A Musical Controller Based on the Cicada s Efficient Buckling Mechanism

Transcription

1 A Musical Controller Based on the Cicada s Efficient Buckling Mechanism Tamara Smyth CCRMA Department of Music Stanford University Stanford, California tamara@ccrma.stanford.edu Julius O. Smith III CCRMA Department of Music Stanford University Stanford, California jos@ccrma.stanford.edu Abstract The cicada uses a rapid sequence of buckling ribs to initiate and sustain vibrations in its tymbal plate (the primary mechanical resonator in the cicada s sound production system). The tymbalimba, a music controller based on this same mechanism, has a row of 4 convex aluminum ribs (as on the cicada s tymbal) arranged much like the keys on a calimba. Each rib is spring loaded and capable of snapping down into a V-shape (a motion referred to as buckling), under the downward force of the user s finger. This displacement of the rib during buckling is measured by a sensor and then passed through a differentiating circuit to get velocity. The velocity is then converted to energy and then used as the input to a synthesis model a physical model of the acoustic elements in the cicada s sound production mechanism. INTRODUCTION Though many bioacoustic systems are similar to those found in musical acoustics [?], the cicada s use of a sequence of rapidly buckling ribs to excite and sustain tones is rather unique. Neither the buckling mechanism itself, nor the use of discrete impulses to sustain musical tones, seem to be used by any traditional musical instruments. Musical instruments generally require the player to supply continuous energy to sustain a tone, as in the continuous motion of the arm while bowing a string instrument, or the continuous blowing required to sustain a note on a wind instrument. Discrete excitations mechanisms such as plucking or striking generally produce tones that decay after a period of time. In this research, a music controller based on the cicada s buckling mechanism was developed so that its potential as a musical instrument can be explored. It provides a mechanical user interface to an already existing synthesis model of the cicada s sound production mechanism [?,?], allowing the user to manipulate the computer model s parameters in a meaningful and intuitive way. This paper will briefly review the cicada s rapid sequential buckling mechanism (which is used to excite the primary mechanical resonator of the sound production system), and discusses how this mechanism is incorporated in the development of a musical controller for an existing 1

2 Figure 1: The tymbalimba physical model. Finally, the issue of interfacing the mechanical model to the physical model will also be discussed. THE CICADA S RAPID SEQUENTIAL BUCKLING MECHANISM The cicada produces its characteristic loud sustained tone by converting the energy of a rapidly contracting muscles into sound energy, using both a mechanical resonator, the tymbal plate, and an acoustic resonator, the abdominal air sac [?]. Tymbal Abdominal air sac Opercula (controls sound output) Tympana (inertial element of the helmholtz resonator) Figure 2: The cicada The cicada s primary sound production organ, the tymbal, is equipped with a plate and a series of connected convex ribs that collapse, or buckle, under the force of a contracting muscle [?]. Buckling is a nonlinear phenomenon that results when a downward force applied to a convex form causes it to spring into a concave form (see figure??) [?]. When the force is no longer present, as is the case when the tymbal muscle relaxes, the rib is free to spring back to its original shape, ready to be buckled again. When the tymbal muscle contracts, the tymbal plate is pulled inward and a central downward force is placed on the adjacent rib to which it is connected. This force is sufficient to cause the first rib to buckle inward and, subsequently, since all the ribs are attached by an elastic resilin, a similar force is exerted on the next rib in the sequence. Depending on the energy generated by the first buckling rib, up to all four ribs on the tymbal may buckle [?]. 2

3 F Figure 3: Inward buckling of a tymbal rib When the first rib in the sequence buckles, the tymbal plate is immediately set into vibration. The buckling of succeeding ribs allows the cicada to maintain the vibration of the plate [?]. The coupling of the the plate to the abdominal air sac causes a smoothing and amplification of the discrete sound pulses generated by the tymbal, resulting in a loud sustained tone. Ribs Tymbal plate Figure 4: A simplified diagram of the tymbal, showing the sequence of ribs and the relative position of the tymbal plate. THE MECHANICAL MODEL The tymbalimba, like the cicada s tymbal, consists of 4 convex aluminum ribs arranged in a sequence, much like the keys on a calimba, so that each rib fits comfortably under the hand s fingers (the spacing between the ribs is adjustable to suit the user). When the user applies a sufficient downward force to a rib, it buckles (see figure??). The energy signal generated by this motion will depend on the applied force and velocity of the user s finger. As with the tymbal ribs, when the user removes his/her finger, effectively removing the downward force, the model s rib will spring back to its original shape. Depending on the species of Cicada, the rate of muscle contractions can occur as frequently as 200 Hz. Of course, the neurogenically initiated muscular contractions of the cicada give it quite an advantage over a human. It would be absurd to expect a human to buckle the mechanical ribs as rapidly as a cicada it certainly wouldn t be long before the pain of repetitive strain injuries was felt. The mechanical controller, therefore, aims to capture the energy generated by the buckling of the first rib. Based on this signal, the computer model accurately produces the impulses that would be generated by additional buckling ribs. 3

