Calculation of Helmholtz frequency of a Renaissance vihuela string instrument with five tone holes

Abstract

A replica of the historical Guadalupe vihuela, a Renaissance string instrument was investigated. As it has five sound holes a formula was developed to calculate its Helmholtz frequency radiated from these five holes. Therefore, using a 128-microphone array, the radiation pattern at the Helmholtz frequency of 138 Hz was measured showing strong radiation at the holes near the center of the body and lower radiation at the holes near the upper top plate boundary. Calculating a mean radius from the single radii and weighting them with their radiation strength, the measured Helmholtz frequency is calculated correctly. This is not the case when including the ornamentation of the sound holes into the calculation which indeed cover 65% of their area. Additionally, the overall radiation from the different top plate parts of this vihuela was compared to that of another much smaller vihuela and those of a classical guitar showing the Guadalupe replica to have a very large frequency range of strong sound hole radiation up to 500 Hz, where the classical guitar is stronger in the bass but its sound hole radiation part is restricted to lower frequencies. This makes the vihuela a mixture between a guitar and a lute.