The Sound of Bells

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Taylors of Loughborough and true-harmonic tuning

My thanks are due to David Bryant, Steve Ivin and Chris Pickford for wittingly or unwittingly providing insights and information which led to the analysis below. Errors and unsubstantiated opinions are of course my own.

In the late 19th and early 20th centuries, Taylor's bellfoundry was the first in the UK to adopt 'true-harmonic' tuning. A working definition of this tuning style is that the prime and hum of each bell are in octaves with the nominal. The innovations made by Taylors eventually transformed the business of UK bellfounding. At the same time, Canon Simpson was publishing the results of his research. To what extent did Simpson influence Taylors in their work? This investigation tries to answer that question by looking at the tuning of Taylor peals from the period, with interesting and unexpected results.

A history of Taylor's activities in the period from the 1870s onwards appears in Jenning's book 'Master of my Art'. The sequence of events given by Jennings in chapter 8, supplemented with other information, is as follows:

With these events as a background, it is illuminating to analyse the tuning of Taylor peals which survive from this period. I have taken the following peals from my collection of recordings to illustrate the changes in tuning which took place:

The evidence from these peals is that Taylors went through a gradual transition in the way they tuned their bells, lasting many years, but with sudden steps forward. The advances made by Taylors over this period probably involved significant changes in the design of their bells (i.e. proportions, shape and thickness) as well as in the methods used to tune them. These changes in shape could potentially have an impact on the relative intensity of partials, which significantly affects the sound, but this aspect has not yet been investigated, primarily due to lack of recordings taken on a consistent basis. What is investigated here is just the inner and outer tuning of the lowest five partials of the peals.

Inner tuning is concerned with the relationship of the partials within a single bell. Outer tuning is concerned with the relationship of the pitches of all the bells in a peal. The first section below deals with inner tuning.

Inner tuning of Taylor peals

The analysis of the chosen peals of bells will only cover five partials: the relationship of hum, prime, tierce and quint to the nominal partial. Other partials could with advantage be investigated, because not only do they affect the sound of the bell, but give clues to changes in shape. This is for later. In a true-harmonic bell, the hum is two octaves or 2400 cents below the nominal, and the prime one octave or 1200 cents below this partial. As tuning skills and bell designs advanced it also became custom to tune the tierce to a minor third above the strike note (i.e. 900 cents below the nominal) and the quint to a fifth above the strike (i.e. 500 cents below the nominal). Though this is sometimes known as 'Simpson' tuning, Simpson himself made no such recommendation about the tierce, suggesting that either major or minor thirds were acceptable. The main determinant of tierce and prime tuning is the design of the bell. It is not practical to make major changes to these partials independant from the others on the tuning machine. The prime is most affected by the thickness of the shoulder, the teirce by the design of the soundbow.

The extent of the changes made by Taylors in their tuning methods is easily seen by comparing the first and last peals in the chosen series. The two plots below are of Hovingham (1876) and Henfield (1913). The plot shows the deviation in cents from these theoretical figures for the four chosen partials across the bells in the peals:

Hovingham partials

Henfield partials

The Hovingham bells are classic 'old-style': hums sharp by up to one and a half semitones (150 cents) and primes flat by a similar amount in the trebles. The variations are less extreme in the tenors. The quint wanders about with no real pattern, but in contrast to all this, the tierce is really quite well controlled in all the bells. Henfield are a complete contrast. Hum, prime and quint are all essentially spot on, but still with variation in the tierce.

To show how Taylors changed the tuning of the various partials, below I show four plots, for hum, prime, tierce and quint. Each plot shows all nine peals of bells. The peals are aligned according to the heaviest bell, which appears as point 12 in the plot. It is to be understood that the point labelled '12' is actually the 10th of 10, 8th of 8 etc. There are two peals from 1892 - Newcastle is the light blue line, Imperial College is dark purple. The bell labelled '4' at Newcastle (actually the second of the old ten) was replaced in 1928, and stands out clearly in all the plots.

Changes in hum tuning

Changes in prime tuning

Changes in tierce tuning

Changes in quint tuning

It is clear, looking at the plots for hums and primes, that a change of considerable significance took place between 1892 and 1897. Both hums and primes in the peals up to 1892 show great scatter, but from 1897 onwards the tuning is quite exact (with the exception perhaps of the bell labelled '6' at Towcester, the 1897 peal). The hums in the back six of the two 1892 peals are perhaps slightly better than in the earlier peals, and the heaviest bells of the second 1892 peal (Imperial) are better than those of the first (Newcastle). It is thought that the Imperial bells were cast later but research is needed to confirm this. On the other hand, the primes of the 1892 peals are significantly and consistently worse than the earlier peals, especially in the trebles. Analysis of additional peals between 1892 and 1897 is clearly going to be of great interest. In 1892, Taylors had perhaps begun to address the tuning of hums and primes, though the evidence is inconclusive. By 1897, they had achieved the true-harmonic ideal.

