode, is mounted on the instrument to direct light onto a vibratory element of the instrument. Vibrations of the vibratory element cause modulations in the intensity of the light which is reflected or partially obstructed before reaching a photodetector. The modulated electrical output of the photodetector corresponds to the vibration frequency of the vibratory element and may be amplified to drive a loudspeaker or processed for transcription or resynthesis.

Abstract: An electromagnetic pickup for use in sensing the mechanical motion of strings includes a ferromagnetic housing of elongate, longitudinally recessed form in which a ferromagnetic core is received. The core includes a plurality of coplanar, spaced, finger-like projections directed at the walls of the recess. Both the walls of the recess and the finger-like projections of the core are permanently magnetized to a common magnetic polarity and thus will concentrate by magnetic repulsion the flux into the gap between the projections. A coil wound around the core then senses the flux changes of these concentrated flux fields due to string motion.

Abstract: A pickup assembly is used with a string instrument having a plurality of strings and an elongated fingerboard against which the strings can be stopped, a bow having a filament adapted to be drawn across the strings, and a frequency synthesizer. The assembly is composed of a pickup on the fingerboard for detecting which strings are stopped, where therealong, and for generating an output corresponding thereto, a pickup connected to the bow for detecting action thereof for generating an output corresponding thereto, and a pickup connected to the strings for detecting which string is being contacted by the bow and for generating an output corresponding thereof. These resultant, mainly analog signals are then fed to a processor that is connected to all of the pickup for receiving the outputs thereof, digitizing these outputs, and feeding the digitized outputs to the synthesizer.

Abstract: A system for facilitating instruction of musicians in playing of a stringed musical instrument of the type having a plurality of strings and a plurality of frets such as a guitar. The system includes means for producing signals representing musical notes to be played, this means including an array of switches (which may take the form of capacitors), one switch being provided for each note. The switches are positioned beneath each string, which may constitute one of the components of respective switches within a group, in vicinity of each fret. Processing means, which may be coupled to the means for producing signals, produces data representing the musical notes when the system is in its input configuration. Means for receiving, storing and playing back data therefrom representing the musical notes are coupled to the processing means.

Abstract: A transducer for a stringed musical instrument incorporating an electrically conductive base plate along with a piezoelectric crystal secured to the base plate by a conductive adhesive. On the other side of the crystal from the base plate is disposed a spring for biasing the piezoelectric crystal against the bridge at a bridge or bridge/body opening. Electrical leads are employed for coupling signals from the piezoelectric crystal.

Abstract: A component multi-necked string-instrument is disclosed. At least two instruments are flexibly connected to enable multiple instrument playing with fluidity and ease. The instruments are reverse-strung, stream-lined, having conventional tunings means angularly recessed rearward of the bridge section. Electrical control means are likewise recessed. A limited headstock is also provided for string anchoring, balance and playing ease.

Abstract: Described is a digital electronic device which selectively intercepts and reroutes the serial data being transmitted between digital music instruments interacting via the MIDI signal standard. Simultaneously, the device performs either transposition or control increment operations by incrementing (or decrementing) only those data bytes which are MIDI addresses of either musical keys or selected controls, (e.g., controls pertaining to volume, pitch bend, tremolo, tone duration, and the like) respectively. The device when equipped with logic gates can operate even faster than a microprocessor-based device performing the same functions, and no programming is required. In fact, a preferred device of the invention built with logic gates and other components available now is capable of operating at 250 kilobaud which is 8 times as fast as the present MIDI baud rate.

Abstract: A transducer for a stringed musical instrument incorporating an electrically conductive ground plane, along with a plurality of piezoelectric transducers and a conductive strip. The ground plane, piezoelectric transducers and conductive strip are secured in an elongated unitary structure with the ground plane and conductive strip disposed on opposite sides of the transducers. A conductive shield is disposed about the unitary structure and electrical leads connect to the ground plane and conductive strip, respectively.

Abstract: A magnetic pick-up is positioned below the strings of a stringed musical instrument having four strings. The pick-up comprises a long and narrow pick-up coil comprising wraps of insulated wire about a magnetic core. A pole piece is physically and magnetically connected to one end of the magnetic core. The pole piece includes a wide first portion which presents pole regions laterally inwardly adjacent the two outside strings of the instrument. It includes a narrower second portion which projects upwardly from the first portion and presents pole regions laterally inwardly adjacent the two inside strings. The coil and the pole piece produce a magnetic field which is elongated laterally of the instrument, generally parallel to the direction of greatest string displacement when the strings are stroked, finger or pick. The strings are located in the magnetic field.

Abstract: An electronic pickup device for stringed instruments having a pivot securely attached to the musical instrument and one rockshaft for each string of the musical instrument. The rockshaft is attached to one end of a string and attached to the pivot so that the other end of the rockshaft vibrates in conformity with the vibrations of the string. The vibrations of the rockshaft are then translated into electrical vibrations typically via a magnet on the end of the rockshaft juxtaposed to an induction coil.

