Patent Publication Number: US-8109146-B2

Title: Measurement of bowed string dynamics

Description:
NOTICE OF COPYRIGHTS AND TRADE DRESS 
     A portion of the disclosure of this patent document contains material which is subject to copyright protection. This patent document may show and/or describe matter which is or may become trade dress of the owner. The copyright and trade dress owner has no objection to the facsimile reproduction by anyone of the patent disclosure as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright and trade dress rights whatsoever. 
     BACKGROUND 
     1. Field 
     This disclosure relates to a measurement system designed to understand the dynamics of a bowed string instrument. 
     2. Description of the Related Art 
     To understand the intricacies and nuances of a bowed string instrument, at least two aspects of a bowed string instrument may be analyzed. First, the physics of a bowed string instrument needs to be understood. Second, how a player controls and uses the bow of a bowed string instrument to produce a range of sound, with respect to the pitch and volume, needs to be understood. 
     Regarding the first aspect, extensive research and numerous studies have been performed in an attempt to understand the physics of a bowed string instrument. This aspect is complex because the way the bow and the string of the bowed string instrument interact affects the sound produced by the bowed string instrument. Certain bowing parameters affect the sound produced by the instrument. For example, the bow speed, the bow position, the bow tilt, and the bow force used on the string all affect the sound produced by the instrument. 
     One feature of a bowed string instrument is that a friction component exists inherent in the interaction between the bow and the string. Players of a bowed string instrument strive to achieve the “Helmholtz motion” between the bow and string interaction. (“Helmholtz motion” occurs when the string forms a corner that travels in a parabolic path back and forth between the bridge and nut of the violin.) In order to achieve the “Helmholtz motion”, the player needs to carefully manage the interaction between the bow speed and the bow force on the string. The bow speed, bow force and position determine how and if the bow sticks to the string. If the bow does not stick to the string, then the string will produce surface sound, which is not desired by the player. If the string does not release from the bow in a timely manner, then the string motion will sound harsh. 
     Achieving the “Helmholtz motion” not only requires skill but also an understanding of the physics of the bowed string instrument. A player also benefits by understanding the relationship between the bowing parameters and the sound produced. The friction component inherent in the bow and string interaction distinguishes the bowed string instrument from instruments that are not bowed string instruments. The friction component creates a “many-to-one” mapping in which numerous variations of bowing parameters can be used to achieve the same sound. Therefore, while a person may be able to predict the sound that will be produced after knowing the bowing parameters, a person will not be able to determine the bowing parameters based solely on hearing the sound produced. 
     The measurement system disclosed herein measures a player&#39;s bowing technique where the system allows the instrument to be played normally, without interference, so as to capture realistic data. Systems exist that can analyze the sound from real violins generated by fixed bowing parameters and that can be used in a laboratory environment which can measure certain bowed string dynamics. However, without a system included with or coupled to a stringed instrument which allows the instrument to be played normally, without interference, the bowing parameters cannot be precisely and accurately measured. 
     Therefore, a measurement system has been created to capture gesture data and audio of a player playing a bowed string instrument, so as to understand the dynamics of a bowed string instrument. The gesture data captured is the data relating to how a player controls the bow. By capturing the gesture data and the corresponding audio produced by the bowed string instrument, the measurement system can aid in understanding the dynamics of a bowed string instrument such as how and why certain bowing gestures produce certain sounds from the instrument. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a physical diagram of a measurement system comprising a bow having a bow system coupled with a bowed string instrument and a computer. 
         FIG. 2  is a block diagram of a measurement system comprising a bow system and base component that measure bowed string instrument dynamics. 
         FIG. 3  is a flow chart of a method of measuring bowed string instrument dynamics. 
         FIG. 4  is a physical diagram of a bow. 
     
