There are many accounts of scientific discovery, and a lot of them go roughly like this: back in the “dark ages” of the subject all was mystery, misinformation and magic, then science got a grip on things and the magic was dispelled. This progression has happened with gravity and the motion of the planets; it has happened to a large extent with medicine; it is happening at the moment with weather forecasting. Now, many people, scientists included, don’t want the magic to go away from music. Perhaps music demystified will lose its emotional impact, or perhaps robots will replace craftsmen and make world-beating violins. Is a book about the science of music and musical instruments going to shine too bright a light into unwelcome corners?
Curiously, the answer is no. Musical acoustics has, to a large extent, resisted the usual trend. It has been studied since at least the time of Pythagoras, and yet it is still remarkably hard to give a straight answer to a violin maker who asks what they should adjust in their woodwork to achieve a particular desired sound quality, such as matching the sound and playing qualities of a famous (and expensive) instrument by Stradivari or Guarneri del Gesu. Certainly, some things are much better understood than they were. There has also been no shortage of innovation: there are many thousands of patents relating to musical instruments, including some entirely new types of music-making devices. And yet, alongside that, the violin is virtually unchanged since the late seventeenth century, and when you listen to the language used by musicians of all persuasions when they are trying to choose a new instrument you still hear plenty of mystery and magic (and probably some misinformation). For a scientist, this is tantalising and occasionally frustrating.
What is going on? This book will mainly be about physical descriptions of vibration and sound from musical instruments, but the agenda and the special flavour of the subject are set by something else: the remarkable subtlety and elusive qualities of human ability, both in the perception of sound and in motor actions to control breath, bows or fingers. Some exploration in these areas is needed before we get down to the business of acoustics.
So what is music? It is widespread, perhaps universal in all human cultures. It is one of those things that is hard to define, but you probably know it when you see it, or more likely, hear it. Music is important to a lot of people, and some people are very good at it, as performers or experienced listeners. These people care a great deal about small details: of the music, its performance, and the instruments on which it is played (including the human voice). “Small details” will be a recurring theme in this book. A musical instrument is a contrivance which allows a performer to use gestures they are physically capable of performing to make sounds that they like. Of course, “like” is a loaded word, the details being highly dependent on cultural background and experience. Nevertheless, all skilled musicians are probing the outer limits of human abilities. There are a lot of violinists and pianists out there, and they are all striving to do better than the others and get the good reviews and the recording contracts. A virtuoso is someone who can do things other people can’t do. Maybe they go only just beyond the limits of other players, but that boundary is where all the attention is focussed.
If the choice of instrument can make a difference, you can be sure that money will be spent to achieve this competitive edge. It is very much like sport: superstars are just that bit better at hitting a ball, or whatever, but that bit is crucial. Manufacturers of sports equipment make huge efforts to tweak design details to give an extra edge, for which serious money will be paid. And they may resort to psychological ploys via careful advertising to convince people to pay out for the latest product. In sport as in music, “psychological” effects are not necessarily “fictitious”. A player, whether of tennis or the violin, may well perform better if they believe they have superior equipment. Conversely, they are only too likely to make errors if they believe that their competitors have an edge.
The science of acoustics is well developed and wide-ranging, and nearly all of it (at least, nearly all the well-funded aspects) are devoted to reducing noise, whether from vehicles, wind turbines or neighbours. Musical acoustics is different. It is very easy to solve a violinist’s “noise problem”: put candle wax on their bow-hair instead of rosin. (This really works, but don’t try it incautiously — it is virtually impossible to get rid of.) But of course that is not the point. The things that matter to violinists and their listeners all revolve around making and controlling sound, down to the level of those fine details. This makes the associated science particularly challenging. It does not satisfy a musician or an instrument maker to be told roughly how things work, they will always press for more and more detailed information.
Everything hinges on the way human perception is believed to work, not only for sounds but for vision, touch and so on. We are each equipped with a huge collection of “feature detectors”, bits of neural circuitry that are tuned in to spotting a particular thing when it occurs among the input data. These different detectors are all running at once, each looking out for their particular thing, and when they hear/see/feel it, they send off a message to “you”. Some of these feature detectors are more or less the same for almost everyone, others may be rather specific to one person’s particular background and training.
