Modal Tuning

Chladni patterns (top), mode phasings (middle) and mode frequencies (bottom) for one of my falcate braced steel string guitars

 The frequency response curve of the steel string guitar pictured above.  Sound pressure in deciBels is on the vertical axis and frequency is on the horizontal axis

The fruit of this research is manifest in my range of guitars.  I invented/learnt a lot of techniques for designing guitars that are not documented anywhere else, so it fell to me to write "the book", with some help from my long time friend Gerard Gilet, who started building guitars whilst I was still at school (which he doesn’t like being reminded of).  It is the application of these techniques that make my guitars more responsive, louder and play more in-tune to the equally tempered scale than most other guitars; and it makes them unique.

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Whilst some low frequency sound comes from the soundhole, mostly sounds originate from the moving surfaces of a guitar, mainly the top. If a guitar top vibrates in a different way, it produces a different sound. Guitars have preferential ways of moving, called modes of vibration. Different modes are characterised by the way the soundboard divides into separately vibrating subsections. The mode shapes and sizes can be observed using Chladni patterns (pictured, top) which define the node lines on the vibrating surface. As one crosses a node line there is a 180° phase change of the motion; i.e. if a surface is moving “up” on one side of a node, it will be moving “down” on the other side. If the modes are tuned to resonate at particular frequencies with particular amplitudes, we can shape the way a guitar sounds.

Four vibratory modes of a guitar are shown at right, labelled with the values for the natural frequencies of the steel string guitar photographed.  Some modes occur at more than one frequency.

The various modes of vibration have greatest amplitude at their resonant frequencies and so sound is radiated most strongly at the mode resonant frequencies. With respect to radiation from the soundboard, very little sound is radiated by motion other than the motion defined by the main vibratory modes, even well off the modes’ resonant frequencies.  Consequently, it is no surprise to find that the peaks in a guitar’s frequency response curve correlate exactly with the resonant frequencies of the various modes of vibration, as we can see below.

As the sound from a guitar is mainly radiated from its vibrating surfaces, the variations in sound between different guitars and between different types of guitar are due primarily to the size, shape, amplitude and natural frequency of the various modes.  To alter the sound of a guitar it is necessary to alter the size, shape, amplitude or natural frequency of a mode or modes.  Because guitars have a generic tendency to vibrate in certain ways, it requires quite a significant change in the bracing structure to precipitate a change in the shape or amplitude of a mode.  Changing a mode’s frequency is a little easier.

Learning how to manipulate the parameters of the modes and, in particular, understanding what the target frequencies should be has been the focus of my research and development efforts over the last 10 years.