    
    
     DETAILED DESCRIPTION 
     Throughout this description, the embodiments and examples shown should be considered as exemplars, rather than limitations on the systems and methods disclosed or claimed. 
     Understanding the techniques employed for bowing a stringed instrument is complex because both the bow and the base of the stringed instrument are moving while the player plays the instrument. (The “base” of the stringed instrument as used herein is the part of the instrument that comprises the strings.”) In addition, in some instances, the bow and the base may move in opposing directions. Therefore, the measurement system described herein detects the 3D movement of both the bow and the base of the stringed instrument. By detecting the movement of both the bow and the base, the measurement system can measure the bowing parameters relative to the violin or other stringed instrument. These bowing parameters include parameters such as the bow force, the bowing direction, the bow tilt, the bow-bridge distance, the bow position and the bow speed. 
     The bow force is the force with which the bow is applied to the string of the base. Knowing the force applied to the strings on the base is helpful in understanding bowing techniques because the amount of force used will affect the sound produced by the instrument. 
     The bowing direction is the direction the bow is moving—upward or downward—with respect to the base. Knowing the direction the bow is moving is another parameter which will aid in understanding bowing techniques. 
     The bow tilt is the tilt of the bow with respect to gravity or with respect to the violin. The bow-bridge distance is the distance of the bow from the bridge of the base. The bow position is the distance between the bow and the violin. The bow speed is the speed the bow is moved in a certain bowing direction on the base of the bowed string instrument. The bow speed may be influenced by the bow tilt. The above identified bowing parameters are essential to describe the dynamics of a bowed string instrument. 
     A Measurement System 
     Referring now to  FIG. 1 , there is shown a physical diagram of a measurement system comprising a bow system  120  and base component  140  coupled with a bowed string instrument and a computer  150 . The measurement system captures the physical bow motion and bowing technique of a player playing a bowed string instrument. The measurement system does not impair traditional bowing techniques and therefore remains convenient to use and play by a performer. The measurement system may be implemented on a variety of bowed string instruments including a violin, a cello, a viola and a double bass. 
     The measurement system works in conjunction with a bow  110  and a base  130  of a bowed string instrument, and a computer  150 . The bow  110  typically consists of a stick with at least four strands of horsehair strung between the two ends of the stick, the tip end  160  and frog end  170 . The bow system  120  portion of the measurement system may reside on the bow  110  of the bowed string instrument. The bow system  120  may comprise a force sensing mechanism  105  and a bow board  115 . In one embodiment, the force sensing mechanism  105  may be installed near the midpoint of the bow. In another embodiment, the force sensing mechanism  105  may be installed along the full length of the bow. In one embodiment, the bow board  115  may be installed near the frog  170  end of the bow  110 . In another embodiment, the bow board  115  may be integrated into the bow itself. The force sensing mechanism  105  and bow board  115  are described in more detail below regarding  FIG. 2 . 
     The bow system  120  is generally a small and lightweight system which is free from unnecessary wires. The purpose of designing a small and lightweight system is to ensure that a player&#39;s movement of the bow remains unconstrained and that the bow remains comfortable to use. 
     The measurement system further comprises a base component  140  that resides on the base  130  of the bowed string instrument. The base component may reside between the bridge  180  and the tailpiece  190  of the base  130 . 
     The measurement system also comprises a computer  150 . Although shown implemented in a personal computer, the systems and methods may be implemented with any computing device. A computing device as used herein refers to any device with a processor, memory and a storage device that may execute instructions including, but not limited to, personal computers, server computers, computing tablets, set top boxes, cellular telephones, video game systems, personal video recorders, personal digital assistants (PDAs), portable computers, and laptop computers. These computing devices may run an operating system, including, for example, variations of the Linux, Unix, MS-DOS, Microsoft Windows, Palm OS, Solaris, Symbian, and Apple Mac OS X operating systems. 
