The eigen frquencies Professor Anderssen refers to are the composite resonant frequencies within a sound, that in combination, make up the tonal quality of the sound. Eigen frquencies are simple tones, or harmonics, described as partial frequencies of piano sound, because of their in harmonic nature.

A vibrating piano string simultaneously oscillates multiple modes of vibration, known as partials or overtones, which combine to produce the composite tonal sound of one note. The result is a superposition of sound waves, blended together into one complex wave. The frequency of the 1st harmonic, known as the fundamental, represents the repetition rate of the resulting complex vibration.¹⁵⁹

Prof. Anderssen reports here that the behaviour of the Stuart string vibration is different to that of the modern piano string vibration, and this also tells us that the tonal colour of the two will be different, because the characteristics of the partial frequencies in each of the string vibrations sounds will be different.

The current sound trajectory for the acoustic piano was laid down in that latter half of the 19th century with standardisation, and is based on variable string vibration modes produced by the pinned bridge.

Stuart writes,

Stuart’s observations of string vibration behaviour and music composition over the past 150 years reveals that the vertical mode of vibration in sound behaviour has developed as the dominant factor in current sound behaviour aesthetics.The old pinned bridge favours an elliptical vibration mode whereas the Stuart agraffe favours the vertical mode. ¹⁶⁰

Changes in the direction of string vibration mode produces damping and variable tuning characteristics. This affects sustain, clarity, harmonic strength and development. The initial strike of the hammer produces a vertical ‘up and down’ motion which then changes to a more horizontal circular motion in the horizontal pinned bridge model. The Stuart agraffe maintains the initial strike in the vertical mode. As mode change and distortion is minimal the vibration is held in the same plane in which it is struck. It is claimed that the attack, sustain and harmonic transients of the Stuart piano tone are different because of this more controlled, vertical vibration mode. ¹⁶¹

Combining the information discussed above with what we actually hear in the sounds of the Stuart and the modern pianos, had illustrated to me that in all probability the Stuart string does actually vibrate in a different manner to the modern piano, and that analysing the vibration would be a thorough way of illustrating the tonal qualities of the Stuart piano sound. The difference in the string coupling is clearly visible inside the pianos, and the sounds of the instruments are audibly different. My enquiry into understanding the vertical nature of the Stuart piano string vibration continued by interviewing piano technicians who had experience in tuning and maintaining Stuart pianos. Interestingly, when the above information about the probability of an enhanced vertical vibration in the Stuart string was discussed, a sense of frustration in a few of the technicians’ responses was noticeable, in that they didn’t actually believe the vibration of the Stuart string could be more vertical than that of the modern piano string vibrations, and thought that this information was possibly a publicity beat up! Each of the technicians

¹⁵⁹ Juan Roederer,The Physics and Psychophysics of Music. 4thEdition (New York: Springer-Verlag 2008),126.
¹⁶⁰ Wayne Stuart, Email interview with author, 4th April, 2012.
¹⁶¹Wayne Stuart, 6 “Innovations In Piano”.