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The previous pages have dealt pretty comprehensively with nominals, primes and the higher partials. Nothing has been said yet of hums, tierces and quints.
I will dispose of quints first. The vibrational mode that gives rise to the quint has a single nodal circle - a stationary ring of metal around the bell - which lies near to the centre of the soundbow. If the clapper hits on this nodal circle, the quint will not be directly stimulated by the clapper stroke. Of course, as the bell vibrates after the clapper stroke, energy can flow from other modes of vibration into the quint, which will begin to sound as time passes. However, if the bells are being rung in changes the next bell will have struck.
To confirm this, in many bells the quint is almost undetectable in a normal recording, though of course it can be made to sound strongly by striking the bell elsewhere than on the soundbow. As a result, quint tuning has very little effect on the timbre of bells, though some say that sharp quints give a glassy sound. The trebles at St. Mary-le-Bow have very sharp quints, as do many old-style bells.
The tierce is far from quiet, in many bells it is the loudest and longest sustained partial. It is also, as shown elsewhere, important in ensuring that the perceived pitch - the strike note - is generated by the ear from the nominal and higher partials. However, the aural effect of the strike note is so powerful that the tierce frequency appears not to affect the impression of pitch in a normally profiled bell. It does affect the timbre - bells with a major tierce have a clearly different quality than those with minor tierces. Examples are given below.
The tierce is almost impossible to tune independently of the other partials. It's relative frequency is set almost exclusively by the shape or profile of the bell. Because of this, tierces in old-style bells are often erratic, though they tend to be a Just major sixth below the nominal (i.e. a Just minor third above the strike) or sharper. This practice carried on into early true-harmonic bells, and it was some while before the founders got them properly under control.
The tuning of the tierce is of importance in carillons, because bells will be rung together or in close proximity to create harmonic effects. Due to the predominance of minor tierces, much carillon music has been arranged to sound its best with minor thirds, and has to re-arranged to sound 'in-tune' on bells with major tierces. Carillon experts tell me that Just tierces sound best in Just (rather rare!) and meantone carillons, but that equal-tempered tierces (about 20 cents flatter) are needed for equal-tempered carillons, as one might expect. The equal-tempered tierce eventually became the norm in UK bell-founding, though Gillett and Johnston often shipped equal-tempered carillons with Just tierces, and produced change-ringing bells with very sharp tierces, nearing the major third.
Recently, Eijsbouts have pioneered bells with major thirds, primarily for use in carillons. Their major third bells have a very unusual shape, with a big bulge in the waist, but major third bells with a 'normal' shape are possible - witness the fifth of the old eight at Dorking, a Wilner bell of 1626, with a tierce at 810 cents below the nominal. One suspects these major tierces in older bells occur through accident rather than design. It's hard to attached much importance to the tuning of (minor third) tierces in change ringing bells, provided there is some level of consistency across the peal.
As a closing example, here are three bells, with a major tierce, a Just minor tierce, and an equal-tempered minor tierce.
In heavier peals of bells, the various partials of the back bells can beat. This can be clearly heard as a rumbling sound after the back bells have sounded together, especially in an ensuing open handstroke lead. The tierce, being a loud and long-lasting partial, plays a big role in formation of these beats. While experimenting with this, I discovered that the beats between the tierces of the 11th and 12th of a true-harmonic peal with equal-tempered tierces are actually at the frequency of the prime or strike note of the 10th. If the 11th and 12th are rung together and set, then after a couple of seconds what sounds like the strike note of the 10th will be quietly heard even though it has not rung. The weight and tuning of the bells of course has to be exactly right for this to occur.
The minor or major 7th hum is said to be one of the classic features of old-style tuning. Though this is true of some of the major foundries - Rudhalls and Whitechapel in particular - other older founders often cast bells with rough octave hums. The hum is one of the easiest partials to pick out with the naked ear because of its low frequency and long duration. However, we must pay attention to the intensity of this partial and our ability to determine its tuning when considering its importance. In many bells rung full circle the hum is quiet to the point of inaudibility. In bigger bells, when the hum is below 200 Hz, as explained earlier it is both hard to hear and hard to determine its tuning due to psycho-acoustic effects. At the time true-harmonic tuning was introduced, a strong defence was made of seventh hums, especially by the Whitechapel bellfoundry. This was probably making a virtue of necessity, due to lack of ability to control and tune this partial. The virtues claimed for seventh hum bells (a clear or harp-like tone) are actually due to prominent upper partials giving a clear virtual pitch.
In a recent piece of work re-creating the sound of the lost ten at Coventry Cathedral, I created a simulation of their sound using bell recordings adapted from St. Peter, Mancroft, Norwich. The tenor of the simulated peal was derived from the 11th at Mancroft and had a hum of 159 Hz, 2173 cents below the nominal (i.e. 2 1/4 semitones above the octave). When I replaced this bell with one adapted from a recording of Great Yarmouth tenor (a Whitechapel true-harmonic bell) the sound in changes was virtually indistinguishable, certainly the ocatve hum made little difference to the sound. In an equivalanet simulation using the tenor at Evesham (a Taylor true-harmonic bell) again the hum made little difference, but in this case the much sharper upper partials came into play.
Even when the hums can be heard, major and minor sevenths are not particularly discordant because, as explained in the section How bells make their sound there are no other close partials to form beats with. I have often noticed when ringing for extended periods on a peal with seventh hums that their sound appears quite normal - one becomes entirely accustomed to it because it is not discordant, just different.
Sharp hums matter most in smaller bells. Little old-style bells with flat primes and sharp hums can sound quite unpleasant close to; here is a flat-primed bell with a seventh hum and an octave hum. The better old-style bells have accentuated upper partials which gives a very prominent pitch sensation. This pitch sensation, rather than the non-octave partials, dominates the sound in changes heard from a distance. Old-style bells, provided they are thick enough, can have their hums lowered on the tuning machine, unlike flat primes, which cannot be sharpened.
A very few bells have substantially flat hums. A classic example of this is the tenor at Dunham Massey (a Taylor bell of 1854).
Many bells have a block of three partials between nominal and superquint. In bells which are true-harmonic tuned, with compatible tierces and strike partials, it has been suggested to me that the intensity and frequency of these three partials can make an audible difference to the sound of the bell. I have not yet investigated this.
Collected together here are examples of many different bell tunings to show the various effects:
To round off this section of the website, here are the bells of St Paul's Cathedral in London being set at the end of a half-muffled quarter of Stedman Cinques on 18th July 2000. In many ways these bells are the apotheosis of pre-true harmonic tuning; octave stretch, shading of nominals to accommodate a slightly flat bell, minor seventh hums apart from the eleventh and tenor which have almost octave hums, relatively high intensity upper partials, but cast to a profile which it is said Taylors had been developing for some years based on their research into Hemony bells of two centuries before. The tower, for those who don't know it, is ideal for the bells - a huge stone box with a solid structure high above the bells to give them space to resonate, and large openings a little above the bell mouths to let the sound out. Can anyone say they aren't magnificent?
Last updated May 8, 2004. Site created by Bill Hibbert, Great Bookham, Surrey