Abstract: In apparatus for detecting string stop position for string instruments, there is provided fret detecting means comprising coils which generate an induced voltage by means of an electric current flowing through each of the frets, whereby the string stop position may be detected on the basis of the induced voltage generated by the coil which corresponds to the fret contacting the string when the string is stopped.

Abstract: A stringed musical instrument has a plurality of strings stretched between two fixed points and over a bridge. The strings are of substantially circular cross section and made from an elastomeric material such as silicone rubber; all strings are monolithic. The bridge incorporates one or more piezo-electric or other transducers each mounted as a bimorphic element in a simple beam mounting between fixed supports on the bridge and in acoustic contact with the body of the instrument through a resilient baffle pad in contact with the face of the piezo-electric element remote from the supports. That is, mounted in a manner in which the transducer can be considered to be a beam extending between load bearing or supporting members at its two ends, the fixed supports, while it is loaded transversely between its two ends by the baffle pad.

Abstract: A stringed musical instrument of the solid body or equivalent type is provided with elongated resonant beams which support the bridge for the instrument strings. The resonance of the beams is lowered by the use of concentrated mass portions in or on the beams so that the resonance of the beams will be lowered and with electrical vibration-pickup means a sound more closely resembling that of a hollow bodied instrument will be achieved. The pickups may be crystal, magneto dynamic or other suitable type which are used to produce an electrical signal representative of string induced beam vibration.

Abstract: An electric string instrument, e.g. an electric guitar, has one or more resistive elements associated with each fret whereby sideways deflection of a string while in contact with a fret creates a change in the effective resistive value of that fret. This may be used to provide "blending" of a note. Each such fret has one conductor, thus enabling a 144 wire harness in the neck of a guitar to be reduced to 24 conductive paths, which may be provided on a printed circuit board. Preferably both the strings and the frets are electrically scanned. The instrument may be employed as a MIDI guitar controller or an audio guitar or simultaneously as a combination of both. A guitarist can use a normal playing style, without special adaptation, to obtain a full range of expression, including pick velocity.

Abstract: A sound pickup assembly for an acoustic string instruments includes a pad element of foam material and shaped to be placed in an interference fit into a sound hole of the instrument. The foam pad element has therein openings for microphones and leads, with the microphones being positioned inside the foam pad element in a manner such that the sound waves inside the resonator body of the instrument may readily strike the surfaces of heads of the microphones without interference.

Abstract: An electronic harp (10) of the type including a plurality of strings (22) corresponding to the diatonic scale is disclosed. Chromatic operation is achieved by selective frequency shifting of individual string frequencies in response to selection by an operator. The harp (10) includes a foot (26) and a handle (24) and is designed to provide for a minimum of mechanical vibration. A channel VSO (48) driven by strings (22) provides an audio output signal.

Abstract: An improved electric stringed instrument which can produce "banjo" sounds. The instrument has a banjo head including a taut flexible membrane mounted on a ring which is mounted on a solid material (preferably wood) body. The ring and body are connected in a conventional manner to a fretted neck extending away from the head. A plurality of strings extend from adjustable securing means at the end of the neck over the flexible membrane to a tailpiece secured to the body. A bridge is positioned between the strings and membrane. One or more recesses in the body below the membrane contain electric pickups. The spaces between the sides and bottoms of the pickups and the adjacent surfaces of the recesses are at least partially filled with resilient foam. The foam beneath the pickups is compressed slightly to keep the upper pickup surface in resilient contact with the membrane.

Abstract: A synthesizer guitar controller pickup and method for generating control signals for a synthesizer. The control signals are NOTE, GATE, and VELOCITY. NOTE corresponds to the pitch, GATE corresponds to when the sound is initiated and stopped and VELOCITY is a signal which is proportional to the force applied to the guitar string. A DC sensor, such as a photo detector or Hall Effect transducer, is employed to detect these signals. The DC sensor measures how far the string deviates from its rest position, this value is the VELOCITY signal. The flyback from the peak deflection initiates the GATE signal to turn on the sound. When the string stops vibrating, the GATE, and thus the sound, is turned off.

Abstract: A transducer for a stringed musical instrument incorporating an electrically conductive ground plane, along with a plurality of piezoelectric transducers and a conductive strip. The ground plane, piezoelectric transducers and conductive strip are secured in an elongated unitary structure with the ground plane and conductive strip disposed on opposite sides of the transducers. A conductive shield made of paper with a conductive coating is disposed about the unitary structure and electrical leads connect to the ground plane and conductive strip, respectively.

