Abstract
The rim partials of a church bell (those with an antinode at the soundbow) generate the strike pitch or perceived note of the bell. The spacing in frequency of the higher rim partials has an important effect on the tonal quality of the bell. Investigations into the partial frequencies of 2752 bells, both bronze and steel, of a wide variety of dates, founders and sizes, show a simple and unexpected relationship between the frequencies of the rim partials. This relationship explains why attempts to tune the higher rim partials independently have failed. A modified version of Chladni’s law provides insight into the musical relationship of the partials, and predicts the partials of individual bells well, but fails to give a simple model of the spacing between the partials seen in bells with different profiles.
Highlights
Church bells have a large number of modes of vibration giving rise to partial frequencies in the radiated sound
Partial frequencies arising from the rim inextensional radial (RIR) modes give rise to one or more virtual pitches in the ear which dominate the tonal effect of the bell
The work reported in this paper investigates in detail the frequency relationships between the RIR partials, given their importance to the overall tonal effect of church bells
Summary
Church bells have a large number of modes of vibration giving rise to partial frequencies in the radiated sound. Partial frequencies arising from the RIR modes give rise to one or more virtual pitches in the ear which dominate the tonal effect of the bell. The strike pitch of a bell is roughly an octave below the RIR partial m = 4 (the nominal) provided that the nominal lies broadly in the range 500 Hz to 1500 Hz. The m = 4, m = 5, m = 6 and higher RIR partials have frequencies which are approximately harmonically related giving rise to the virtual pitch. The work reported in this paper investigates in detail the frequency relationships between the RIR partials, given their importance to the overall tonal effect of church bells
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