Acoustic function of sound hole design in musical instruments

Abstract

Sound-hole, an essential component of stringed musical instruments, enhances the sound radiation in the lower octave by introducing a natural vibration mode called air resonance. Many musical instruments, including those from the violin, lute and oud families have evolved complex sound-hole geometries through centuries of trail and error. However, due to the inability of current theories to analyze complex sound-holes, the design knowledge in such sound-holes accumulated by time is still uncovered. Here we present the potential physical principles behind the historical development of complex sound-holes such as rosettes in lute, f-hole in violin and multiple sound-holes in oud families based on a newly developed unified approach to analyze general sound-holes. We showed that the majority of the air flow passes through the near-the-edge area of the opening, which has potentially led to the emergence of rosettes in lute family. Consequently, we showed that the variation in resonance frequency and bandwidth of different traditional rosettes with fixed outer diameter is less than a semitone, while the methods based on the total void area predicts variations of many semitones. Investigating the evolution of sound-holes in violin family from circular geometry in at least 10th century to the present-day f-hole geometry, we found that the evolution is consistent with a drive toward decreasing the void area and increasing the resonance bandwidth for a fixed resonance frequency. We anticipate this approach to be a starting point in discovering the concepts behind the geometrical design of the existing sound-hole geometries, and helping the musicians, instrument makers and scientists utilize this knowledge to design consistently better instruments.