Abstract: A guitar-like electronic musical instrument for use with a synthesizer has six pitch strings on the neck which the player depresses onto conductive frets to determine the selected semitone. A transducer senses if the player forces the string laterally on the fret and if the string is so laterally forced (bent) beyond a threshold, further pitch detection is inhibited. The fret construction can be much simplified and there is no danger of spurious notes being caused by contact with adjacent strings.

Abstract: An electronic stringed instrument includes strings, a plurality of metal frets, an ultrasonic transmitter/receiver, and a fret discriminator. The strings are kept taut above an instrument body. The frets are arranged below the strings along their extension direction. When a player depresses a given string to be picked, at least one of the metal frets is brought into contact with the given string. The transmitter/receiver is coupled to specified positions of the strings and causes ultrasonic vibrations of the strings and receives an echo vibration generated as a reflection of the ultrasonic vibration at a fret contacting the given string. The fret discriminator discriminates the fret contacting the string among the metal frets according to the time difference between the generation of the ultrasonic vibration and the receipt of the echo vibration by the transmitter/receiver.

Abstract: The preferred embodiment relates to a musician operated electric guitar having a plurality of metal strings and at least two pickups for transforming mechanical vibrations of the metal strings into electrical signals proportional to such mechanical vibrations, where the electrical signals from the at least two pickups are added together into a single guitar output circuit.

Abstract: A guitar controller for an electronic music synthesizer utilizes a multiplexed string energization and fret acquisition system wherein a high impedance buffer allows voltages to be detected off the strings at the various frets without drawing current through the frets or fret/string contacts. Unique string bend and string vibration sensors and expression auxiliary sensors are additionally disclosed.

Abstract: Electric stringed musical instruments having an elongated fingerboard, an upper headpiece and nut and a lower tailpiece and bridge, with a first set of primary frets placed in regular sequence along the fingerboard from its upper end to is lower end and a set of secondary frets each placed intermediate a pair of primary frets along the fingerboard. Each secondary fret is so placed between two primary frets that upon depression of a string of the instrument between any selected pair of frets comprising a primary fret and an adjacent secondary fret, accompanied by plucking or strumming of the string, two harmonically resolved musical notes are generated. One of such notes is related to the length of the portion of the string between the lower fret of the selected pair of frets and the lower bridge of the instrument and is picked up by a pickup head of a lower magnetic pickup assembly.

Abstract: An electric stringed instrument such as a guitar having a sound reproducing element on the top of the neck for feeding the tones of the strings back into the guitar. (A sound reproducing element being a speaker or an electromagnetic transducer.) The tones of the strings are sent from the pickup to an amplifier and then to the sound reproducing element. This feedback will either prolong the note played or one of its harmonics or will not have any effect depending upon which note is played. Two wires are imbedded in the back of the neck to bring the electric signal to the sound reproducing element.

Abstract: An optical pickup system for converting the vibration of the string of a musical instrument into electrical signals, adapted to be used with a pitch calculator system. The pickup is constructed with the plane comprising the optical emitter and detector substantially parallel to the body of the musical instrument. Side walls of the optical pickup prevent the vibration of any string from interfering with the pickup for adjacent strings. The pickup uses a very narrow aperture optical emitter to maximize the signal of the noise ratio of the pickup system. A separate signal from each string is then routed to the pitch calculator circuit.

Abstract: An electromagnetic pickup for an electric guitar or similar stringed instrument incorporates a magnetic pickup assembly having pole pieces whose heads are slotted. The heads are positioned directly below the strings of the guitar. By orienting the slots so that they are perpendicular to the strings a percussive sound characteristic is obtained. By rotating the heads so that the slots are parallel to the strings, a sound characteristic typical of dual pole pickups is achieved.

Abstract: An electronic musical instrument of the stringed type wherein bending of a string results in a change in a parameter of the sound produced. At the bridge of the instrument, each string is connected with a leaf spring which is moved towards the nut end of the instrument when the string is bent. Each leaf spring is connected with a Hall effect device, and the spacing between it and a permanent magnet is changed when the spring moves, thus causing a variation in the output of the Hall effect device, which variation alters a parameter of the audio output produced by a tone generator means.

Abstract: A guitar-like electronic musical instrument for use with a synthesizer (18) has a body (20) and a neck (22). The neck carries six pitch strings (40) which the player depresses onto conductive frets to determine the selected note. The body carries six trigger strings (50) which can be plucked or strummed to initiate or trigger the desired notes. Alternatively they can be triggered by six keys (70). The trigger strings (50) and pitch strings (40) are at an angle to each other. The three lower strings and the three higher strings can be triggered together by group trigger keys (300,302) and all six strings triggered by a master trigger key (204). If either of switches (200,202) are actuated, notes will be triggered automatically as soon as the pitch string is depressed onto the fret. Touching of the string is detected by an a.c. waveform superposed on a d.c. potential. Hall effect devices are used to sense triggering by the trigger strings (50) or keys (70).

