Commuted Waveguide Synthesis of the Clavichord

The clavichord is one of the oldest keyboard instruments, and it is still often used in performances and recordings of Renaissance and Baroque music. The sound of the instrument is pleasant and expressive but quiet. Consequently, the instrument can only be used in intimate performances for small audiences. This is the main reason why the clavichord was replaced by the harpsichord and finally by the modern piano, both of which produce a considerably louder output. Attempts have been made to amplify the sound of the clavichord using a piezoelectric pickup (Burhans 1973).

One of our motivations in this research is to give the clavichord a new life in the digital world, where the faint sound level of the instrument can be amplified by simply turning a volume knob. The suggested synthesis model is based on digital wave-guide modeling of string instruments (Smith 1992, 1998; Välimäki et al. 1996; Karjalainen, Välimäki, and Tolonen 1998) and uses the principle of commuted waveguide synthesis where the soundbox's response is incorporated in the excitation signal (Smith 1993; Karjalainen and Välimäki 1993; Karjalainen, Välimäki, and Jánosy 1993). Special sampling techniques are also employed. Musical examples produced using the proposed synthesizer will be included on a forthcoming Computer Music Journal CD.

Acoustics of the Clavichord

A photograph of the clavichord used for the measurements in this study is shown in Figure 1. The instrument is an Anthony Sidey clavichord manufactured by Heugel in Paris, France, in 1988. This clavichord is an unfretted one, so any combination of notes can be played. The range of a clavichord is anywhere from three octaves to over five octaves. Our clavichord has 51 keys ranging from C2 to D6. The instrument was tuned about a whole tone lower than the standard modern tuning (A4 = 440 Hz): the nominal frequency of A4 is 395 Hz. The Werkmeister tuning system was used.

For each key of the clavichord, a pair of strings is tuned in unison, as sketched in Figure 2 (see, for example, Thwaites and Fletcher 1981; Campbell and Greated 1987). However, the two strings are always slightly detuned around the same note, because exact tuning is impossible manually. Every key forms one end of a lever that has a tangent attached to its other end. When a key is depressed, the tangent hits the string pair and initiates vibration. One end of the strings has been damped with felt, and the other end goes over a bridge to the tuning mechanism. Thus, the strings are freely vibrating between the bridge and the tangent, which works as both a hammer and a termination. The tangent mechanism is rather noisy, as it excites modes of the soundboard but also itself causes sound from its moving parts owing to friction.

When the key is released, the tangent falls back with the aid of gravity, and the string vibration is allowed to propagate to the felt-covered end of the string, which efficiently damps the vibration. At the end of each note, another knock is heard as the tangent returns to its resting position. The somewhat mistuned strings of each pair are coupled via a non-rigid bridge, and thus both beats and a two-stage decay result (Weinreich 1977).

Figure 1.

Clavichord used in this study.

The first thing that people usually notice about the clavichord is that the sound level is very low. The maximum sound pressure level at 1 meter is only about 50 dB or 60 dB, depending on the individual construction of the instrument. This makes this ancient instrument a sound source less efficient than a human speaker. There are many reasons for the weak output (see Campbell and Greated 1987; Fletcher and Rossing 1991). The strings are thin and their tension is low, and they radiate sound inefficiently. The soundboard is small and light, and it cannot amplify the sound much.

A particularly interesting feature in the clavichord is the mechanical aftertouch known as Bebung. When the player increases pressure on a...