With the upcoming release of The Harmonic Canon Remixes, we talk physics, the harmonic series and the intriguing and unusual science behind bells.
The Harmonic Canon: Remixed | Sat 2 Jul, Stephen Lawrence Gallery // more info + tickets >>
Firstly, let’s get back to the basics of sound
Image a string that’s held in place at either end. The points at either end are usually called nodes.
If I were to pluck this string with my finger, the string would move up and down (or vibrate), making the air around it compress and expand. When this compression and expansion reaches my ear, I perceive it as sound.
The amount of times the string moves up and down depends on its length, thickness, tension and density, but let’s say this string vibrates 55 times a second, or at 55 hertz. This means that when the vibrations reach my ear, I perceive an A.
But this isn’t the only pitch you can hear
The first four partials in the harmonic series
If you only wanted to hear an A pitch, you would have to make sure that the vibration of the string is controlled to make sure it vibrates exactly like the diagram above. But in the real world, this is pretty impossible – you would have to ensure the nodes were evenly distributing the string’s tension, for example, or that you were plucking the string dead on centre.
Because of this, what actually happens is that the string not only vibrates as a whole, but in a whole manner of different ways, forming other pitches that accompanies the main – or fundamental – pitch. And because the string is still held in place by nodes, the other vibrations divide into multiples of the whole string, creating a fixed scale known as the harmonic series.
The result of this is a richer, more complex sound than what you would get from just hearing the fundamental pitch.
This exploration of the harmonic series has often been used in contemporary classical music by the likes of Tristan Murail, Gerard Grisey and – more recently – Katja Saariaho, Jonathan Harvey and Steve Lehman. One famous example is Grisey’s Partials, in which he uses a low trombone as the fundamental pitch, and then orchestrates the other instruments to play the other notes that are derived from this note.
So what’s so special about bells?
Due to the way bells – and some other metal percussion instruments, such as cymbals and gongs – are constructed, the partials naturally drift away from the harmonic series and sound out of tune with each other, making the partials ‘inharmonic.’ That’s why when you hear a metal instrument, sometimes it’s not always easy to hear what the fundamental pitch is. It has a noisier, messier tone quality to it.
This is similar to bells. Depending on how they’re constructed, they tend to have a complex set of pitches when the bell is struck, an accompanying low hum (which, technically, is the bell’s fundamental) and a whole host of other pitches that you can hear. There are also auditory beatings present, due to the out of the tune partials.
The Harmonic Canon
Although Dominic Murcott’s Harmonic Canon looks organic in appearance, the custom-made double bell has actually been constructed using Finite Element Analysis, a type of structural analysis that can predict the vibration patterns of the bell.
One of the bells has been cast in the traditional way – i.e. having a fundamental pitch and a prominent major 3rd (in this case an A and C-sharp) – but the other bell has been cast so that the fundamental is a semitone higher and has a prominent minor 3rd instead (B-flat and D-flat). C-sharp and D-flat are enharmonically equivalent to each other (i.e. they sound the same), meaning that when both bells are played at the same time, you get the dissonant sound of the fundamental pitches being a semitone apart, yet they share the same second partial, creating a overarching hum.
