Minimal physical model of the cristal Baschet

Abstract

The cristal Baschet is a musical instrument created during the 1950’s by Bernard and Francois Baschet. It is composed of a large number of glass rods arranged in a chromatic scale. The sound produced results of vibrations induced by friction between wet fingers and the glass rods. Each glass rod is connected to an assembly of threaded shafts and a mass. Mechanical properties of this assembly determine the pitch of the note. Then vibrations are transmitted to large metal panels or cones that act as radiating elements. The manufacturing and tuning of this instrument is based on empirical knowledge and involves many parameters whose effects are not clearly understood. One of the encountered problems is the difficulty to produce sound in the high register of the instrument. In an attempt to understand the influences of these parameters on playability, a minimal physical model of the cristal Baschet is developed. It focuses on the interaction between the finger and the isolated resonator. The dynamic behavior is described by a set of modes obtained from a finite element model or from experimental modal analysis. The musician’s gesture is described by two control parameters: the velocity of the finger along the glass rod and the normal force applied by the finger on the rod. To describe the interaction between the finger and the resonator, a friction law is implemented. The influence of different parameters is studied by means of linear stability analysis and time-domain simulations. Specific criteria are developed to highlight the role of design parameters on playability.

Keywords

• musical acoustic
• self-sustained oscillation
• friction induced vibrations
• linear stability analysis
• stick-slip