Tuning a pentangle—A new musical vibrating element

Abstract

As part of a program in musical acoustics, it was required to design a non-regular but reflection-symmetric pentagonal gong, made from steel rod, of such geometry that the first 5 or 6 of its planar normal modes provide partial tones in nearly harmonic relationship, in order to achieve a musically satisfactory bell-like sound. Techniques are described for exploring the accessible configuration space to reach this objective, using a combination of analytic solution and finite-element analysis. The results and methods, which may be of wider applicability and interest, are described in detail, as also are two independent solutions reached to the design problem. The final gong has markedly different tone quality depending upon whether it is struck so as to excite the harmonic in-plane modes or the inharmonic out-of-plane modes.