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Conservation by Re-use

Helping churches acquire surplus and/or redundant bells to be hung for

English-style full-circle bell-ringing.

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Simpson’s Proposed Harmonic Relationship for Bells

Changing the bell's shape allows some of the inharmonious partials (e.g. the Quint and Upper Third) nodal circles to be located at or near to the soundbow resulting in reduced partial intensities when the bell is struck on the soundbow. Experimentation with the shape and thickness of bells by some founders, in particular John William Taylor14, resulted in an acceptable compromise between Simpson's ideal relationship and what could be achieved. The Hum, Prime and Quint were brought into line with the Nominal but the Tierce was made into a minor third instead of Simpson's suggested major third. The ratio between the Nominal and Upper Quint changed to 2:3 but the Upper Octave remained a higher frequency than the ideal. Although slightly different to Simpson's ideal, this combination is widely known as the Simpson scale.

Sound of Bells – Simpson’s Hypothesis continued

Simpson was puzzled why bell-founders quoted a strike note an octave lower than the Nominal. He thought that this was an error by the bell-founders and was not aware of its true significance.

Research this century13 has shown the Strike Note is an apparent frequency heard by the ear shortly after a bell has been struck. The human ear interprets the combination of the short-duration high-intensity Nominal and Upper Quint partials as a note of half the frequency of the Nominal partial. The clarity of the strike note is improved if additional high-order partials are present, e.g. the Double Octave. For a clear strike note the frequency relationship of the Nominal, Upper Quint and Double Octave partials should be 2:3:4. By extending Simpson's proposed Harmonic series from 5 to 8 partials, the Strike Note would be the same frequency as the Prime, making the Strike Note and long-duration note in unison. Unlike Simpson, John William Taylor14 is sure to have been aware of the significance of the Strike Note, and he almost certainly extended Simpson's theories to the high order partials.

The figure on the previous page shows that the Nominal, Upper Quint and Upper Third partials for a typical 19th  Century bell have a high initial intensity then decay quickly, whereas the Upper Octave is practically non-existent. The bellfounder would need to reduce the intensity of the Upper Third partial, increase the intensity of the Upper Octave and change the frequency ratio of the Nominal, Upper Quint and Upper Octave partials to 2:3:4. The shaded part of the table shows Simpson's theories extended from the first five partials to the eight principal partials.