Fonderia Allanconi

The acoustics of a bell
A bell is a musical instrument of the idiophones family, which emits sounds thanks to the impact of the clapper on its body. The percussion causes a deformation in the bell - imperceptible to the eye - and therefore a series of prolonged vibrations over time that decrease progressively until the return of the so-called state of calm.
The sound spectrum of a bell is very complex. This is because the particular shape of the bell generates a collection of different ways of vibrating, known as 'partial tones', which produce different notes simultaneously.
The point where the clapper impacts determines the evolution and direction of several waves, creating a decidedly complex mapping of Ventral Areas (of maximum energy) and Nodal Areas (of zero energy), different for each partial tone.
The note of a bell is in effect a psychoacoustic perception originated by the sum of all partial tones developed by the bell. This is called 'nominal note' by which the 'musical name' of a bell is identified.
A good bell originates more than 50 partial tones. The main ones, that is the more intense ones, are defined according to their height with respect to the nominal note: Hum Note, Fundamental, Minor Third, Fifth, Nominal, Twelth, and Double Octave. For example: a bell whose nominal note is C1 has partial tones that correspond, respectively, to the notes C0, C1, D#, G1, C2, G2, C3. The more the height of these partial tones corresponds to the musical range (and therefore the partial tones form a specific musical arrangement) the more the sound of the bell will be pleasant.
A sound has three important characteristics: height, intensity and timbre, indispensable to define the peculiarities of each note.
The duration of a sound is conventionally divided into three parts: Transitory Moment of Attack, Central Moment and Transitory Moment of Extinction. In a bell, similarly to what happens in all percussion instruments, the transitory moment of attack coincides with the very brief moment the clapper enters in contact with the bell. The central moment, i.e. the stationary state, is virtually null, since - once the clapper moves away from the bell - no energy maintains the vibration constant (differently from the wind instruments or the human voice). Instead, it is the transitory moment of extinction to be of particular importance. This has a considerable length, that starts just an instant after the clapper has touched the bell, and ends with the return to the steady state. It is during the latter that the characteristics of the sound and the distribution of the partial tones are evident.
In the design phase of a bell, the final result is calculated depending on the destination of the bell. In other words, if the bell is going to be placed in an existing chime, the new bell must necessarily have a tonal character and shape similar to that of the other bells, so as to preserve the same 'sound-related identity' of the chime.
Once a bell and its shape have been designed, other factors that affect the performance and the final result must be taken into account.
The accuracy of execution in all various steps of processing and the materials used are two fundamental aspects. Bells are made of bronze, an alloy that can have different compositions but which must necessarily consist of copper (Cu) and tin (Sn). The latter, which is silver-white, has many acoustic properties, thanks to its elevated elasticity. Copper, instead, which is light red, is more resistant than tin, but has less acoustic properties. Bronze combines the acoustic properties of tin with the resistance of copper, forming a perfect material for its high acoustic properties and its high tensile strength, essential to avoid early cracking of the bells themselves.
Decisive steps are the fusion process of the bell, at over 1000°C, in which the alloy must maintain certain characteristics, and the subsequent cooling phase of the bronze, which must be maintained for the right time in order for the interweaving of the metallic crystals to take place.
The last step consists in rectifying the partial tones, so as to correct the newly melted bell and take it to the final result, according to the original project. This is done by mechanically removing bronze - just a few millimiters - from the inside of the bell, from the so called sound vessel, at heights specifically calculated for the correction of individual partial tones.
Finally, once the new bell has reached the final result, it is tested to verify that the timbre is homogeneous, that there are no vibration beats and that the vibration has a decreasing trend, with the lower octave partial tone adequate in length to the size of the bell, until the steady state is reached.