Some examples may make this clear. In visual processing, we have “low-level” detectors which allow us to recognise different colours, simple shapes, and simple kinds of movement. But we also have high-level detectors that are finely tuned to recognise, for example, a human face. That is why we so easily see “faces” in flames, rock formations or clouds. Look at the photograph below, near a waterfall in Iceland. Do you see a face in profile in the shape of the foreground grass? The top pair of birds are in the eye socket.
Your “face detector” is very specific: it only works really well if the face is the right way up, and of a reasonably familiar type. It is hard to recognise a photograph of a friend if it is upside down, and most “western” folk are familiar with the feeling that “all Chinese faces look the same” (and of course the Chinese say the same about European faces). Look at the two faces in Fig. 2. Can you immediately be sure if these are two different people, or if the picture is a composite of two images of the same man? But if you turn your head round to view the picture the right way up, it will probably be immediately clear that they are two different people — they are identical twins, Captains Scott and Mark Kelly, both NASA astronauts. The simple act of turning a picture upside down would pose no problem to a computer, but human perception behaves quite differently.
When you see a scene, all these feature detectors are doing their own thing, sending back messages like “there’s Fred’s face over there”, and “a bird just flew across the path”. If you are a bird expert, your detectors will tell you what kind of bird, but most of us haven’t trained our detectors up well enough for that. The same goes for species of trees, or for violins: an expert may recognise a particular instrument seen across the room, when most of us just get the message “violin”.
The high-level and low-level feature detectors allow you to look at a scene in different ways, by “directing your attention” to one question or another (whatever that really means — but luckily we don’t need to grapple with philosophical issues of consciousness here). A familiar scene will be full of high-level alerts from recognised objects, but if you are painting a picture of the scene, you can also concentrate on, for example, the exact range of colours in a patch of sunset cloud — low-level information.
Hearing is similar. There are low-level detectors, which are using information about things like loudness and frequency content (to be discussed more carefully in the next chapter), but at the same time there are high-level detectors listening out for particular things: a sound with a musical pitch, or the speech patterns of someone with a particular regional accent, and so on. Just using the low-level information means you have only coarse and generic things to go on, disregarding all the subtle and particular things you have learnt to recognise. Think of listening to your native language, compared to taking a dictation test in a foreign language that you are learning.
Skilled musicians, by long hours of practice, have trained up a set of high-level feature detectors; not only for the sound of their instrument but also for details of what it feels like to play a martelé bow stroke, or to control a difficult high note on a trumpet. These musicians may be exquisitely finely tuned to differences between instruments, especially when they are playing them rather than just listening to them. Whether they are explicitly conscious of these distinctions, or can talk about them in a way that makes sense to anyone else, is another matter. But unconscious perceptions can still be important: as an extreme example there is a well-studied family of mental conditions related to “blindsight”, in which a person with brain damage in the visual cortex can sometimes point accurately at an object, or reach out and pick it up, while maintaining that they can’t see it. People can act on sensory input that they do not think they have.
The low-level/high-level distinction is one reason that it is so hard to quantify musical judgements by scientific measurement. It is relatively simple to match, and indeed exceed, a lot of low-level human abilities using computer processing, but it is another matter entirely to match the high-level perception abilities of a normal human brain. That is true for vision, or speech recognition, or natural language understanding, or for assessing musical instruments. A lot of research is being done on these things, and the ability of computers is improving, but they are still a long way from matching what people can do.
An expert may be able to recognise the difference between two violins when they listen to a recording of them, so the information about that difference must be present in the recording. But to recognise this difference by computer processing would require you to find out what specific aspects in that information are being used by the high-level feature detectors of the discriminating listener. There is a big difference between things that are easy to measure and things that matter for musical decisions. It would probably be simple to use a computer to show that the two recordings were different. But that would not mean that the right differences had been found. Think of photographs of faces again: it is one thing to know “these are not the same photograph”, it is another entirely to be able to say “these are two pictures of the same person, but he has shaved his moustache off in the second one”.
