Coupling between Clavichord Unisons and its Effect on Tuning

From: British Clavichord Society Newsletter No. 4 (February 1996)

Vibrating objects which are physically close to each other often have a mutual influence. If the mouths of two flue organ pipes face one another and their pitches are nearly equal, the pulses of air from one mouth sometimes reach the other strongly enough to affect the air movement at the lip of the other pipe. When this happens, two pipes which separately would sound slightly different pitches will synchronise at an in-between pitch. Piano strings which lie side-by-side behave in a similar way (Gabriel Weinreich,‘The Coupled Motions of Piano Strings’, Scientific American, Jan. 1979, pp. 118-127). This linkage between vibrating objects is known scientifically as ‘coupling’.

In the case of piano strings, usually a set of three unisons, the main coupling agent is the vibrating bridge, since the nut on the wrestptank is too rigid to have a significant effect. Each string causes the bridge to move and the bridge movement has an effect on the other strings. This also happens in the clavichord, where the unisons are in pairs, but this instrument has a much stronger coupling agent in the tangent. Whereas the piano nut is rigid, the clavichord tangent has to be light and mobile since it is also the sounding agent. The coupling between unison strings on the clavichord is therefore much greater than on the piano, and this is why it causes some very noticeable effects, particularly on the earlier types of clavichord with very light keys.

Anyone experienced in tuning clavichords will have noticed that notes can sound ‘dead’ or ‘alive’ according to how the unison pairs are tuned together. As one of the unison pairs is tuned to the other, a point is reached when the sound of the two strings becomes quiet and lifeless. A small extra turn of the tuning key brings the sound to life again, still without any beats, but if it is turned too far the two strings become out-of-tune with each other and beats will be heard.

The only published references to this effect that I have seen were written by Ralph Kirkpatrick: ‘I first began to tune when I got that clavichord (a 4-octave Dolmetsch made in 1932) … It was from him (Arnold Dolmetsch) that I first got the trick of tuning the unison strings ever so slightly apart and which Challis still does and most other clavichord makers don’t ’ (Margaret Campbell, Dolmetsch: the man and his work, London 1975, p. 253). Kirkpatrick also mentioned this in 1981: ‘There are minute differentiations that can be set up in the tuning of unisons when and if desirable by tuning one string infinitesimally higher. This often serves to give a certain life and warmth to the upper registers of the instrument that will help to balance its weakness against the overspun strings of the bass’ (Ralph Kirkpatrick, ‘On playing the clavichord’, Early Music, July 1981, p. 305). Kirkpatrick’s description ‘tuning the unisons ever so slightly apart’ is somewhat misleading since there is no actual separation of pitch between the strings, and it is doubtful whether he, Challis or Dolmetsch knew the scientific explanation of what was happening.

Imagine an experiment in which a note is struck on a clavichord with the first string free to vibrate and the second string momentarily damped but released immediately afterwards. The first string will vibrate the tangent and the tangent will in turn vibrate the second string. The second string will readily respond to these vibrations because it has been tuned in unison with the first string. The laws of mechanics show that the vibration of the tangent will lag 90° or a quarter of a cycle behind that of the string which is causing its vibration. Similarly the vibration of the second string will lag a quarter of a cycle behind that of the tangent which is causing its vibration. The result is that the second string is caused to vibrate with a 180° lag, i.e. exactly out-of-phase with the first string, so that when the first string is up the second string is down and vice versa. The second string will absorb energy from the first, via the tangent, and will increase its amplitude of vibration until the two vibrations are equal and opposite.

What happens normally when a note is struck with both strings free to vibrate is that the two strings begin by vibrating in phase, since they are set in motion by the same impact of the tangent. Each string immediately begins to affect the other through the vibration of the tangent and soon the two strings are vibrating out-of-phase as in the above experiment. This is called a state of interference and it is assumed that the two strings are accurately tuned to the same frequency. Theoretically this should produce no sound at all, but in practice the tuning is never exact and the two strings are never identical in all respects so the sound is weak rather than non-existent. It is easy to prove that interference is taking place, because if one string is touched to stop it vibrating soon after the note is struck, the sound will increase in volume.

The way to avoid this weak sound is, as Dolmetsch taught, to alter the tuning of one string very slightly. Then the two frequencies which the strings would each sound in the absence of the other will be slightly different, and the resulting common frequency will be half way between them. The string with the higher natural frequency will be retarded by the coupling effect, while that with the lower natural frequency will be accelerated, the vibration of the tangent being the main agency keeping the two vibrations in synchronism. The phase difference between the string vibrations is altered from 180° and so the sound is strengthened because the two vibrations no longer oppose one another.

Naturally, the tuning alteration mentioned above must not be too much, otherwise the natural frequencies of the two strings will be too far apart and the tangent vibration will fail to keep the two strings in synchronism. Then they will vibrate independently and beats will be heard.

The strong coupling between the unisons is a fortunate characteristic of the traditional clavichord and contributes to its tonal qualities. It also helps to explain its excellent tuning stability.