I have a theory...

Paul Harris discusses the fascinating (and sometimes enigmatic) side of music that we know as music theory.

When thinking of ‘theorists’ – those who indulge in the study of theory as a career for example – we probably imagine a group of very earnest and rather solemn-looking scholars sitting at desks, surrounded by books and thinking, occasionally committing their deep thoughts to paper and publishing them in weighty tomes. Such people live in a land far away from those of us who spend most of our time at the coalface, teaching our pupils to play music. But that doesn’t mean that we shouldn’t take the odd trip into their world. We may learn fascinating things. In very general terms, Music Theory is about what makes music work. It’s the story behind the notes; it concerns all the stuff that falls in that area that is ‘about’ music. 

In this article I’d like to look at the theory and history behind some of the areas we usually think of as music theory and uncover some other areas that don’t often make their way into theory exams. And in the next article we’re going to return to some of those topics often assembled together in those ‘theory exams’ and explore how they can support our practical work and look at ways of incorporating them in our regular teaching. 

So let’s begin with sound. After all, music is sound (or ‘organised sound’ as many theory definitions would have it), so it would seem reasonable for musicians to want to know something about it. There’s much to learn about how we actually hear the sounds our instruments make – how the ear and brain processes these magical vibrations and turns them into music that can affect us so much. There’s the whole fascinating area of harmonics (yes, harmonics really can be fascinating!) – which are present in all sounds and the reason behind why different instruments actually sound different. Did you know that there is one instrument (possibly more than one) that produces no harmonics (or overtones)? This gives that particular instrument it’s very distinctive sound. (All will be revealed in the next article.) 

The harmonic series (that naturally occurring series of notes that are linked mathematically to any fundamental tone) also has an interesting bearing on the way harmony has developed and goes at least part way to unlocking the reason why music in a major key sounds happy and in a minor key sounds sad. Then there’s the vast subject of tuning and temperament, an area of music theory that Bach himself was particularly interested in. If he hadn’t have been, we may never have got the ‘48’ and music may have developed in quite a different manner. 

What about all our various scale patterns and the intervals we can divide them into? How did all that come about? Some say it’s all the result of a certain blacksmith and his occasional visitor, the great philosopher Pythagoras of Samos, some time round about 400BC. Pythagoras realised that the size of the hammer (hitting the anvil) caused sounds of different pitches and that these sizes and their pitches were related. He worked out all sorts of mathematical connections – which is probably where the age-old connection between music and mathematics began. The origins of all the millions and millions of scales that we play with such varying degrees of pleasure, began their life in that little Greek island of Samos in the eastern Aegean Sea. It ought to be a regular place of pilgrimage for all musicians!

And had you ever wondered why we split the perfect octave up into twelve units? If you keep going round the circle of fifths from a C you will eventually land back there 12 notes later. Hence the twelve notes of the chromatic scale. But in fact it needn’t have been twelve. It turns out that twelve is simply a number of pitch sub-divisions that the human ear can organise with reasonable ease. And each of those semitone intervals is divided into 100 cents, although of course it isn’t always 100 cents as those with a knowledge of different temperaments will know! And that, on a very practical level, is where things get really interesting. For a real sensitivity to (and knowledge of) fine tuning begins to open up the huge and wonderful world of pitch nuance. How should we tune that leading note – a little up or down? Which would be the more expressive? Where exactly does a minor third fit into a perfect fifth to make a really meaningful minor chord? Is D sharp the same as E flat? It isn’t! There’s not much we can do about it on the piano, but for all non-fixed pitch instruments (and voices) we can begin to produce and savour some very expressive and evocative sounds.

What about the great Hucbald the One-legged? He wrote perhaps the first book on music theory (sometime around 900 and a must-read for all theory enthusiasts) and was responsible for rationalising musical symbols, many of which we still use today. And we mustn’t forget Guido d’Arrezo’s ‘Guidonian Hand’ – perhaps the first attempt at a ‘fun’ way to learn to sight-sing. Guido is another medieval theorist and is regarded as the inventor of modern musical notation.

And I wonder if you’ve ever thought about why is the treble clef so called? Here’s the (perhaps unexpected) answer: in early contrapuntal music the tune was usually in the tenor accompanied by an alto line. Sometimes there was a third line too, higher in pitch and called the treble (the third line). Here are a couple more: why is a stave made up of five lines? What is the golden section and why were Debussy and Bartók so fascinated by it? Such questions are seemingly endless and represent just the tip of the iceberg (my allotted number of words hasn’t allowed me to answer them here – but I hope you’ll be inspired to go off on your own voyage of discovery!). Some of them really can help us in our teaching (to a certain degree anyway) and some of them not so much. But they are all interesting and many of our pupils may be truly fired up by having their imaginations guided in these unusual directions. 

In fact if we think of Music Theory as being all about firing our pupils imaginations, it turns it into a very different beast. Theory is about discovering and understanding all those things that lie behind so much of what goes on in our lessons. You don’t need to know how an engine works to get about in your car – but it can make a big difference if you do.