     Referring now to  FIG. 2 , there is shown a block diagram of a measurement system comprising a bow system and base component that measure bowed string instrument dynamics. The measurement system comprises a bow system  120  and a base component  140  coupled with a computer  150  (as shown in  FIG. 1 ). 
     The bow system  120  comprises a force sensing mechanism  105 , and a bow board  115 . The bow board  115  comprises a board with circuitry to aid in capturing the data related to the bowing parameters. In one embodiment, the bow board comprises a printed circuit board. The bow board  115  comprises an acceleration and angular velocity sensing mechanism  220 , a position and speed sensing mechanism  230 , a data communication module  240  and a power module  250 . 
     The force sensing mechanism  105  measures the bow force, including both the downward bow force and the lateral bow force. The force sensing mechanism  105  comprises two force sensors having a large bandwidth and minimal hysteresis. Force sensors with large bandwidth and minimal hysteresis are useful in ensuring that the rapid changes in bow force are accurately recorded. These force sensors are each composed of four foil strain gauges placed in a Wheatstone bridge configuration. A Wheatstone bridge is an electrical bridge circuit used to measure resistance. These force sensors may be placed around the midpoint of the bow. The force sensors may be installed by adhering the sensors and wiring the sensors to the stick of the bow. In another embodiment, the force sensing mechanism may comprise an array of force sensors placed along the length of the bow. For example, as seen in  FIG. 4 , an array of force sensors  420  can be placed along the bow  110 . The axis  430  illustrates that the bow will be moving in three dimensions and the array of force sensors along the bow aid in measuring the downward and lateral bow force. In another embodiment, the force sensing mechanism may comprise quantum tunneling composites. In another embodiment, the force sensing mechanism may be impregnated into the bow. 
     The force sensing mechanism  105  may further comprise a digital to analog converter. The digital to analog converter maximizes the dynamic range of the force measurement by offsetting any imbalance of the Wheatstone bridge after installation. 
     The acceleration and angular velocity sensing mechanism  220  measures the bow direction and the bow tilt with respect to the violin. The bow tilt parameter is related to the area of the bow hair which is in contact with the string. In one embodiment, the acceleration and angular velocity sensing mechanism comprises a six degrees of freedom (6DOF) inertial measurement unit (IMU). The 6DOF IMU comprises three 3-axis accelerometers and three gyroscopes. The accelerometers can be piezoelectric accelerometers and MEMS accelerometers, or other 3-axis accelerometers. The gyroscopes can be piezoelectric vibrating gyroscopes, MEMS gyroscopes, or other gyroscopes capable of sensing an angular velocity of at least a maximum of ±300°/s. The acceleration measurements are calculated using the accelerometers, while the angular velocity measurements are calculated using the gyroscopes. 
     The position and speed sensing mechanism  230  measures the bow position and bow speed. In one embodiment, the position and speed sensing mechanism comprises a thin strip of resistive material that is attached to the length of the bow stick and extends from the tip  160  of the bow to the frog  170  of the bow. Material which can be used for the thin strip includes carbon-impregnated plastic, or any other material which has a resistance of approximately 20 kΩ. The tip end  160  and frog end  170  of the resistive strip transmit square wave signals which are received by an antenna mounted behind the bridge of the violin base. The corresponding magnitudes of the signals received may be used to measure the bow position and the bow speed. 
     In another embodiment, the position and speed sensing mechanism  230  comprises a resistive strip that does not extend the full length of the bow. Instead, the length of the resistive strip is slightly decreased such that it is further from the player&#39;s grasp, and the width of the resistive strip is increased at the frog end of the bow. In this embodiment, the attenuation of the signal is decreased because the player&#39;s hand is not as close to the resistive strip. In another embodiment, a time domain multiple access (TDMA) technique may be implemented to lower the power consumption of the position and speed sensing mechanism. In another embodiment, the position and speed sensing mechanism may comprise optical sensors. In another embodiment, the position and speed sensing mechanism may comprise magnetic sensors. In another embodiment, the position and sensing mechanism may comprise an array of force sensors spanning the length of the bow so as to measure the position. 
     The bow-bridge distance may be calculated using the following equation:
 
