THERE is something different about Symphony No. 3 by Ross Edwards, one of Australia’s leading composers. It is not just his use of uniquely Australian sounds, such as Aboriginal chants, that makes his composition unusual. It’s also the hundreds of bells that ring out as the symphony ends.
Bells are rarely used in orchestral compositions because they produce a complex sound that jars with other musical instruments. But that is not a problem for Edwards. He has a unique set of bells designed by acoustic engineers to blend, rather than clash, with an orchestra. Not only are these new designs purifying the tones of bells, they are giving musicians new sounds to play with.
The secrets of these bells were revealed last July by their inventors, Neil McLachlan and Anton Hasell, working at the company Australian Bell in Mia Mia, Victoria. To eliminate the jarring overtones, they turned to computer modelling and acoustic analysis. The solution, they found, involves completely rethinking the shape of these delicately sculpted musical instruments. Gone is the traditional bell shape and in its place is a range of new designs, including some that look more like large metal beakers.
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Listen carefully to a church bell or clock tower striking the hour. As the sound fades, you should be able to hear a second, higher note humming in the air. This is the overtone that gives European-style bells their distinctive sound. It also clashes with other instruments when it is used to create part of a chord or a harmony. So when composers want a bell-like effect they tend to mimic it using “cleaner” instruments such as chimes, rather than wrestle with the real thing.
But not Edwards. He had no fear of dissonances when he scored Symphony No. 3 to mark the centenary of Australia’s federation in 2001. That’s because McLachlan and Hasell’s bells produce only pure harmonic overtones – integer multiples of the main or fundamental frequency, which sound at the same time as the fundamental note.
McLachlan and Hasell aren’t the first to try to fix the racket bells make. The tuning of bells was developed into a fine art in the Netherlands during the 17th century when the Alsatian bell founders Pieter and François Hemony teamed up with a musician named Jacob van Eyck.
Van Eyck played an instrument called the carillon, a series of bells operated by a keyboard. Carillon bells have the potential to generate a cacophony of dissonances – and they often did. But van Eyck and the Hemonys worked out how to tune them so that their overtones sounded more pleasant and harmonious. In 1643 they created a carillon for the Dutch town of Zutphen that sounded far sweeter than any made previously. Unfortunately no one else knew how they did it. When the Hemonys died, their knowledge died with them.
The art of carillon tuning was lost for 200 years until an English bell enthusiast, the canon Arthur Simpson, rediscovered the secret in 1895. Simpson had noticed the prominent overtones in the bells at his church in Fiddleworth, Sussex. To see whether there was some way to tune them so that they sounded less dissonant, he began a series of experiments in collaboration with John Taylor Bell Founders in Loughborough, Leicestershire. He published his findings in an article entitled “Why bells sound out of tune” in Pall Mall Magazine, in which he noted that a traditional bell generates a whole series of overtones that are not always in tune with one another.
The root cause of the problem is the complex way bells vibrate. When, say, a violin string is plucked, the vibrations that travel back and forth along the string create a pattern of standing waves that are heard as the fundamental note and its harmonic overtones. The loudest of these, the fundamental, is a single standing wave with a wavelength as long as the string; the second harmonic waves have half the wavelength and twice the frequency; the third harmonic has three times the frequency of the fundamental; and so on.
When Simpson compared all the overtones produced by a bell, he discovered what makes a bell sound out of tune. Unlike a violin string, a bell’s third overtone is 2.4 times the frequency of the fundamental. In musical parlance, it is an octave and a minor third (three semitones) on the musical scale above the fundamental.
Simpson followed up his 1895 article about out-of-tune bells with another entitled “How to cure them”, though he failed to eliminate the problem completely. Like van Eyck, Simpson realised that for carillons to sound more harmonious, the first five or so overtones in each bell have to be finely tuned.
To do this, Simpson and the foundry cast the bells with walls slightly thicker than they needed. Then they gradually removed metal from the inner wall with a lathe until the overtones sounded “true”. This process was a matter of trial and error. It also relied on a good ear and was hampered by not being reversible. Nevertheless they succeeded in producing a series of harmonic-tuned bells that were installed in St Paul’s church in Bedford in 1896.
But Simpson and the foundry failed to cure the problem of the minor third, which is quite conspicuous. Even well-tuned bells can come unstuck by this when played together or with other instruments. If a major third, one of the most common chords in western music, is played while a minor third overtone is still ringing in the air, the result is a nasty clash.
A century later McLachlan and Hasell, armed with the latest computer-aided design, set out to use physics and computation to produce a bell that would do away with the pesky minor third altogether. They wanted to invent a set of harmonic bells that could take pride of place in an orchestra, producing overtones that were integer multiples of the fundamental frequency. To work out the acoustic properties of bells, they had to pinpoint which parts of the bell vibrate and how its shape determines these resonances.
