A harmonic partial is any one of a series of pure tones (sine waves) which usually accompany the prime tone (fundamental) produced by the vibrating or resonant components of a musical instrument. The fundamental is the string tone produced by the vibration of the whole string, or the entire column of air in the pipe; the partial tones are produced by the vibration of fractional parts of that string or air-column. Harmonic tones such as these are also obtained, on any stringed instrument which is stopped (guitar, violin, zither), by lightly touching a nodal point of a string.
Harmonic partials in bells
Various types of bell sounds are differentiated by their partials. You will see in campanology texts and sales literature various ways of illustrating this. Some use a musical staff with middle C being the fundamental, and the partials being shown above and below C.
It has been established that there are five predominant harmonic partials that impart a basic recognizable bell tone. These are named:
- Hum (one octave below the fundamental)
- Prime (fundamental)
- Minor Third or "Tierce" (Major third bells have seen some limited production)
- Perfect Fifth or "Quint"
- Nominal or "Octave" (one octave above the fundamental)
The Hum, Prime and Nominal should be the same note in their respective octaves. The strike tone of the bell (apparent musical pitch) is always one octave below the Nominal, but not necessarily in tune with the Prime (depending on the quality of the bell).
For many years this basic bell theory was lost until being rediscovered in the late 17th century by an English clergyman named Canon Simpson, who worked with Taylor as well as Gillett and Johnston bell foundries to improve the sound of their bells. It is therefore sometimes called the Simpson five-tone harmonic principle, even though we know that 16th century Flemish founders François and Pieter Hemony made use of the principle, but failed to teach it to their successors before their demise.
A bell's strike tone is what determines the actual pitch of the bell, and is often influenced by higher partials. In some bells, it may be a difference frequency between the nominal and octave above the nominal that occurs in the listener's ear. Especially in larger bells, if the higher partials are not also tuned, there may be beats (exhibited by a wow-wow sound as the bell's sound decays).
Some campanologists think that the Quint is so short lived (in decay time) that the octave quint is more important for tuning (especially in larger bells).
Smaller bells will often only exhibit two to four partials that need tuning, simplifying the process to the point that an automated lathe equipped with a microphone and DSP analysis software can be employed during manufacture to reduce cost.
The Strike Tone
This harmonic gives us the perceived pitch of the bell at the time it is struck.
The strike tone is not directly measurable but is definitely perceptible as a subjective harmonic. Generally it can be found by setting an oscillator by ear to match the perceived note of the bell. Multiply the oscillator's frequency by two and you will generally find that the result matches the measured frequency of the Nominal partial. We have tested this theory even on really bad sounding bells. It somehow always works.
When the ear-brain hears combinations of high tones, we think we hear a single lower tone. For instance a combination of a Nominal with an octave-Quint sounds like a single tone lower than them both. This may explain why Big Ben sounds to most listeners like an A even though it was cast to be an E. This effect may lead some seniors, with a limited range of hearing, to say that cast bronze bells sound out of tune to them.
references
Andre Lehr - The Art of the Carillon in the Low Countries
Andre Lehr - Contemporary Dutch Bell-Founding Art (English trans R. Selman and T. Marton)
John Glanville and William M. Wolmuth - Clockmaking in England and Wales in the Twentieth Century: The Industrialized Manufacture of Domestic Mechanical Clocks