φ 1 ( x,y )+φ 2 ( x,y )= B   1   /x+B   2 ,
 
where Φ 1  is the potential from one end of the strip and Φ 2  is the potential from the other end. In one embodiment, a camera may be implemented on the base component so as to measure the bow-bridge distance.
 
     The bow position may be calculated from the magnitudes of the square wave signals received from the position and speed sensing mechanism  230  of the bow system  120  using the following steps. 
     First, the potential (φ) in space (in the z=0 plane) is measured and the 2D relationship of the bow antenna and the base component antenna are given with the following equation: 
               ϕ   ⁡     (     x   ,   y     )       =       (         A   1     ⁢     tanh     -   1       ⁢         x   2         x   2     +     a   2             -     A   2       )     ⁢     (         A   3     ⁢   y     -     A   4       )             
where α is the width of the short dimension of the resistive strip.
 
     Second, using the TDMA protocol, the potential of one end of the strip is raised to V, while the other end is grounded. Then, this step is reversed and repeated so that the signal is emitted from both the tip and the frog ends of the bow. 
     Third, the potential field in space is inverted by changing the sign on y, 
               ϕ   ⁡     (     x   ,   y     )       =       (         A   1     ⁢     tanh     -   1       ⁢         x   2         x   2     +     a   2             -     A   2       )     ⁢     (         A   3     ⁢   y     -     A   4       )             
And
 
Φ 1 ( x,y )=Φ 2 ( x,−y )
 
     Then, the approximation for bow-bridge distance, x, is determined with the following formula: 
                   ϕ   1     ⁡     (     x   ,   y     )       +       ϕ   2     ⁡     (     x   ,   y     )         =         -     A   1       ⁢     A   4     ⁢   coth   ⁢         x   2         x   2     +     a   2             +       A   2     ⁢       A   4     .               
as x→∞, Φ 1 (x, y)=Φ 2 (x, y)→0. Therefore, A 2 /A 1 =coth(1)≈1.3104. If
 
             α   =           ϕ   1     ⁡     (     x   ,   y     )       +       ϕ   2     ⁡     (     x   ,   y     )             -     A   1       ⁢     A   4               
then x can be solved as:
 
     
       
         
           
             x 
             = 
             
               
                 
                   i 
                   ⁢ 
                   
                     
                       acoth 
                       ⁡ 
                       
                         ( 
                         
                           
                             coth 
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                           + 
                           α 
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       
                         - 
                         1 
                       
                       
                         α 
                         2 
                       
                     
                     + 
                     
                       
                         1 
                         
                           α 
                           2 
                         
                       
                       ⁢ 
                       
                         acoth 
                         ⁡ 
                         
                           ( 
                           
                             
                               coth 
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                             + 
                             α 
                           
                           ) 
                         
                       
                     
                   
                 
               
               . 
             
           
         
       
     
     Finally, in the last step, y can be solved with the following equations: 
                     ϕ   1     ⁡     (     x   ,   y     )       -       ϕ   2     ⁡     (     x   ,   y     )         =         2   ⁢     A   3     ⁢     y   (         A   1     ⁢   coth   ⁢         x   2         x   2     +     α   2             -     A   2       )       ⇒     
     ⁢   y     =           ϕ   1     ⁡     (     x   ,   y     )       -       ϕ   2     ⁡     (     x   ,   y     )           2   ⁢     A   3     ⁢       A   1     (       coth   ⁢         x   2         x   2     +     α   2             -     coth   ⁡     (   1   )         )             ⁢                       and   ⁢                               ⁢       y   =           ϕ   1     ⁡     (     x   ,   y     )       -       ϕ   2     ⁡     (     x   ,   y     )             -   2     ⁢     A   3     ⁢       A   4     ⁡     (         ϕ   1     ⁡     (     x   ,   y     )       +       ϕ   2     ⁡     (     x   ,   y     )         )             ,           
which is a linear function of Φ 1,2 (x,y). This above equations provide an approximation, since the equations assume that the bow is always parallel to the bridge antennae and that the position estimates are calculated in a planar system where z=0.
 