Much of the work in mapping the vibrations was carried out using an engineering technique called finite-element analysis. This breaks down the complex structure of a bell into elements whose movements are easier to work out than the instrument as a whole. A computer program analyses the forces acting on each element separately, then coordinates them to give an overall picture of what is happening to the entire bell.
McLachlan and Hasell applied the technique to the vibrations of bells with various shapes and cross sections. With these virtual bells, they could effectively cast and lathe the instruments, shaving some material off here and thickening it there. After each step, they looked at the resultant vibrations and the sounds produced. Bit by bit, McLachlan and Hasell edged their way towards a bell with a perfect harmonic series of overtones. Collaborating with Josef Tomas and Behzad Keramati Nigjeh at the engineering firm Advea in Wheelers Hill, Victoria, the researchers then spent almost a year optimising the design.
Cast of thousands
The key to harmonic bells, they found, is to identify shapes whose vibrations wrap around the bell like a girdle rather than rippling from top to bottom (see Graphic). They also discovered that there is no unique shape for a harmonic bell: a variety of profiles will work, including cones with tapering wall thickness and concave shapes. It should have been simple to alter a bell’s pitch by simple scaling, but those needed for high notes would have very thin rims, making them too fragile to ring. So some of the smaller bells had to be redesigned with thicker walls.
To turn their computer designs into the real thing, the Australian Bell team used lasers to cut steel plates into the shape of the bells’ profiles. These were then mounted on turntables to plough out the bell shape in a stiff slurry of sand mixed with a curable resin. This later acted as a mould for casting in bronze alloy. Some of the small bells were turned on computer-controlled lathes, rather than cast. And some of the larger bells needed fine-tuning on a lathe after they had been made.
But McLachlan and Hasell haven’t stopped there. They have also created a whole range of new designs that produce effects quite unlike any traditional bell. They have even created bells that enhance inharmonic overtones, such as the minor third, rather than suppress them. These “polytonal” bells each produce two or more notes of equal loudness. That makes it hard for someone listening to a polytonal bell to say which note it produces. Such ambiguous sounds, McLachlan says, are particularly well suited to modern musical styles. And he believes polytonal bells can create a much richer sensory experience than classical tones and timbres.
Last year, Australian Bell installed a collection of 39 harmonic and polytonal bells in Birrarung Marr Park by the Yarra River in Melbourne, where every morning, noon and evening they play an hour or so of specially commissioned music. Known as the Federation Bells, these instruments are fixed to the tops of tall poles and played by computer-controlled hammers while visitors wander among them in a forest of sound. The company has also made a set of 2001 harmonic handbells for the Melbourne Symphony Orchestra together with a range of larger harmonic bells that cover two octaves.
Bells on a budget
McLachlan is hoping that his company’s bells will reach a wider audience. To make them affordable to schools and anyone else who wants one, his team is designing bells with constant wall thickness that can be spun and pressed at a fraction of the cost of the Federations Bells. “We are now looking for investors to help us take these designs to international markets,” McLachlan says. The team has also entered a proposal for a commemorative bell installation at the site of the World Trade Center in New York, and is looking for other opportunities to build interactive arrays of bells in public spaces.
Of course, there is another reason why orchestras rarely use church bells: their sheer size. On the rare occasions when church bells do appear in a score – as they do in Puccini’s Tosca and Wagner’s Parsifal – the percussionist strikes a set of tubular bells instead. The trouble is, the sound of tubular bells does not come close to the real thing.
In the early 1990s, the Australian composer Moya Henderson teamed up with physicist Neville Fletcher of the Australian National University in Canberra to produce a new instrument, the tosca alemba, which they hoped would overcome this problem. The tosca alemba is an array of steel bars bent into a shape similar to a pentangle.
It evolved from a contraption called the alemba, devised 10 years before by Henderson. The alemba is a triangle connected by a cord to a tubular resonator to amplify the sound. But its high-pitched ring still doesn’t sound much like a bell. So Henderson asked Fletcher, an expert in acoustics, for help to turn the alemba into something louder and more bell-like.
They set out to capture the complex mix of overtones, including the distinctive minor third. To increase the degree of freedom and offer more scope for fine-tuning, Fletcher increased the number of sides of the alemba from three to five. His calculations showed that a bar bent into a shape more like an open-ended coat hanger than a regular pentagon gave the most realistic sound.
Having found the approximate shape by pen-and-paper calculations, Fletcher then refined the design using finite element analysis. And he made a series of these pentangles to cover the full octave range of the bells in Tosca. To boost the instrument’s volume, he connected the bars to a resonating soundboard with an elastic cord. The full tosca alemba, with its bell-like tones, is loud enough to hold its own with a small orchestra.
So now bells can take their place in the orchestra pit, bringing new life to old works and providing a new range of sounds for composers to conjure with. And it may not stop with bells. McLachlan believes that every class of musical instrument could benefit from new designs and manufacturing processes. The entire orchestra could be about to get a makeover.
- You can listen to Melbourne’s Federation Bells at