FEM-Based Optimal Design for the Tuning of Sixxen Instruments
54º Congreso Español de Acústica — Tecniacústica 2023
Abstract
For his composition Pléiades, Iannis Xenakis imagined a metallophone instrument that is called Sixxen. Inspired by the sonorities of Indonesia music, it consists of a series of 19 metal bars arranged according to a microtonal tuning system built with uneven musical intervals. On the occasion of Xenakis’ centenary, the percussion sextet from the Portuguese Chamber Orchestra decided to perform this composition, for which a set of six sixxen was built specifically. The designed instruments were made of aluminium bars with U-shape cross-section, using two different geometries. For a given bar profile, tuning was achieved in a two-step methodology including model updating. It combines 3D modal analysis, optimization techniques and acoustic measurements, and pursues the tuning of the dominant radiating mode by adjusting the bar length. Each instrument was tuned according to a predifined musical scale, built with a similar structure to an Indonesian scale and including random variations. The method leads to sixxen instruments with absolute tuning deviations typically below 7 cents, that is inaudible, illustrating the efficiency of the proposed methodology.