The Sound of Bells

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Painswick, Gloucestershire, St Mary the Virgin, 14, 25-2-19 in D

Recorded: WAH 23/2/01
Analysed: WAH 26/7/01, 13/10/01

The bells at Painswick are a famous and early peal of twelve on which many notable performances have been rung. At their heart is a complete Rudhall ten of 1731, of which one was replaced a year after installation. As these bells were installed so close to the Rudhall foundry at Gloucester, one can imagine Rudhalls saw these bells as a showcase peal. They have not since been tuned, and therefore show what this prolific family of founders considered their best work. Their sister peal at Wrexham, of near identical date and weight, were tuned by Taylors about 100 years ago.

This venerable peal is however on its fourth set of trebles. The first were provided by Rudhalls, in 1819, but were almost immediately replaced, again by Rudhalls, in 1821. There must have still been something unsatisfactory about these bells, as they were replaced by Mears in 1887. These were replaced again by Whitechapel in 1993, who also provided an extra treble at the same time. They had previously provided a flat sixth in 1986. The Whitechapel bells were cast to Rudhall profiles and appropriately tuned. I do not yet have a recording of the Rudhall back ten, but here is the front ten (with a mix of Rudhall and Whitechapel bells) recorded from the churchyard. I am most grateful to the tower captain, Alan Hodges, for welcoming me on two separate visits to the tower and providing much useful information.

Bell Founder Tuning
extra treble, 1, 2 Whitechapel 1993 -
3 - 6 Rudhall 1731 none since
flat six Whitechapel 1986 -
7 Rudhall 1731 none since
8 Rudhall 1732 none since
9 - 12 Rudhall 1731 none since

Opinions about these bells differ. In 1779, Samuel Rudder in 'A New History of Gloucestershire' wrote: "And if agreeable and musical tones have any effect on a distempered mind, the ten bells in this tower have as much merit as any peal in the Kingdom". (Quoted from 'Church Bells of Gloucestershire' by Mary Bliss and Fred Sharpe, who say "Painswick bells have long been regarded as a fine, musical ring".)

On the other hand, we must thank David Herschell for his extracts from Bell News published in the Ringing World of September 7th, 2001, page 908. It's worth quoting the extract (from The Bell News and Ringers' Record Saturday, September 7,1901) in full:

There was a long letter from Mr. H. Drake regarding the current state of the twelve bells of Painswick, Gloucestershire, in which he reported: 'Perhaps the readers of "Bell News" would be interested to hear what is actually being done in the case of the well-known bells of Painswick. For although it appears to be almost too late for any alteration to be made in the present fate of these particular bells, yet a principle is involved which should be thrashed out, and on which ringers should have every opportunity given them of expressing a correct opinion.

'It will be remembered that some time ago it was mentioned that the bells were at Messrs. Taylor's foundry to be refitted but not tuned; and that the Rev. C. D. P. Davies wrote to say that he was glad of this, as the very idea of tuning such bells made him shudder. So matters stood until the last meeting of the Midland Counties' Association at Loughborough; at that time the members who visited the foundry were naturally curious to hear how the bells sounded when on the ground, and conveniently placed for contrasting their tones. The result was so unsatisfactory that when the authorities at Painswick heard of it, the matter of tuning them as well as possible without recasting, was discussed. Ultimately deputations were sent from Painswick to Loughborough; the fact that the bells are badly out of tune was clearly evidenced, and the members of the deputations were so dissatisfied with their present condition, that it was decided that something must be done. They seem however to have fallen back on a "multitude of counsellors," but instead of the proverbial wisdom, they have obtained such contradictory advice, that not knowing what to take, they have taken none, and are having the bells rehung as they are.

'As I am staying for a few days at Loughborough I rode over yesterday to the foundry and was pleased to find the bells are still there, though the fitting work is nearly completed. By the courtesy of Messrs. Taylor I was allowed special convenience to examine them. For instance we had the 5th and tenor struck consecutively a number of times. This octave I was told was the best in the peal, and of course it should be, seeing what an important place it holds in a twelve-bell peal. Now Mr. Davies may - figuratively - shudder at the thought of tuning bells; but if he will go over to Loughborough and hear these two bells, I promise him that he will physically shudder at the discord. A musical friend who was with me said the interval was more than a quarter of a tone short. That is to say that the 5th bell would be better placed were it rung as the 6th. Moreover the tenor in itself was distinctly discordant. The top-note (or "fundamental") was more than a tone out from the hum note... I may say that I have not got the sound of that discord that should have been an octave, out of my ears yet. Two questions obviously arise: if the bells are so discordant whence their reputation?... And again: can improvement be guaranteed without destroying any sentimental attachment to antiquity in the bells?