Abstract: A bridge pickup for a string instrument includes a sensor assembly mounted in a U-shaped base. The sensor assembly includes a cast member encapsulating a holding means which holds an array of piezo sensor elements. The cast member extends below the sensor elements and includes an upper crest portion for supporting the strings of the instrument. A groove formed in the cast member at a point below the sensor elements extends to the lower electrode contact faces of the sensor elements, and a conductor placed in the groove provides an output. A U-shaped channel holds the sensor assembly and the conductor. Preferred conductive and casting materials are shown, and a method of manufacture is described.

Abstract: An electronic sensing system is disclosed for sensing fingering on a stringed and fretted musical instrument, such as a guitar, to produce therefrom electronic signals truly representative of the music created by the musical instrument. Sensing includes detection of the musical pitch created by each selected string and fret combination, as well as detection of the vibration state of the selected string and any pitch variations induced by the performer through string bending.

Abstract: A variable power amplifier having a constant current differential amplifier driving a cascaded driving amplifier, a variable power amplifier including a vacuum tube for selectively amplifying output signals wherein the drive of the variable power amplifier is determined by the plate shunt resistive loading of the vacuum tube, a push-pull amplifier including an output transformer operatively coupled to the variable power amplifier and to an amplifier output terminal to amplify and apply to the amplifier output terminal a selectively amplified output signal, and a variable damping circuit including a sensing element for sensing the loading on the output tranformer and a circuit for defining a feedback loop for producing a feedback signal having magnitude and polarity which are determined by the sensing element and wherein the variable damping circuit includes a circuit for applying the feedback signal as an input to the constant current differential amplifier to control the current level thereof as a function o

Abstract: An electronic stringed musical instrument having an electrically insulating fingerboard is disclosed. The fingerboard is provided with a number of segmented frets attached across its upper surface at desired points along its length. Each of the frets includes a number of electrically conducting fret segments each of which are electrically insulated from one another. Any number of strings may be provided on the instrument each string is disposed adjacent to and associated with a single fret segment of each of the segmented frets. A top-octave generator and octave dividers are utilized to selectively provide a fret segment of one of the frets with an electrical signal of at least one known referencing frequency. The strings are attached to the instrument in a spaced relationship with respect to the fret segments. Displacing a string to contact one of the fret segments completes an electrical circuit having at least one frequency equal to a frequency of the signal provided to that fret segment.

Abstract: An improved, easily-transportable, electric double bass viol having a non-resonant body and rigidly supported fingerboard for enhanced string sustain and tonal brilliance, collapsible body extensions for providing the customary physical dimension and reference points found in traditional double basses to render the instrument easily playable by bassists trained on traditional double basses, and a piezoelectric bridge pickup structure having a piezoelectric element and flexible and inflexible portions such that string motion is transmitted to the piezoelectric element while acoustic energy in the body is substantially prevented from exciting the piezoelectric element, thereby eliminating unwanted acoustic feedback, while providing a tonal characteristic similar to an acoustic double bass.

Abstract: A musical instrument sound quality enhancement device comprised of a circular shaped planer sound hole cover adapted by opposingly positioned underside sets of spaced angularly outward and downward projecting pliable affixment fingers to thereby enable insertably installed occlusive attachment of the cover within the circular shaped sound hole opening of a guitar, banjo, ukulele, dulcimer or any similar such stringed instrument the use of which eliminates feedback interference otherwise common to an amplifier equipped instrument of the type described, or with a ported variably occlusive sound hole cover version thereof not only accomplish amplifier feedback interference elimination when employed in a port fully closed configuration but when employed in a port variably set occlusive sound hole cover partially open configuration alternately effect instrumental tonal variations.

Abstract: A guitar controller for an electronic music synthesizer utilizes a multiplexed string energization and fret acquisition system wherein a high impedance buffer allows voltages to be detected off the strings at the various frets without drawing current through the frets or fret/string contacts. Unique string bend and string vibration sensors and expression auxiliary sensors are additionally disclosed.

Abstract: A method of (and apparatus for) extracting the fundamental pitch period of a complex electrical signal V.sub.2 (t), that includes the serial steps of deriving a time varying reference signal V.sub.ref (t) from the complex electrical signal V.sub.2 (t), which reference signal V.sub.ref (t) adapts continuously (i.e., each cycle of the complex electrical signal) to peak amplitude excursions of the complex electrical signal V.sub.2 (t); sensing ascending values of the signal V.sub.2 (t) to a first point at which the maximum magnitude of the signal V.sub.2 (t) of one polarity is reached and reversal of direction thereof occurs; storing the first substantially instantaneous difference in magnitude between the complex electrical signal V.sub.2 (t) and the time varying reference V.sub.ref (t) at the point of maximum magnitude of the signal V.sub.2 (t); thereafter sensing a point at which the magnitude of the signal V.sub.