A Haptically Accurate Practice Carillon Joseph B. Brink* Ying (Jean) Zheng1* John B. Morrell^ Yale University Department of Mechanical Engineering and Materials Science ABSTRACT Mastery of musical instruments remains both a rewarding and chal­ lenging haptic task. The carillon is a particularly difficult instru­ ment to practice due to its public nature and variability from loca­ tion to location. A dynamic model of the carillon key (baton) is presented and a design for a haptically accurate practice carillon is proposed. The Passive Dynamics Practice Carillon (PDPC) is able to emulate a range of actual carillons using adjustment of passive masses and a spring. To evaluate the necessary fidelity of such a design, a study was conducted in which participants were asked to discriminate between batons with differing impedance parameters. The results showed that subjects are more sensitive to the force parameter and less sensitive to the stiffness and inertial parameters. In all cases, the passive adjustment increments on the PDPC were well below the sensitivity of the test participants. This leads us to two conclusions: a) a passive dynamic system is sufficient for a haptically accurate practice carillon and b) the Passive Dynam­ ics Practice Carillon can be simplified to be less accurate but more cost effective while still sufficiently matching the haptic feel of real carillons. Keywords: carillon, haptics, passive dynamics Index Terms: H.1.2 [Models and Principles]: User/Machine Systems—Human Factors; 1 INTRODUCTION Figure 1: The Yale Memorial Carillon resides in Harkness Tower (a). Mastery of musical instruments is one of the most challenging All 54 bells (43 tons in total) are arranged in a space in the tower haptic tasks that humans undertake. Many musical instruments, called a bellfry. A medium-sized bell with clapper in rest position whether string, woodwind or percussion rely on precise control of is depicted on the upper right (b). When a carillonneur plays this force, timing and muscle impedance. Depending on the instrument, note on the keyboard in the playing cabin (c), the clapper will swing it may require precise control of the fingers or recruit larger muscle towards the bell and impact, producing a sound. groups in the arms and torso. The majority of instruments are prac­ ticed in relative privacy and students master certain skills before performing. The carillon is an instrument that consists of bells of In this paper, we present a design for a practice carillon that em­ varying sizes (20 - 7000 kg) that are struck by clappers or weighted ulates the haptic feel of a real carillon. The proposed design is pendulums. The clappers are connected by wires to wooden batons adjustable so that it may be configured to match the characteristics that are arranged similarly to a piano keyboard in a playing cabin of a variety of real carillons. We also present the results of a haptic typically just below the bellfry (Figure 1). The carillon presents a fidelity experiment in which we measured carillonneurs' and non- particularly interesting training challenge in that each instrument is carillonneurs' ability to discriminate between various impedance physically unique with the masses of the bells and clappers vary­ parameters. From this work, we were able to understand the design ing from note to note and from carillon to carillon. Students of requirements for haptic fidelity in practice carillons and make sug­ the carillon must learn how much force to give each baton in order gestions that are likely to extend to other physical tasks that require to achieve the appropriate note velocity and timing. Because the arm coordination and timing. instrument is impossible to silence, every session is a public per­ formance. Practice carillons are able to replicate the arrangement 2 BACKGROUND of keys but the mechanical impedance of the batons rarely matches that of the real instrument, and therefore does not provide a realistic The carillon is a public instrument. Whether listeners are purpose­ practice experience. fully attending a concert or just passing by the tower, they are al­ ways part of the carillonneurs audience. The fact that the carillon * e-mail: [email protected] is always heard is both a joy and a curse. Most musicians are eager t e-mail :y ing. zheng@y ale. edu to share their art with the public, but all musicians need to prac­ J e-mail:john.morrell@yale. edu tice. For a carillonneur to practice privately, he must play a practice carillon. IEEE Haptics Symposium 2012 A practice carillon consists of manual keys (batons) and pedals 4-7 March, Vancouver, BC, Canada arranged similar to a real carillon. The batons are tied to small tone 978-1-4673-0809-0/12/$31.00 ©2012 IEEE bars that produce quieter sounds. A player may use a practice car- 57 illon to acquaint himself with the geometry of a