     The potential discussed above can be created using a 100 kHz square wave signal, or any other frequency signal that can allow coupling between the position and speed sensing mechanism  230  of the bow system  120  and the position and speed sensing mechanism  270  of the base component  140 . 
     In one embodiment, the position and sensing mechanism  270  of the base component  140  may comprise a gain filter stage tuned to the frequency potential from the signals transmitted from the position and sensing mechanism  230  of the bow system  120 . The position and sensing mechanism  270  may also comprise a peak detector in which a low pass filter of the peak detector includes a notch filter to handle in one embodiment, up to 60 Hz noise. In another embodiment, a digital notch filter may be used. 
     The data communication module  240  transmits the data captured by the various sensing mechanisms to the base component  140 . In one embodiment, the data communication module  240  comprises a microcontroller. The microcontroller may include an eight-port 12-bit analog to digital converter. The microcontroller may also include a two-port digital to analog converter. The data communication module  240  may also comprise a wireless interface, such as a Bluetooth interface, to transmit the data to the base component  140 . The data communication module  240  acquires the signals from the force sensors and the six inertial measurements (the 3D acceleration and the 3D angular velocity), and also generates two position signals. The method for transmitting the data to the base component  140  is described in  FIG. 3  (below). 
     The power module  250  provides power to the bow system  120 . In one embodiment, the power module  250  comprises a lithium polymer single cell rechargeable battery. The lithium polymer single cell rechargeable battery is an example of a lightweight and small battery. Use of a lightweight and small battery ensures that the bow system remains lightweight, thereby allowing a player to use the bow in an unrestricted and convenient manner. Such a bow system ensures that the physical bow movement data captured is a true sample of the bowed string dynamics. The power module may also comprise an integrated switching supply and charger circuit used to charge the battery in the power module  250 . The power module may also comprise a charging connector consisting of two charging pads and a mechanical cutout designed to accommodate a mobile phone charging cable or connector, or a USB connector. The power module may also comprise an audio cable connected to the computer  150  to capture and store the sound produced by the bowed string instrument. 
     In one embodiment, the base component  140  comprises an acceleration and angular velocity mechanism  260 , a position and speed sensing mechanism  270 , a data communication module  280 , and a power module  290 . The base component  140  may consist of a printed circuit board having components for the acceleration and angular velocity mechanism  260 , the position and speed sensing mechanism  270 , the data communication module  280 , and the power module  290 . 
     The acceleration and angular velocity mechanism  260  of the base component is similar to the acceleration and angular velocity mechanism of the bow component. In one embodiment, the acceleration and angular velocity sensing mechanism comprises a six degrees of freedom (6DOF) inertial measurement unit (IMU). The 6DOF IMU may comprise one 3-axis accelerometer and three gyroscopes. The accelerometers can be piezoelectric accelerometers and MEMS accelerometers, or other 3-axis accelerometers. The gyroscopes can be piezoelectric vibrating gyroscopes and MEMS gyroscopes, or other gyroscopes. 
     The position and speed sensing mechanism  270  aids in measuring the bow position and the bow speed parameters. In one embodiment, the position and speed sensing mechanism  270  comprises one antenna that is mounted behind the bridge of the violin. This antenna receives the signals transmitted from the position and speed sensing mechanism  230  of the bow system  120 . In another embodiment, the position and speed sensing mechanism  270  comprises four antennas to receive signals from each of the four violin strings. In another embodiment, the position and speed sensing mechanism comprises optical sensors. 
     The data communication module  280  of the base component  140  receives data from the bow system  120  and transmits the data to the computer  150 . In one embodiment, the data communication module  280  comprises a microcontroller. The microcontroller may include an eight-port 10-bit analog to digital converter. The microcontroller may also include an interface, such as a USB, IEEE 1394 or Bluetooth interface, to interact with the computer  150 . The data communication module  280  may also comprise a cable, such as a USB cable, to carry the audio signal produced by the bowed string instrument. 
     The power module  290  provides power to the base component  140 . The power module  290  comprises an interface, such as a USB interface, that is connected to the computer  150 . This interface which is connected to the computer  150  may power the base component  140 . 
     The measurement system comprises a computer  150 . The computer  150  may power the base component  140  and/or the bow system  120 . The computer  150  may store and archive the data captured from the bow system and the base component. 
     The measurement system may be calibrated to interpret the data captured from the bow system and the base component in S.I. units. In addition, to obtain an accurate estimation of the bowing parameters, additional components may be implemented on the measurement system. In one embodiment, a real-time Kalman filter is implemented to obtain accurate and precise data regarding the bowing parameters. A Kalman filter is a recursive filter that estimates the state of a dynamic system from a series of incomplete and noisy measurements. The Kalman filter can be implemented using a software program, module or component. The Kalman filter may take as input the data received from the data communication module  280  of the base component  140 . The Kalman filter may then output the filtered data to another software program, module or component where the filtered data reflects the bowing data having minimal error. 
