Air and structural modes of a harpsichord

Abstract

The acoustical behavior of a harpsichord modeled after 17th-century Flemish prototypes was studied using both experimental and analytical techniques. The vibrational modes of its enclosed air volume were measured and found to correspond closely to those predicted by the Jo and J9 solutions to the Bessel equation for a wedge shaped space. A modal analysis of the complete harpsichord revealed that the soundboard has 36 vibrational modes over a frequency range of 0 to 600 Hz, and that there are numerous modes where the instrument's case has a significant amplitude of motion. Additional information is reported showing that the acoustic output of the harpsichord is reasonably flat over a frequency range of 50-2000 Hz. It is concluded that the resonance behavior of both the soundboard and the enclosed air are important to the tone quality of the harpsichord, and that its generally uniform acoustic output results from the excitation of a large number of wood and air modes by the string partials. PACS numbers: 43.75.Mn, 43.75.Gh LIST OF SYMBOLS co circular frequency, radians • viscous damping factor c velocity of sound, m/s A wavelength, m •p, eigenfunction (mode shape coefficient), air •w eigenfunction (mode shape coefficient), soundboard

Sound Synthesis of the Harpsichord Using a Computationally Efficient Physical Model

“…The soundboard has its own modes depending on the size and the materials used. The radiated acoustic response of the harpsichord is reasonably flat over a frequency range from 50 to 2000 Hz [11]. In addition to exciting the air and structural modes of the instrument body, the pluck excites the part of the string that lies behind the bridge, the high modes of the low strings that the dampers cannot perfectly attenuate, and the highest octave of the 4 register strings.…”

“…In other words, the modeling is divided into two parts so that the soundboard filter models the reverberant tail while the attack part is included in the excitation signal, which is fed to the string model. Reference [11] discusses the resonance modes of the harpsichord soundboard in detail.…”

“…In this section, we describe briefly the construction and the operating principles of the harpsichord and give details of the instrument used in this study. For a more in-depth discussion and description of the harpsichord, see, for example, [9,10,11,12], and for a description of different types of harpsichord, the reader is referred to [10].…”

Harpsichord and Clavichord

“…In its lowest mode, the soundboard simply vibrates in and out like the lowest mode of a drumhead, while at higher frequencies the mode shapes divide it into progressively smaller areas, each one of which vibrates in anti-phase to its neighbors. Sketches of some of these mode shapes have been given by Savage et al (1992).…”

“…Of course, all these resonances overlap to some extent because of vibrational and acoustic losses. The whole situation is very complicated, and a detailed study by Savage et al (1992) identifies 36 vibrational modes below 600 Hz. There will be many more above this frequency.…”