4 Figure 5: The controller s buckling motion The cicada has 2 tymbals, one on either side of its abdominal air sac, which can be controlled and tuned individually to create inharmonic sounds. Another benefit of the controller s design is that the independence of the controller s ribs (and the fact that the buckling sequence is generated by the computer model) effectively provides the user with 4 tymbals, all controllable with only the motion of the finger. Depending on how the ribs are mapped in the computer model, gestural motions such as drumming the finger over all 4 ribs can create very interesting sound effects. A public demonstration of the controller at an early stage in its development showed that users were captivated by the the responsiveness of the mechanism itself even though at this stage they were not actually controlling any sound output. The way the spring loaded mechanism caused the ribs to bounce back up at the user every time they were buckled, created an animated excitement in some users and clearly showed the importance of physical stimuli in 4

5 haptic user interfaces something which is far too often overlooked in the design of musical controllers. Since this demonstration, and the addition of sound controlling capabilities, experiments have shown that the rebound buckling, or outbuckling, is also very useful for repeating notes quickly (see figure??). Figure 6: The blurr from the finger s motion suggest the agility with which the user is able to buckle the ribs The cicada can also change the amount of energy released by a buckling rib by changing the curvature in the ribs [?]. This is accomplished in the model by adjusting the stops at the end of each rib (see figure??). Letting the stops out will flatten the rib and make it less difficult to buckle. Though this will produce a lower amplitude impulse, it has the benefit of allowing the user to play notes in more rapid succession. Likewise, pushing a stop inward increases the slope in the rib, making it slightly more difficult to buckle yet generating a higher amplitude signal at the point of buckling. Figure 7: Adjusting the tymbalimba s stops The user can change the signal generated by the buckling of a rib by varying the gesture of the attack, that is, by changing the velocity and/or force of the finger motion. A higher amplitude signal will cause a greater number of ribs to buckle in the sequence. As with most 5

6 traditional musical instruments, the user is therefore able to control the sound based on a single gestural input rather than tweaking an overwhelming myriad of knobs and buttons that control single independent parameters. INTERFACING TO THE PHYSICAL MODEL What is measured by the controller is not the force input of the user, but rather the energy generated by the ribs that are buckled by the user. Hall Effect sensors are placed to the side of each rib and a magnet is placed directly on the rib itself. During buckling, the magnet passes over the sensor and the displacement of the rib is measured. The voltage representing displacement then passes through a differentiating analog circuit (see figure??) to obtain velocity. The velocity is converted to energy inside the model, and becomes the input signal to the physical model. Figure 8: The signal conditioning circuit for the Hall Effect sensors The voltage from the sensors (Vs on the far left of figure??) represents the displacement of the ribs during buckling. The electronic components surrounding and including the first op-amp make up a differentiating circuit. The displacement voltage from the sensors passes through the differentiator to obtain a signal representing velocity. Since positive numbers are more easily handled from the Basic Stamp chip, additional circuitry (seen at the second op-amp) is used to add a DC component to the signal. An analog to digital converter reads the voltage values from 4 channels (one for each rib) and sends it to the Basic Stamp (BS2SX) microcontroller where it is redirected in digital form, via the serial port, to the computer. 6

7 Figure?? and?? illustrates the velocity voltages produced while a rib is being buckled, as measured by an oscilloscope in the background. During downbuckling (top of figure??), an upward impulse can be viewed on the scope. During upbuckling (bottom of figure??, occurring when force is no longer applied to the rib, there is a very clear downward impulse on the scope. Figure 9: The output signal generated by an downbuckle and an upbuckle. Figure 10: The signal generated by a series of up and down buckles, as measured from the the computer. Different sounds will result from impulses having different amplitudes and widths, both because this is true of any resonator with a varying impulse excitation mechanism, and also because the computer model will produce a different number of buckling ribs depending on the initial impulse. Figure?? shows the output of the model for the tymbal plate after a controller 7

8 rib is buckled (only the downbuckle motion is shown) with enough force to set off all 4 ribs in the sequence. The four impulses are very apparent in the resulting waveform. It is interesting to observe the decrease in amplitude by the time the 4th rib buckles showing an apparent loss in the system during one buckling cycle. Figure 11: Output for the model of the tymbal plate after a downbuckle from the controller normalized amplitude time(samples) Figure 12: Output of the model for the abdominal air sac with figure?? as input. Once the output of the tymbal plate passes through the model of the abdominal air sac, the individual impulses become much less noticeable (both visually and audibly) and the resulting waveform (see figure??) is much smoother. There is also an expected increase in amplitude since the abdominal air sac is tuned to the same resonant frequency as the fundamental mode of the vibrating tymbal plate. The controller provides a more accurate input signal to the physical model than the arbitrary impulse signals previously being used [?,?]. Because the user is playing a real mechanical system, s/he is not denied the important haptic information required when playing a musical instrument [?]. Changing the impulse is all the user need do to get a responsive change in the produced sound, and this can now be done with the use of a single gesture. Physical modeling synthesis tends to be extremely parameter-rich, often requiring too much attention to individual variables to be suitable for real-time performance. The previously 8

