How Is a Bell Made to Sound Right? Casting Metal to a Calculated Shape

A bell is a thick shell that vibrates in several patterns at once, each with its own frequency, and what a listener hears is the combination. Unlike a string or an air column, those frequencies are not simple multiples of a lowest one, so a badly proportioned bell produces a discordant set of partials and sounds wrong even though it is perfectly made. The thickness varies from the thin lip to the thick sound bow where the clapper strikes and up to the crown, and that profile is what sets the relationships between the partials. Founders arrived at successful profiles by copying and adjusting over generations, and the relationships were only measured and understood in the nineteenth and twentieth centuries.

A well-tuned bell has a recognised set of components in specific relationships:

• •The hum, the lowest partial, tuned an octave below the nominal
• •The prime or fundamental, tuned to the named note of the bell
• •The tierce, a minor third above the prime, which gives bells their characteristic sombre colour
• •The quint, a fifth above
• •The nominal, an octave above the prime, which is what determines the perceived pitch
• •Higher partials that contribute brightness and decay quickly

The traditional process is essentially unchanged and is worth describing. A mould is built in two parts, an inner core shaped to the inside of the bell and an outer cope shaped to the outside, formed using a sweep board cut to the intended profile and rotated about a central spindle, with the space between them being the bell. Inscriptions and decoration are applied in reverse to the cope. Bell metal, a bronze of roughly four parts copper to one of tin, is melted and poured, and the casting cools slowly over days, since cooling too fast cracks it. The bell is then broken out, cleaned and tested, and tuning follows by mounting it on a vertical lathe and machining metal from the inside, which lowers particular partials according to where the metal is removed.

How a bell is mounted determines what can be done with it and the traditions diverge sharply. A bell hung dead and struck by an external hammer can be sounded precisely on demand, which is what a clock chime and a carillon require, and a carillon player operates dozens of such bells from a keyboard with considerable musical control. A bell swung on a headstock rings when its clapper strikes as it moves, which gives a richer sound and far less control over timing, since the bell's swing sets the rhythm. The English practice of hanging bells on full wheels allows them to rotate through a full circle and gives enough control over timing to ring them in changing sequences, which produced a mathematical tradition of permutations that is unique to those islands and is essentially a performance of group theory.

Tuning is subtractive and therefore one-directional, which shapes the whole craft. Removing metal from particular zones inside the bell lowers particular partials, since each pattern of vibration has regions where thickness matters more, and a skilled tuner works partial by partial while monitoring the frequencies. Nothing can raise a partial, so a bell cast too thin or with a partial already flat is scrap. Casting is therefore deliberately a little heavy to leave material for tuning. True harmonic tuning of all the main partials became routine only after the principles were rediscovered in the late nineteenth century, using measurement rather than ear, and many older bells are not tuned to modern standards and are valued anyway for their voice. Recasting an old bell destroys it, which is a live issue in conservation.

A bell sounds several partials that are not simple multiples of one another, so the thickness profile rather than the size alone determines whether it sounds right. Hum, prime, tierce, quint and nominal are the components tuned, with the tierce giving bells their sombre colour. Tuning removes metal and cannot raise a partial, so bells are cast deliberately heavy.