The Sound of Bells

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How bells make their sound

How bells make their sound is a complex but interesting subject. The discussion here is restricted to bells of typical 'western' profile, rather than those of the east which have a very different shape. Western bells are usually hit by an iron clapper at a point on the inside, near the bottom, or by an iron clock hammer at an equivalent point on the outside. This impact causes the bell to vibrate in a number of different ways or modes. Each mode can have a different frequency, intensity, attack and decay time, and can be characterised by 'stationary' points or nodes, both around the rim, and vertically up the bell.

In instruments with vibrating strings or columns of air (pianos, guitars, flutes, trumpets, organs etc.) the frequencies of the various modes or vibration are related approximately by simple arithmetic ratios. This means the various modes of vibration are 'in tune'. Also, the sound is more or less sustained, which makes for ease of study. In bells, as in gongs and drums, the unique shape means that the various frequencies of vibration are not automatically related in simple ratios. Also, the impact of the heavy clapper and the rapid decay of some of the partials means that measurement and investigation is not easy.

Western bells assumed something close to their present shape about 1000 years ago. Since then, bell founders have attempted to produce a 'better' shape through a process of experimentation and development. The actual shapes used are a compromise between the sound quality or timbre of the bell (which is heavily influenced by its shape or profile), ease of casting and tuning, and certain other characteristics such as weight and basic dimensions of importance when the bell is rung full circle in the English style. The history of the improvement of bell sounds is one of periods of dramatic progress (for example, by the Hemonys in the 17th century, by various English founders in the late 19th / early 20th century, and in the mid to late 20th century as the result of detailed research). At other times, when economic and production factors have gained the upper hand, progress has slowed and even reversed. Even today, there is no one formula for the profile of a bell that guarantees the best results for all purposes, and founders regard their bell profiles as commercially sensitive information.

This section of the website covers in considerable detail the sound produced by bells. The physical processes within the bell and the details of how each mode of vibration or 'partial' is tuned have been researched extensively elsewhere and references are given where required. The subsections of this part of the website cover; the main partials in a bell and how they are tuned; the meaning of the pitch of a bell and what determines the pitch or 'strike note'; the various uses to which bells are put and how this impacts their design and tuning; the variation of partial intensity over time; a comparison of Perrin et al's detailed research into the physical modes of vibration of a bell with the actual sound it produces; and an introductory discussion of the effect of building structure and materials on bell sound.

To illustrate the differences in timbre, here are a number of bell recordings, adjusted to have the same nominal, with rather different sounds:

Despite all these bells having the same nominal, I can also hear differences in pitch between them. This is an example of a most important effect - the pitch or strike note of bells - which I have been researching in considerable depth. The next section but one on the pitch of bells explains and demonstrates the effect. In brief, it has been traditional for the note assigned to a bell, the strike note, to be taken as an octave below the nominal, without any explanation as to why this should be. It was Rayleigh who first stated this assumption in a scientific context, though an explanation waited almost a century. The work in the early 80's of Terhardt proves the principle that a bell's strike note is a virtual pitch effect, generated in the ear from a number of bell partials, and that of Eggen and Houtsma shows the dependance of a bell's pitch on the nominal, superquint, octave nominal and other partials. A recent article of mine shows the practical effect in a couple of UK rings of bells.

The various articles on how bells produce their sound can be accessed via the links below:

Basic principles of tuning

Musical pitch of bells

Doublets or warble in bell sounds

How the usage of bells affects assessment of their quality

Time variation of bell sounds

Modes of vibration and the Perrin research

Comparison of the Perrin results with the actual bell sound

Effect of clappering on bell sound

Building acoustics


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