9 Figure 13: A sequence of up and down pulse can be seen on the oscilloscope during normal playing. developed physical model of the cicada [?] suffered from this problem when determining the parameters of a rather complex system of buckling ribs. How many ribs should buckle? What is the rate of buckling? What is the rate of muscle contractions (the time before re-starting the sequence of buckling ribs)? What is the energy difference between the IN and OUT buckling cycle or between the buckling of the first and last rib? Just as the cicada varies each of these parameters during vocalization, so should the user be able to manipulate, in real-time, all the factors that determine the physical model s sound. Of course, it is impossible to be aware of so many individual parameters when playing any musical instrument (electronic or acoustic) yet this does not mean it is impossible to control them. Since it is generally not desirable to remove functionality from a physical model by eliminating some of its parameters (just to make it more controllable), it would be useful if these parameters could be obtained from functions representing one single action or gesture which the user could learn to do in various ways to produce different results. In the case of a piano for instance, the pianist is able to achieve a very wide variety of sounds simply by deciding which key to play and with which velocity to play it the complex hammer mechanism striking the string, the lengths and tensions of which are already set, takes care of the rest. By buckling one rib, the user uses one motion to produce a signal that is sent to the physical model. From this input signal, the physical model can derive many of its parameter values without relying on additional user input. From one gesture, the model obtains information about the envelope of the impulse (which effects both timbre and volume in the sound), the number of ribs that will buckle in the sequence (which is derived from the amount of energy in the signal), and, if each rib is mapped to a pitch, frequency information can also be obtained. Since the parameters are determined by one motion of the user, they will change only as the motion changes. With time and practice, the user will eventually learn how varying the motion changes the quality of the sound produced, and will be much more successful in playing the instrument. BUILDING THE MODEL As much of the work in this project involved designing and building the mechanical controller, a section is included here describing the methods used. 9

10 Machining Methods The parts of the model were machined from aluminum (6061-T6) on a CNC mill at Stanford University s Product Realization Lab (PRL). Fixturing of the ribs (T-parts) was done with each part attached to a block of aluminum via socket-cap screws. Each screw was placed at each of the 3 tips of the T-parts, taking advantage of the need for holes in these locations to place the axial shafts when assembling the device. Figure 14: Fixturing the T-part for CNC machining Figure 15: A side view of the T-part when fixtured for CNC machining The blocks which suspend the ribs, referred to as the L and C-parts, were also machined on a CNC mill. They are attached to the base plate through a long channel cut into the plate, using socket-head screws. The user need only adjust the screws to loosen the L and C-parts so they can slide easily through the channel, thereby adjusting their relative position to one another. Assembly A rather challenging part in the assembly of the parts was to find the proper springs, A and B from figure??, to achieve the desired response from the the device. The springs cannot be too stiff, or they would require too much effort to buckle. The primary spring controlling tension in the ribs is spring A, a compression spring; the primary spring responsible for the rebound buckling is spring B, an expansion spring without it, the spring would be stuck in the downward position. A change in one, therefore, requires a change in the other. Much experimentation involving different users was done to find the preferred string stiffness. Since 10

11 these are not variables in the controller, any further adjustments in the tension of the ribs can be done using the stop mechanism (see figure??). A A B B Rest Position Buckle Position Figure 16: The expansion and compression of the springs during buckling. FUTURE WORK An addition to the instrument, currently in progress, will allow the user to change the sounding pitch with the left hand, while controlling the buckling mechanism with the right. It is an extension of the base plate, and will contain 4 linear force sensing resistors (FSR) (one for each octave). Specially formed grooves in the plate will allow the user to easily locate the tempered placement of pitches on the FSR, while still permitting the finger to slide between the them. Future work may also include creating different sizes of the controller. For example, it may be interesting to create a scaled down version so that it fits easily in one hand, and buckling occurs when one makes a fist. Another alternative may be to increase the number of ribs, and therefore the size of the device, so that a full keyboard range is supported. CONCLUSION The Tymbalimba goes beyond simple on-off triggering devices. Measuring the energy generated by the mechanical controller provides the computer model of the cicada with an input signal that accurately represents the user s gestures, as well as the buckling motion of the ribs. 11

12 Not only does this eliminate the encumbrance of controlling the numerous individual parameters normally associated with physical models, but it allows the user the satisfaction of playing a responsive haptic interface and hearing the results of the intriguing sustained tones of the cicada s vocalization. ACKNOWLEDGMENTS Many thanks to the teaching assistants at Stanford s Product Realization Lab (PRL) for the endless help and suggestions they provided during the development of this model. We extend our thanks also to Bill Verplank, the instructor for the Human Computer Interaction class at CCRMA, who helped us tremendously with his insightful comments and the time he generously gave to help make video demonstrations (from which many of the pictures in this document are taken). 12