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Session 07 - Percussions

Making of a computer carillon
M Karjalainen, V Välimäki, P A A Esquef
Helsinki University of Technology, Acoustics Laboratory, Espoo, Finland

In this paper we present an analysis, modeling, and synthesis approach to bell sounds. Recorded bell sounds are first analyzed by high-resolution frequency-zooming modal estimation technique where each partial is described typically by 2-3 submodes in order to include the warble characteristics due to envelope beating in the partials. The bells are then modeled by inharmonic digital waveguides in order to achieve a computationally highly efficient yet parametrically controllable synthesis model. The third step is to make a set of bells and related parametric controls in order to build a 'computer carillon'. Since basic digital waveguides are inherently harmonic models, special means are needed to approximate the strongly inharmonic bell sounds, paying particular attention to the accuracy of the lowest partials. In the waveguide modeling the easiest way to realize the beating of the partials is to use auxiliary resonators to add to the basic digital waveguide response. The control of the bell models in the computerized carillon is through triggering of wavetables that store the initial part of the residual signal obtained in the modal decomposition process. Changing or modulating the modal parameters allows for sound effects that are not possible in real physical bells.

Normal modes of the elephant bell
R Perrin¹, T R Moore², R Felce³, A Robinson³, B Deutsch³, G M Swalloweº
¹Massey University, Intitute of Fundamental Sciences, Palmerston North, New Zealand; ²Rollins College, Department of Physics , Winter Parks, FL, United States; ³Rollins College, Department of Physics, Winter Parks, FL, United States; ºLoughborough University, Physics Department, Loughborough, United Kingdom

The Indian elephant bell consists of a hemispherical shell from whose rim hang a number of identical and equally spaced tines. The tines usually number between 10 and 20 and have a slight inward curvature. The normal modes of this bell have been investigated using electronic speckle pattern interferometry, finite-element modeling and group representation methods. The experimental results are in fair agreement with the models and both are consistent with the predictions of group theory for the normal modes of a system with symmetry group Cnv where n is the number of tines. It is found that the important part of the spectrum can be understood by regarding the tines as a set of identical oscillators coupled in series within a closed loop, with the hemispherical crown merely holding them in place, supplying the coupling and, perhaps, acting as a sounding board.

Rayleigh's bell model revisited
R Perrin¹, G M Swallowe²
¹Massey University, Institute of Fundamental Sciences, Palmerston North, New Zealand; ²Loughborough University, Physics Department, Loughborough, United Kingdom

It is now well over a century since Lord Rayleigh published his model for western-style bells. He used a hyperboloid of revolution plus a flat circular plate for the crown. By limiting himself to inextensional modes of a very restricted type and exploiting the hyperbola's parametric form, he produced an equation whose roots give the locations of nodal circles. Remarkably this equation involves neither the wall thickness nor physical properties of the bell material and this approach remains the only available analytical way of making such predictions. Although he gave adequate accounts of the derivation and method of solution of his equation, Rayleigh did not present any real comparison of its predictions with experiment. Rather he focussed on using it to explain the fact that, in church bells, the Hum note never has any nodal circles but is usually the only one with this property.
In the present paper we consider how well profiles of some modern church and handbells can be fitted by hyperbolas. We compare the model's predictions for these bells with data for a considerable range of inextensional modes and report a new, surprisingly accurate, approximate analytical solution of Rayleigh's equation.

The HANG: A hand-played steel drum
T D Rossing¹, U J Hansen², F Rohner³, S Scharer³
¹Northern Illinois University, Physics Department, DeKalb, United States; ²Indiana State University, Physics Department, Terra Haute, United States; ³PanArt, Bern, Switzerland

The HANG is a new steel percussion instrument, consisting of two spherical shells of steel, suitable for playing with the hands. Seven to nine notes are harmonically tuned around a central deep note which is formed by the Helmholtz (cavity) resonance of the instrument body. By means of holographic interferometry we have studied the modes of vibration in a HANG developed by PanArt, Switzerland.

Vibrational modes of five-octave concert marimbas
J Yoo¹, T D Rossing², B Larkin³
¹Seoul National University, Physics Education, Seoul, Republic of Korea; ²Northern Illinois University, Physics, DeKalb, United States; ³Iowa State University, Department of Music, Ames, Iowa, United States

We compare the bending mode frequencies in two five-octave concert marimbas, one by Yamaha and one by Malletech. In both instruments, the second mode is accurately tuned to the 4th harmonic in the first 3-1/2 octaves, after which the interval decreases. Similarly, the third bending mode is tuned to the 10th harmonic in the first 2 octaves, after which the interval decreases. The fourth mode in both instruments varies from the 20th harmonic in the lowest bars to about the 6th harmonic in the highest bars. Four to five torsional modes observed in the Malletech marimba have frequencies intersperced with the bending modes. The lowest torsional mode lies between the two lowest bending modes, while the second torsional mode lies between the second and third bending modes. Coupling between bending and torsional modes is discussed.

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