One particular kind of low-level analysis of sound is called frequency analysis or “Fourier analysis”. We will look properly at this in the next chapter, but a preliminary comment is in order. There is a persistent folk belief, even (in fact especially) among scientists, that everything about musical sound quality can be revealed straightforwardly by this approach, leading to a common question about musical acoustics “Is that a real subject? Surely its all just frequency analysis?” But when a skilled listener is able to distinguish between the sound of two violins sufficiently acutely to think that it might be worth paying a million pounds for one of them, are they “just” doing Fourier analysis? Simply listening to the relative loudness of the different harmonics in the sound? If it were that simple, everyone would be able to do it because low-level information of this kind is available to us all. It seems intuitively clear that there must be much more to it than this: the expert has learned to assemble a variety of information into a high level judgement not possible to most people. So we have to guard against the hubris of scientists, and be prepared to listen to musicians and expert instrument makers, even when the language they use to express themselves may not have the sharpness of scientific terminology.
Having said all that, for most of this book these issues arising from the slipperiness of human perception will be in the background. We will try not to lose sight of them entirely, so that we address questions about the physics of music and musical instruments which have real relevance to musicians and instrument makers. But a cardinal rule of scientific research is to do the easy things first, to give a secure base from which to reach out towards the harder problems. “Easy” in this context really means “well understood by physicists”: how closely that corresponds to your notion of “easy” may be a matter of opinion. We need to introduce some key concepts about acoustics and vibration. Our aim is to apply these to musical questions, but the same ideas are needed to understand and improve the soundproofing between rooms in a building, or the vibration of suspension bridges caused by high winds, or the way that offshore oil platforms or railway lines can fail by “fatigue” as a result of long exposure to vibration.
Virtually all ideas and techniques developed in modern acoustics and dynamics turn out to have musical applications. A simple example is the “tuned mass damper”. When the famous “wobbly” Millennium Bridge in London had to be closed because it vibrated too vigorously as people walked over it, a major part of the “fix” was to add structures underneath the bridge that are designed to vibrate at the troublesome resonance frequency of the bridge, and suck the energy out of that vibration. These are tuned mass dampers, and they are used in many other contexts: to protect buildings from excessive vibration in earthquakes, and to reduce the vibration of hand-held power tools, for example. They are also used as “wolf note eliminators” in cellos: we will talk about this in Chapter ?.
There are many other examples of musical applications of acoustical ideas and of vibration engineering methods. Shock waves are responsible for sonic booms from fighter aircraft or flying bullets, and also for the characteristic “brassy” sound of a trumpet when it is played loudly (see Chapter ?). The design of loudspeakers for good sound radiation at low frequencies is mirrored by the design of the bodies and soundholes of violins and guitars (see Chapter ?). Computer optimisation of design has been used to achieve particular vibration behaviour of components of jet engines or machine tools, and also to design a new kind of church bell (see Chapter ?). Sophisticated techniques developed to predict the vibration of complex structures like cars and satellites also explain the acoustical significance of the apparently decorative cut-outs in a violin bridge (see Chapter ?).
Not all the science we need to consider is physics, though. There are also established scientific techniques that have been developed to give quantitative information about human perception of sound: the general subject is called psychoacoustics. Again, these methods can be applied to musical questions, as we will explore in Chapter ?. Most psychoacoustical research has concentrated on low-level aspects of perception, such as the minimum detectable change in the loudness or pitch of sounds of various kinds, or the way that one sound can mask the perception of another. The biggest problem we will come up against when trying to apply these methods to music is that the most interesting questions concern higher-level perceptual processing, and so far it has proved very hard to design experiments on these questions that reconcile the conflicting requirements of scientific respectability (enough data for reliable statistics) and musical relevance (retaining some sense of musical content and context for the listening subjects).
There are also things to be learned from the world of music technology and computer synthesisers. Computers can be used to make many kinds of sound, and naturally composers have been very keen to explore ways to harness these to interesting musical effect. In terms of understanding the perceptual ingredients of the sound of conventional instruments, this work on computer synthesis poses a new kind of hazard. Composers are only interested in the effect of a sound: they don’t really care about the exact way that a promising sound is achieved. If they want a computer sound that is a bit like a clarinet, say, they don’t in the least mind whether it is in fact created in a way that mirrors how a conventional clarinet works. But if we want to do synthesis for the purpose of understanding the clarinet, we do care about this, and we may regard the tricks of computer synthesis as “cheating”. Just because it sounds like a clarinet, it doesn’t necessarily tell you anything about how you might adjust the reed or the tone-holes of a normal clarinet to modify the sound. But still, if it really does sound like a clarinet then it is surely telling us something important about the perception of “clarinet-ness”. We will look at some issues relating to computer synthesis of sound in Chapter ?.