Tuning now to the tierces, a quite different picture emerges. The 1878 bells at St Paul's show moderately consistent tierce tuning in all but the back three. In the rest of the peals the tierce tuning is not at all consistent, with nothing like the control shown of hums and primes in the later peals. In all except St Paul's, there is a general drift towards flatter tierces in the smaller bells, which suggests some transition of design from front to back. In the last peal (Henfield, in 1913) the slope from front to back is beginning to level off and the scatter is less. Even in this peal, Taylors were not tuning the tierce to the theoretical value.

The 1928 bell at Newcastle (bell 4 on the light blue 1892 line) has a tierce very close to the target value of 900 cents below the nominal, as do the front two bells at Bromham (cast in 1931). Analysis of other Taylor bells of these dates suggests that they made a further change to their bell designs in the 1920s, and from the mid/late 20s were consistently producing minor third tierces.

The last plot shows quint tuning. The quint is usually not an important partial, as it is very quiet in most bells. In the recordings I analysed for this study, it could not be detected in a number of the bells. In most of the peals examined here, there is even less pattern in the quints than in the tierces. But strikingly, in the last peal (Henfield, 1913) the quints are tuned almost exactly to the theoretical value. The two previous peals, of 1903 and 1908, show this partial slowly coming under control. The two front bells at Bromham, of 1931, also have quints tuned exactly to the theorectical value.

In summary, there was a dramatic change in Taylor's tuning of hums and primes beginning perhaps in the early 1890s, and complete by 1897. By 1897, Taylors had mastered true harmonic tuning. But it wasn't until just before the furst world war that they discovered how to tune the quint, and it took until the 1920s and a further change in bell design for them to finally master the tierce. The irony is that they mastered the quint first even though it is the tierce, much the louder partial, which has the greater effect on the timbre of a true harmonic bell. With this basic roadmap through the transition, there are clear pointers as to the dates of peals to be analysed to confirm the sequence of events.

Outer tuning of Taylor peals

It is not possible to show the transitions in outer tuning in such a simple way. This is because there is not one right way to tune the nominals of a peal of bells. They can be tuned in equal temperament (in which all semitones are the same size), just tuning (which is the easiest to calculate by hand), or in many other temperaments. In addition, bells are from time to time tuned with stretch, so that the trebles are sharper than one would expect. For some background on this see the section of this website on nominal tuning.

The plot that follows shows the tuning of all the nominals of the peals. The vertical axis shows the cents deviation of each bell's nominal from equal temperament:

Changes in nominal tuning

The three oldest peals on the plot - Hovingham in 1876, St Paul's in 1878 and Poynton in 1887 - show nominals which are pretty scattered. The St Paul's bells also have considerable stretch. This might be present in the two sixes also but it would be speculative to assume this across such a small number of bells. Clearly, in these peals Taylors were not tuning their nominals at all accurately and so it is not practical to say what temperament or tuning style was being used. Research into Taylor's records would be necessary to see on what principles they tuned their nominals.

In the next two peals - Newcastle and Imperial College, both cast in 1892 - a pattern is beginning to emerge. Apart from the three bells labelled 5, 6 and 8, all the bells have nominals which are very close indeed. (The 4th at Newcastle is a replacement bell.) However, the two peals have slightly different pitches, so were not tuned against each other. Both peals are stretched, a little. Neither conform to any particular temperament.

The plot below shows the nominals of the later peals alone on a larger scale, for clarity. The bells added to the 1908 Bromham peal in 1931 are shown with a dotted line.

Later changes in nominal tuning

By 1897, when the Towcester bells were produced, the nominals were being tuned much more accurately. The last three peals - Lahore in 1903, Bromham in 1908 and Henfield in 1913 - are tuned in something close to Just - shown by the sharpness of the bell labelled 11, and the flatness of the bells labelled 6, 7 and 10. The Henfield and the (1931) Bromham trebles are sharp, giving some stretch across the peal, and giving the relative flatness of the bells labelled 6 and 7 required for Just tuning. The Towcester bells follow a similar shape, but the bell labelled 10 is rather sharp. The tuning of all the nominals in the last four peals is much closer than anything in the earlier ones.

There is clearly something interesting happening here with the nominal tuning, but analysis of further peals is needed to be certain what Taylor's intentions were. The tuning books of the time give intended frequencies as well as actual achieved on the tuning machine. Research in these records would probably shed a lot of light on what principles guided the choice of nominals.

The open question

One fascinating question is the influence which Simpson had over Taylor's true-harmonic tuning. Did he start the process with his letter in 1894 or were Taylors already experimenting? The evidence from this analysis is inconclusive and more work is needed!


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Last updated March 15, 2002. Site created by Bill Hibbert, Great Bookham, Surrey