The Sound of Bells

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Tuning of primes

The prime is an odd partial - there is not even agreement as to its name. It is known variously as the prime, the fundamental, the extra or the second partial. I avoid the use of fundamental as a name for this partial to avoid confusion with the missing fundamental, a term in acoustics with quite a different meaning.

Prior to the advent of modern profiles and tuning methods the prime was a hard partial for the founder and tuner to control. The best area of the bell to tune the prime without affecting the other partials too much is right at the top of the bell in the corner between waist and crown. It is only in the last hundred years or so that tuning machines in the UK have been able to work this high inside the bell. For example, Elphick on page 102 of The Craft of the Bellfounder explains how the earliest English tuning machine, constructed by Rudhalls, moved to Whitechapel by 1846 and used by them for several years, relied on an elm pad inside the crown of the bell to locate the rotating shaft holding the cutting tool. This arrangement would preclude tuning high in the waist or on the crown.

In true harmonic bells, the prime is tuned to an octave below the nominal, and therefore its frequency is the same as that of the pitch or strike note of the bell. This is the only example (apart from doublets) where two significant tones from a bell have about the same frequency. However, the different origins of the two frequencies (one being a physical vibration of the bell, the other being a psycho-acoustic effect in the ear) mean that beats will not be generated, and that differences between prime and strike note will not sound as discordant as they would, for instance, on a piano. However, it is possible to distinguish the two frequencies. When a bell is being rung up and the clapper is still striking gently, the prime can sound louder than the strike. Also, in some bells the prime dominates as the sound of the bell dies away a few seconds after the clapper hits.

The prime in bells cast before the introduction of true-harmonic tuning is usually flat, more so in the lighter bells of a peal. The flat prime, with the sharp hum, is the main contributor to the distinctive sound in changes of old-style bells and, because of basic constraints in the tuning process, cannot be materially sharpened. Here are the primes of an old-style eight (Ranmore in Surrey, cast by Mears in 1859) relative to the nominal. True-harmonic bells would have primes at roughly -1200 cents or one octave below the nominal.

Bell 1st 2nd 3rd 4th 5th 6th 7th 8th
Cents -1379 -1377 -1357 -1265 -1229 -1237 -1241 -1195

In smaller old-style bells heard from close proximity when chimed, the flat prime sounds quite unpleasant. It is remarkable that founders of the time did not try to understand or correct this. Heard from a distance, in changes, bells with flat primes sound merely characterful rather than nasty. Old-style bells often have more accentuated upper partials than true-harmonic bells, giving a very clear sensation of pitch from a distance. Here is an example of a bell, chimed, with a flat prime, and the same bell with an octave prime. The most distinctive old-style sound, that of small bells with flat primes and sharp hums, will be further discussed later.

Sharp primes are also sometimes encountered, and bells with them have an unmistakable sound. Sharp primes can often be flattened by tuning in the shoulder if the bell has enough thickness of metal. Very sharp primes seem to have a deadening effect on the tone of a bell, probably because the sharper the prime, the closer in frequency to the tierce (which is often very loud immediately after the clapper strike).As the prime and tierce are similar modes of vibration, each having a single nodal circle but at differing heights above the soundbow, it could be that having these two partials close in frequency means the two modes interfere, causing the tierce to decay more rapidly than normal and hence giving a less resonant sound.

In my opinion, the (re-)discovery by Taylors in 1896 of a profile or shape for lighter bells allowing the prime to be tuned to an octave was the critical innovation allowing the introduction of true-harmonic tuning, a changed that transformed bellfounding.


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Last updated April 24, 2004. Site created by Bill Hibbert, Great Bookham, Surrey