Artists in resonance

The tonal qualities of great instruments continue to prove profoundly enigmatic when we seek to unlock their secrets, as Martin Horvat explains

Lutherie

The size of the f-holes is a determining factor for the pitch of the air tone. Left–right F-holes of three violins: the 1743 ‘Carrodus’ Guarneri ‘del Gesù’; 1784 Guadagnini; 1859 Vuillaume (all taken from The Strad Calendar 2023)

‘CARRODUS’ PHOTO COURTESY AUSTRALIAN CHAMBER ORCHESTRA. GUADAGNINII PHOTO COURTESY J&A BEARE. VUILLAUME PHOTO COURTESY INGLES & HAYDAY

Even though the acoustic magic of bowed stringed instruments has attracted great scientific interest, there are no satisfactory explanations for many of its key characteristics. They have been variously attributed to the varnish, to the special qualities of the wood, or even to fungus-treated wood. Invariably, the tweaking of some minor detail is supposedly (and miraculously) key to achieving superb results.

As a luthier and musician I have been pondering these questions for more than three decades. Some have changed or have lost their significance, while others have emerged over time. The search for ‘secrets’ has been eclipsed by a willingness to engage in closer observation. And this, in turn, has led me to realise that my continued fascination with this quest stems from the fact that in violin family instruments, elemental simplicity and immense complexity combine to form a unique whole. They are at once objects of utility, tools and works of art. Every detail of the delicate body of a stringed instrument, whose shape can be constructed from simple circular strokes, serves different aesthetic, static, or acoustic functions. But everything is aligned towards a common goal: building a vessel for musical sounds.

RESONANCE IS BOTH AN INTEGRAL PART OF THE VIOLIN AND SOMETHING THAT IS DESIRED

FORCED VIBRATION AND RESONANCE

A string is made to vibrate, and this vibration is transmitted to the soundbox through the bridge. It is a simple principle: the same thing happens when we strike a tuning fork and place it on a table. The vibration is amplified by larger surfaces. This is called forced vibration: a body is ‘forced’ to resonate by periodic excitation. In the violin, the excitation spans a frequency range from approximately 196Hz to 4,500Hz. Including harmonics extends the frequency range upwards.

However, vibrating bodies also have so-called natural frequencies, or eigentones. These frequencies are induced when a body is vibrated by a single stimulation (e.g. by knocking) and is then left untouched. These natural frequencies, which depend directly on the stiffness of the vibrating body at a given point, also determine how it reacts to periodic excitation at a certain frequency, depending on whether or not the excitation is similar to a natural frequency. If it is, this leads to a phenomenon known as resonance: the vibrating system will react particularly strongly to the excitation and this reaction can build up to such an extent that it can lead to its own destruction under certain circumstances. Examples of this are known from civil engineering.

EIGENTONES AND OVER-RESONANCE

Both forced vibration and resonance play a role in stringed instruments, where the body possesses special characteristics owing to its ingenious structure and the materials from which it is made. It has a particularly large number of natural frequencies and all of them, because of the physical properties of this resonating body, lie within the range of the excitation frequencies. Thus, resonance is both an integral part of the violin and something that is desired.

FIGURE 1 Eigentones depend directly on the stiffness of the vibrating body at a given point: (left) Flat arching and thin plates give lower eigentones. (right) Increasing the arching height and/or plate thickness result in higher eigentones.

FIGURE 2 The same overall stiffness can be obtained through different distributions of the mass over the bass-bar’s length. For example: (left) mainly concentrated in the central/bridge area (right) more equally distributed over the whole length.

ILLUSTRATIONS MARTIN HORVAT

But if many natural frequencies correspond to many excitation frequencies, how is it that resonance in bowed stringed instruments does not build up in an uncontrolled way? How is it that good instruments do not resonate excessively? This is partly down to the special material properties of wood, which combines great strength with optimal vibrational characteristics. However, the main reason lies precisely in the large array of natural frequencies themselves, which are created by the structure of the resonating body. The associated zones of varying stiffness mean that genuine resonance in the violin body at a certain excitation frequency remains limited to very specific areas of the resonating body. On the other hand, neighbouring areas with different stiffness counteract any over-resonating.

CONTROLLABLE RESONANCE

Ideally, this creates a controllable, genuine resonance that only really occurs when the musician wants it to. An even distribution and formation of the natural frequencies over the entire range is conducive to controllable resonance. It results in something like mutual control. If this balance is disturbed and a natural frequency is particularly prominent, then the over-resonating produces a wolf tone.

In an even distribution, both the frequency difference and the way in which an eigentone is formed come into play, and the distance between the individual resonance frequencies tends to be greater in the lower register, which features particularly strong eigentones. For example, the air tone, a particularly strongly formed eigentone, is intended to resonate with an entire tone row. An irregular, random distribution of these natural frequencies over the resonating body generally causes an unbalanced resonance, often accompanied by wolf tones and a one-dimensional sound quality.

MATERIAL PROPERTIES

Violin makers consciously or unconsciously work on these natural frequencies through the way they understand and take material properties into account during the construction process. The shapes of elements such as the outline and archings play just as much a role as the thicknesses of the individual parts (figure 1).

As well as the air tone, for example, the bass-bar’s eigentone is one of the so-called ‘main resonances’ of the resonance body. The eigentone of the bass-bar increases with its stiffness. It is interesting to note that the same overall stiffness of the bass-bar can be achieved in different ways; for example, through different distributions of the mass over its length (figure 2). While the eigentone remains the same, this has an effect on the timbre. This opens the door to a new subject area that would require its own comprehensive presentation.

CONTEMPORARY TASTE

Changes in contemporary taste have led, to a certain degree, to the desirability of ‘over-resonation’. A particularly strong response is often achieved by ‘imposing’ it on the instrument through the set-up and a certain way of playing. If a violin maker imbues an instrument with it, this leads to deeper natural frequencies in certain areas. It depends on the aesthetic ideal one has in mind. Approaching the limit at which resonance tends to become excessive can be exploited by musicians who wish to express themselves mainly in a more blunt and extrovert manner.

However, the increase in volume often results in the partial or total loss of other dimensions of sound. It causes us to move away from what could be called the ‘resonance idea’ built into the body of stringed instruments, something that can be experienced by looking (and listening) closely and carefully.

After all, the wonderful thing about this special, delicate and ingenious sound creator is its capacity for controllable and self-regulating resonance, and how, in a subtle way, forced vibration and resonance interact within a body that allows us to shape and animate sound. This manifests itself with great clarity in exceptionally fine instruments and never ceases to amaze those who deal with them on a daily basis in their capacities as makers or musicians. The resulting sublime musical sound has the ability to speak directly to the listener’s heart.