The main text of this book will be fairly chatty (or in scientific jargon, “hand-waving”). However, each section has links that give more detail for the technically curious. These will open in a separate tab, so you needn’t lose your place in the main text: so this site works best on devices that support multiple tabs. Crudely, the main text is aimed at musicians who would like to know a bit about science, while the extra links are aimed at scientists who would like to know a bit about music.
Both “musicians” and “scientists” here should be interpreted very broadly: anyone interested in music, and anyone with the mindset and at least a little of the training of a scientist. I make no apology for including some of these technical details in an account of “popular science”. To get an impression of how a scientist, particularly a physical scientist, views the world it is important to grasp that mathematics is the true language of science. It provides the means to distill ideas into a precise and unambiguous form, in a way that mere words can never quite do. The ideas can then be tested rigorously, usually by other scientists who are not convinced by something which seems so very compelling to its originator.
Even if you do not feel the need to face the details and are happy to leave the mathematical material tucked away, there is an underlying message that is important. This concerns the power of that elusive concept, “theory”. Because we use phrases like “I know that’s true in theory but….”, there can be a sense that “theory” automatically implies something tentative, likely to be wrong if examined closely. Well, it is true that all theories are approximate, but some run very deep in a way which is hard to convey to the non-practitioner. Others are indeed quite limited. The power of deep theory is often not grasped by many people, including some professional scientists, especially experimentalists.
There are some kinds of thing for which there is believed to be a good theoretical understanding, at least in general terms. If a measurement seems to show something which contradicts expectation based on one of these deep theories (such as Newton’s laws of motion, or the conservation of energy), it either means that the experimentalist is on track for a Nobel prize or, more likely, that there is something wrong with the measurement or its interpretation. Even when someone is in fact on track for the Nobel prize with some remarkable discovery that flies in the face of what everyone believes, they still have to convince people that their results are right. There are famous examples of radical overturning of conventional ideas: Alfred Wegener was initially ridiculed for the idea of continental drift whereas now it has become established orthodoxy in the theory of plate tectonics. However, it is very much more common for the opposite to happen: a dramatic announcement may be made of some great new discovery, only to be revealed as an error or a misinterpretation after careful checking.
But these “errors” can still be the germ of creative developments: that is how science works, by a continual competitive race to find and prove new ideas that stand up to the most determined critical scrutiny. We will repeatedly come up against frontiers of scientific research in the course of this book. Not, on the whole, the glamorous kind of research that wins Nobel prizes, but the everyday research of scientists as they work away at the giant jigsaw puzzle that makes up currently accepted scientific knowledge. The cumulative effect of many scientists putting pieces into this puzzle is ultimately what gives science its power: big pictures gradually emerge from patient and persistent work in specialised corners. Most individual pieces of research can seem to the non-specialist uninteresting, even trivial, because they are so tightly focussed on one small question. Only by stepping back occasionally to look at the bigger picture does it become clear that progress is gradually being made.
In the course of this story we will see many examples of human ingenuity, across many cultures. There is the ingenuity of Stradivarius, doing whatever it was he did which makes his instruments so expensive now. There is the ingenuity of Trinidadians, turning disused oil drums into musical instruments armed only with a hammer and a bonfire of old tyres. There is the experimental ingenuity of Hermann von Helmholtz, in the nineteenth century before the invention of electronic measuring equipment, managing to decode the unexpected way that a violin string vibrates when you draw a bow across it. This pattern of vibration will tell us something about what violinists mean when they comment that one instrument is “easier to play” than another. We will glimpse why it is easy to make a fairly realistic computer synthesis of the sound of piano, but harder to do a clarinet, and harder still to do a violin. And is there really a “secret of Stradivarius”?