     Description of Methods 
     Referring now to  FIG. 3  there is shown a flow chart of a method of measuring bowed string dynamics. 
     In  310 , the bow system  120  receives bow sensor data. The bow sensor data comprises data from the force sensing mechanism  210  and the acceleration and angular velocity sensing mechanism  220  of the bow system  120 . In one embodiment, the data communication module  240  receives the bow sensor data via an analog to digital converter. In another embodiment, the sensor data is sent via PWM or a digital serial interface such as I2C or SPI. 
     In  320 , the bow sensor data is sent to the base component  140 . In one embodiment, the bow sensor data is sent via a Bluetooth module that exists as part of the data communication module  240  of the bow system  120 . The bow sensor data can also be sent using UHF or a Microwave radio system. 
     In  330 , the bow system  120  creates position data. The position data comprises data from the position and speed sensing mechanism  230  of the bow system  120 . The position data includes information regarding whether the position signals from the tip end  160  and frog end  170  of the bow  110  are on or off. The position data also includes information regarding the measurements of the position signals from the tip end  160  and frog end  170  of the bow  110 . 
     In  340 , the position markers are sent via Bluetooth, and the position data is sent via the low frequency electric field radio to the base component  140 . In one embodiment, the position data is sent via a Bluetooth module that exists as part of the data communication module  240  of the bow system  120 . In another embodiment, the position data could be sent over the radio. 
     In  350 , the base component  140  receives the bow sensor data and the position data. The bow sensor data is received by the data communication module  280  of the base component  140 . The position data that the base component  140  receives may be multiplexed. If the position data is multiplexed, the base component may de-multiplex the data at this stage. 
     In  360 , the base component  140  receives the base sensor data. The base sensor data comprises data from the acceleration and angular velocity sensing mechanism  260  of the base component  140 . In one embodiment, the data communication module  280  may receive the base sensor data via an analog to digital converter. 
     In  370 , the base component  140  combines the base sensor data with the bow sensor data and the position data. The base component  140  then outputs all of this data (the base sensor data, the bow sensor data and the position data) to the computer  150 . The computer may also receive audio data relating to the sound produced by the bowed string instrument. 
     Once the computer  150  has received all of the data, the computer  150  may store and archive this data. The computer  150  may store and archive this data in a variety of ways. 
     In one embodiment, the data—both the bowing parameter data and the audio data—may be stored and archived in a database. The database may be accessible by a network such as, for example, the Internet. The database may be searchable based on keywords or filenames. The database may also include features such as implementing a stroke group. A stroke group is one way of classifying the bowing parameter data and the audio data. The stroke group may correspond to a certain bow stroke recording that includes the bowing parameter data and the audio data for a certain bow stroke. The stroke group may include all files related to the original player&#39;s recording. The database may also allow multiple files to be uploaded at the same time. For example, the database may allow up to ten files, or any number of files, to be uploaded at once. The database may allow a user to control the files he or she uploads. For example, a user may wish to control who has permission to access his or her files. In addition, the user may wish to categorize the files he or she updates. The database allows for storing, archiving and retrieving data captured by the measurement system. 
     Closing Comments 
     The foregoing is merely illustrative and not limiting, having been presented by way of example only. Although examples have been shown and described, it will be apparent to those having ordinary skill in the art that changes, modifications, and/or alterations may be made. 
     Although many of the examples presented herein involve specific combinations of method acts or system elements, it should be understood that those acts and those elements may be combined in other ways to accomplish the same objectives. With regard to flowcharts, additional and fewer steps may be taken, and the steps as shown may be combined or further refined to achieve the methods described herein. Acts, elements and features discussed only in connection with one embodiment are not intended to be excluded from a similar role in other embodiments. 
     Additional and fewer units, modules or other arrangement of software, hardware and data structures may be used to achieve the systems and methods described herein. 
     For means-plus-function limitations recited in the claims, the means are not intended to be limited to the means disclosed herein for performing the recited function, but are intended to cover in scope any means, known now or later developed, for performing the recited function. 
     As used herein, “plurality” means two or more. 
     As used herein, a “set” of items may include one or more of such items. 
     As used herein, whether in the written description or the claims, the terms “comprising”, “including”, “carrying”, “having”, “containing”, “involving”, and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of”, respectively, are closed or semi-closed transitional phrases with respect to claims. 
     As used in the claims, the terms “comprising”, “including”, “carrying”, “having”, “containing”, “involving”, and the like are to be understood to be open-ended with respect to each limitation of the claim. 
     Use of ordinal terms such as “first”, “second”, “third”, etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. 
     As used herein, “and/or” means that the listed items are alternatives, but the alternatives also include any combination of the listed items.