Acoustics
The subject of acoustics applied to stringed instruments, referred to by scholarly musicologists as ‘chordophones’, is so tenuous and has received so little attention, compared with other fields of science, that some measure of bravado or, perhaps, frivolity is needed to appraise it.
In offering the following imperfect notions assembled from my own limited experience I hope that they will be accepted for their own worth without any proper authority. They may be a stimulus and provide some direction for others to pursue for themselves.
Physics and the engineering of raw materials need to be combined with intelligent balance. If attempting to unravel the complexities of the subject of applied acoustic essentials the luthier best beware that inexactitudes are lurking to misguide the unenlightened. Not in the application of the theory of the associated principles, due to the sublime mathematical processes that prevail, but in the choice, design and physical assemblage of the components that, for the most part, are from natural materials. The 21st century offers some changes that, whilst attractive to the contemporary luthier with the inclination to ‘modernise’, will have limited appeal for the ‘purist’ who attempts to preserve a traditional attitude.
It is quite likely that many luthiers will refer to plans that have been sourced from another designer who, by offering a drawing with dimensions and material specifications will have obviated the need for the maker to consider such complex issues as acoustic principles. This calls for a measure of trust by the maker, who will be relying on a third party to have produced details based either on an original model, or created a design from scratch with maybe some reference to similar instruments. Either way, few luthiers have the urge to enter the hazards of acoustic theory when, unimpeded by such distractions, they can set about the making of the instrument from an existing plan. But, for those who bring with them an element of curiosity into the workshop, wishing to grasp the underlying physics of the lutherie project, a few suggestions are set out here by this author, a fellow adventurer using strings and wood in the exploration of noise creation.
My own experience relevant to the subject, prior to my becoming involved in lutherie, included the study of mechanical engineering in theory and practice for the first eight years after leaving school. I was aware of the importance of science, physics, mathematics and geometry as supports to the design of functioning mechanisms and their components. It became therefore normal for me to consider such elements when viewing the design of an instrument. In fact, it became almost impossible for me to look at any structure, be it a chair or a motor car without evaluating its component parts and how they might have been assembled.
It is not appropriate to set out a full-scale thesis within this presentation and I am currently working on a comprehensive piece, ‘Plucked-string Acoustic Science’ for publication in the near future. However, in the following I offer a few basics as guidance to those who may be new to the subject but who may also enjoy meddling in its somewhat elusive constitution. I have tried to restrict the content to the practical with minimum theoretical references.
Sound is created by vibrations that are transmitted through the air or other medium and may be received by the human ear. Fairly obvious stuff but let us look a little closer. Oscillations are repeated cycles, not the type with pedals, the type that is a sequence of recurring processes. If that sounds complicated, think of a pendulum in an old-fashioned clock swinging to and fro. This is called an oscillation. We are especially interested in the speed of oscillation, from a musical point of view, because the frequency of the oscillation affects the pitch of the sound being created. Pitches are referred to as ‘higher‘ or ‘lower’ when compared on a frequency-related scale; we usually call them notes and they differ in ’pitch’.
Musical instruments vary in their characteristics of volume, tone and resonance. A convenient way of understanding these characteristics is in the ADSR scheme, where A stands for Attack, D for Decay, S for Sustain and R for release. These simple components are expressed in terms of time. A is the time taken for the generation of the sound from its initial activation, (of the string in this case) to the achievement of its maximum volume. D is the time taken to reach the resonance level, a little less volume than was found in the peak of the Attack. S is where the volume is maintained after the decay has settled. R is the time taken for the volume to diminish to silence. It is obvious that different instruments behave differently. For instance, a bowed string takes longer to activate than a plucked string but it may be sustained for as long as the player continues to bow it, unlike the plucked string which has a limited sustain and begins to release relatively quickly.
Let’s think about vibrations. We are concerned with how the vibrations are created, transmitted, amplified and resonated
It is obvious that the guitar family relies upon the plucking of the string to get the system working. Whether this is achieved by the application of the finger (with or without nail) or with a plectrum doesn’t matter. Well, it matters to the player in terms of technical application and its volume and quality of tone , but for the purposes of this study they are treated as similar. OK, let us assume the string had been plucked. It has been set into vibration and that vibration will be received by the bridge. In turn the bridge transmits the vibration to the soundboard for amplification. Of course, the same vibration is received by the nut at the top end of the neck, but there is relatively little response or transmission to be had there.
One of the terms used frequently is ‘resonance’, although sometimes ‘sustain’ is misused in its place. Resonance occurs when a sound chamber, such as a guitar body, responds to a sympathetic vibration transmitted from something nearby, or by direct connection to it. For instance, a loud noise, such as a cough or even a sneeze can produce an answering twang from the strings, without the human generator being in contact. This means that within the sibilation of the cough or sneeze was a note of a frequency to which the instrument responded, or, resonated. Hollow bodies can produce a fundamental note when struck, such as if the bridge on a guitar is tapped, setting all the strings in motion simultaneously. This sound will mix with some of the fundamental notes produced by the guitar body itself. Some Gorillas are famous for the beating of their chests to produce a drumming as a threatening signal to others of their species, but they don’t produce tunes you could sing in the shower.
That’s it in a nutshell. However, (there is nearly always a ‘however’). Each of the components involved in the structure of the instrument has its specific function in the scheme of things, independently and interdependently speaking and therefore each has to be considered in what way it either contributes to, or impedes, the generation of the sound.
This will be dealt with more thoroughly in my essay ‘Acoustic Science of Plucked Strings’ available soon as an e-book.
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Acoustics