The Sound of Bells

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Tuning and doublets

Doublets arise in a bell which is not round, i.e. not symmetrical about an axis down through the middle of the crown. Doublets give rise to beats, as demonstrated elsewhere. If a significant partial, especially the nominal or the prime, has a closely spaced doublet (less than about 7 Hz) the effect is very noticeable as a rapid oscillation in the sound - a boing - oing - oing - oing effect. If the doublet is more widely spaced, the beats cannot be heard clearly as they oscillate too fast, but the sound produced is unpleasant and noisy rather than pure. When bells are rung in changes the gap between clapper strokes for adjacent bells may not be enough for the oscillation to be heard, but the discordant effect is still noticeable.

It is very difficult to produce a bell entirely free of doublets, though nowadays founders take great care both in casting and tuning to ensure the bell remains round. The plot below shows a bell (William Eldridge, 1675 - the larger of the two bells at Great Bookham in Surrey) with a doublet on its prime. The two frequencies are 497.4Hz and 500.6Hz - giving beats three times a second. The beats can be clearly heard in the churchyard when the bell is chimed.

Doubletted prime

The effect of doublets can in principle be lessened by turning the bell so that the clapper strikes at some optimal point. Factors such as the need to turn a bell so the clapper hits a fresh point on the soundbow, fitting of a bell with canons to the headstock, or ensuring the inscription is visible usually preclude this.

Doublets have an interesting role in the history of bell tuning. Before the advent of electronic motion detectors able to detect microscopic movements over the surface of a bell, investigators relied on doublets to discover the nodes of a particular mode of vibration around the bell's circumference. The paper by Rayleigh elsewhere on this site describes how he used doublets in his work.

Some authors have suggested that rather than attempt to eliminate doublets by producing bells which are perfectly round, they be produced with deliberate gross asymmetry (e.g. a groove milled up the inside of the bell) to localise the two modes of vibration and ensure that with the clapper striking at the right point, only one mode would be stimulated. I am not aware of this being tried in practice, though Whitechapel used to have a small bell in their yard with holes drilled through the soundbow at the four points of the compass which struck two notes a significant interval apart.


Last updated April 1, 2004. Site created by Bill Hibbert, Great Bookham, Surrey