particular carillon keyboard, but timing and dynamics are not easy to learn on a prac­ tice carillon due to the lack of haptic fidelity. Transitioning from instrument to instrument can be challenging even for professionals since each carillon has a unique design with varying numbers of bells, musical transposition, keyboard geometries, and mechanical impedances. Practice carillons have improved substantially in audio quality over the last decade. State-of-the-art practice carillons have done away with tone bars and are now electronic MIDI instruments that play samples of real bells, often recorded on the matching carillon. While the fidelity of audio has improved a great deal, the haptic feel of most practice carillons has not. Adjustable practice carillons have received some attention in the recent past. A practice carillon developed by Timothy Hurd [8] has adjustable key geometry, allowing the user to set the instrument to the geometry of many different carillons. y Some newer commercial practice carillons come "weighted" [3]. Generally, this means adding small weights to the batons that represent the heaviest bell clappers, a little bit less weight to the ^player octave above, and so on. The result is a practice carillon that feels very smooth but unrealistic. \ Mimicking the haptic feel of a real carillon in practice caril­ FT lons is challenging and a few different designs have been proposed. The literature describing these attempts is sparse and in some cases Lbaton anecdotal. Recently, the haptic dynamics of carillons have been an­ alyzed by Havryliv et. al. [6, 7, 8, 9]. A detailed analytical model Figure 2: Model of the carillon mechanism. Wires, bellcrank and of the carillon dynamics as well as a design for an electromechani­ transmission parts are assumed to be rigid and frictionless since the cal, actively controlled single baton is presented in [8]. mass of the clapper is quite large and the stiffness of the human Examples of research merging haptics and the piano can be hand and arm is much lower than that of the wire. This model is found in patents [15, 18, 17], and an actively controlled piano sim­ used to predict optimal haptically accurate practice carillon clapper ulator [5, 10]. A tactile stimulator that simulates plucking a guitar parameters. Many carillon bells do not have the assist and return string is described in [2], interactive music modules are proposed springs represented by Fa and Fr. in [1], and work with a theramin-like device is described in [14]. In this paper, we describe our efforts to design, fabricate and evaluate a practice carillon with accurate and adjustable mechani­ and forces in the system. cal dynamics that can recreate the haptic feel of the real instrument. In order to replicate the feel of the mechanism shown in Figure 2, Our objectives include the ability to rapidly adjust the instrument we need to obtain an equation for the force between player and to replicate the feel for a wide range of real carillons. In the next baton, Fpiayer. If the PDPC is capable of mimicking this force, then section, we propose a dynamic model for the carillon baton as ex­ the instrument will be haptically accurate under the assumptions perienced by the player. From this model, we were able to analyze outlined above. The derivation of Fpiayer begins by presenting the a number of existing carillons and propose a design that uses ad­ second-order linear equation of motion of the carillon mechanism. justment of passive masses and springs to recreate accurate haptic dynamics - The Passive Dynamics Practice Carillon (PDPC). We conclude with a preliminary assessment of players' sensitivity to L 2 -L\ +FL—F L =I 0 (1) the various impedance parameters. Wcsm(Oo + 0)LCM-Frplayer r r a a C 3 DYNAMIC MODEL To calculate Ic, we assume that the clapper is a solid bar rotating We present a dynamic model of a typical carillon bell in this section. about one end with a point mass for the bulge in the clapper. Some carillon bells will have a return spring applying a force F on the A single carillon bell is shown in Figure 2. Variables in this figure r clapper and others will have a return spring applying a force F in are defined in Table 1 in the Appendix. The clapper hangs from the a middle of the bell at an angle offset to the vertical, 0Q, and extends a the opposite direction. These springs are typically constant force springs but may be extension or torsion springs as well. F and F distance from the fulcrum. A wire is attached from the clapper to r a a bell crank that connects another wire to the baton on the keyboard. can be split into two components, a constant term and a displace­ As the carillonneur plays the baton, the baton is deflected a distance ment dependent term: yd (measured at the wire) and the clapper moves towards the bell until it makes contact, sweeping out an angle 6^.