A bell exhibits one type of behaviour at the start of a note, and different behaviour as the note decays. Experiments show that there are, in fact, three distinct phases to the sound. The first is the strike — the sound of one large lump of metal hitting another. As you would expect, this is enharmonic, and it dies away quickly. The second phase is the strike note, and this is dominated by a handful of strong, low harmonics. Finally, the note's lingering energy is radiated by a sub-harmonic an octave below the fundamental.
Figure 8: Representing the three phases of the bell's sound.
The strike note is particularly interesting, because the perceived pitch is not necessarily the pitch of the lowest energetic partial. Do you remember the organ builder's trick I mentioned when I discussed frequency-shifters back in January's instalment of this series? I described how, if the partials of a sound lie in an harmonic pattern based on a fundamental frequency that isn't present in the signal, the human brain inserts the missing pitch, and you 'hear' the fundamental, even if it's not actually there (see
Synth Secrets January 2002 to read the whole article). The strike note of a well-tuned bell does the same thing. The dominant partials can be tuned to produce frequencies in the ratios 2:3:4, so that the listener hears the implied pitch of '1'. For example, if the dominant partials vibrate with frequencies 100Hz, 150Hz and 200Hz, you will 'hear' a fundamental of 50Hz.
Putting all of this knowledge together, we can create Figure 8 (above). This is only a graphic representation, but it shows the three phases of the sound in an easily understood form. As you can see, an initial burst of enharmonic partials is followed by an extended period in which the low harmonics (some of which grow progressively sharper with increasing frequency) determine the sound. Below these, there lies the subharmonic that dominates the sound in its final moments.
Of course, the sound of a real bell is much more complex than this. I have ignored numerous factors such as the changes that occur when the bell is struck with clappers of different materials or at different speeds, as well as those that occur when bells are cast of different alloys, or of different sizes and relative dimensions. Fortunately, we can ignore all of these here, although we must include one additional factor if we are to synthesize realistic bell sounds. Like most adults in the bath, bells warble... rather than producing a steady 'boing', many bells make a noise closer to 'boii-yoy-yoy-yoiinnnggg' because their modes can be almost degenerate. This means that bells produce two partials of almost (but not quite) identical frequencies, and these interfere (or 'beat') in the same way as do two synth oscillators of similar frequency.
