Tuning of musical glasses through material removal
Thomas Guignard, Vincent Martin · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2004
Generalities and studied problem Traditionnaly, a musical glass is shaved just over the stem to obtain the desired pitch. Can the physical cause of this traditional method be identified? In preamble, some vibrational modes of a glass and its frequency spectrum are observed. (a) 710Hz (b) 1430Hz (c) F4 (fond. freq. 705Hz) Figure 1: Modal forms and spectrum of a vibrating glass It is commonly admitted that the first circonferential mode affects the first partials. The number of harmon-ics when the glass is excited (Figure 1(c)) and the fast disappearance of the higher orders when the glass is no longer excited are noteworthy. This spectrum cannot be fully explained as of today. Chosen approach In the case of a glass of very simple geometry, A.P. French [1] gives in 1983 an expression of the eigenfrequencies that puts the way to considering the tuning problem. In fact, if n is the order of the circonferential mode (n ≥ 2) and m the order of a flexion mode of a generatrix of the cylindrical glass, the frequencies are described as fmn = Kh