Geometry of an English Church Bell

The axisymmetric geometries of both internal and external profiles of church bells, along with the properties of the bell metal, are of vital importance to their acoustics. The role of “golden geometry” in determining the visual characteristics of the outer profile of a modern English church bell is presented. It is shown that a golden rectangle, a golden triangle, and a golden angle are all important factors. Three angular parameters are identified as measures of these attributes of the bell’s “goldenness”. Two of these features are shown to result from an underlying regular pentagon with one side defined by the bell’s mouth. The centre of this pentagon determines the location of the bell’s shoulders. Further minor features are also shown to be determined by golden geometry. The evolution of the three angular parameters over the previous millennium is included, showing a tendency to trend quickly towards the golden values in all the cases. Ultimately, the angular parameters for the English church bell of focus here are used for comparison with other modern European bells studied previously. The bells considered all displayed at least two of the three major golden features to an agreement of better than 1%.