We will come back to Mr Drake's opinion of these bells later. But first, the technical stuff.

Tuning of main partials

Tenor nominal: 581.8Hz. You can hear (or analyse) all fourteen bells by clicking on the links in the table.

Bell Hum Prime Tierce Quint Nom'l Front 10 S'quint O'nom. Founder
extra 1 -2307 -1202 -857 -341 2128 1631 625 1106 Whitechapel
1 -2307 -1203 -880 -353 1929 1432 656 1169 Whitechapel
2 -2306 -1201
-1202
-900 -356 1727 1229 676 1205 Whitechapel
3 -2332 -1462 -925 -340 1625
1624
1128 683 1215 Rudhall
4 -2303
-2300
-1306
-1311
-884 -353 1421 924 669 1192 Rudhall
5 -2305
-2308
-1216
-1212
-896
-898
-268 1219 722 688 1231 Rudhall
6 -2261
-2263
-1219
-1214
-895
-894
- 1122 - 688 1229 Rudhall
flat 6 -2315 -1197 -856
-857
-453 1005 508 676 1214 Whitechapel
7 -2199 -1235
-1229
-873 -250 894 397 683 1227 Rudhall
8 -2311 -1236 -882 -446 701 204 685 1230 Rudhall
9 -2240 -1175 -877
-876
-287 497 0 694 1251 Rudhall
10 -2306 -1214
-1205
-890
-889
- 403 - 690
692
1242 Rudhall
11 -2238
-2231
-1201
-1193
-869 -392 196 - 687 1233 Rudhall
12 -2137 -1183 -853 - 0 - 675 1224 Rudhall

(The figures in this table are all given in cents. For all partials except the nominal, the partials are given from the nominals of the bell. Cents of the nominals are relative to the tenor. An extra column has been added showing the nominal tuning of the front ten. Pairs of values indicate a doublet. Frequencies for the quint are often not given, especially if inaudible.)

The description below divides conveniently into two parts. First, I cover the orginal Rudhall ten. On a second page, there is a description of the new Whitechapel bells and how they have been fitted into the peal, together with recordings of all the bells.

Intensity plots - back ten

Here are various spectral plots for the tenor, and the treble of the original ten:

Painswick tenor

Painswick third

And here are the back 4:

Painswick back four

Commentary - back ten

First, as usual, the nominals. In these bells, the nominals of these bells are tuned quite closely to equal temperament, but with stretch of about 23 cents per octave. The equal temperament tuning is surprising, as all musical instruments at the time would have been tuned in meantone. The advantage of equal tuning for a bell-founder is that it permits casting for stock, a practice for which Rudhalls were noted. I know of other Rudhall peals of about the same date tuned both equal and meantone.

Mr. Drake in his Bell News letter writes "a musical friend says the interval [between 5th and tenor] was more than a quarter of a tone short". That this is not so is quite clear from the figures above. The 5th is slightly sharp, not flat, but only by 19 cents or less than a fifth of a semitone. It is not clear which partials Mr Drake’s musical friend was listening to, to draw this conclusion. In old-style bells, what is heard in changes (where each bell only sounds for about 250 milliseconds before the next strikes) can be quite different from what is heard listening to a single bell over several seconds.

The trebles in this peal are stretched, i.e. tuned sharper than the musical scale would suggest. This is almost certainly because of the flat primes in the trebles. The pitch of a bell - the note assigned to it by a listener - is an effect created in the ear by the various partials, known to acousticians as the ‘missing fundamental’. In a true-harmonic bell, with the main partials in octaves, the pitch is about an octave below the nominal. In old-style bells, the situation is more complicated, and a loud, flat prime can lower the pitch. Old-style founders conpensated for this on higher numbers by sharpening the nominal so that the overall effect in changes sounds in tune.

The primes in the back eight here are good - except for 7 and 8, surprisingly good. Rudhalls could not tune this partial and had to rely on shape to get it as close as possible. The primes in the front two are quite flat, as is often the case, due to a lack of understanding of how to extend the design of the larger bells into the trebles. The plot below shows the differences of the nominals from equal temperament, together with a straight-line fit to the data.

Painswick back ten nominals

The back six bells are nicely in tune, with no stretch. The stretch kicks in with the 6th, which is rather sharp, but then the front three are tuned astonishingly close to the theoretical values. The only criticism one can make is the large gap between the 7th, which is on the flat side of correct, and the 6th, which has a near-octave prime but a rather sharp nominal.

Now to the tone of the back bells. Mr Drake in his Bell News letter makes considerable criticism of the tenor. He writes "the fundamental was more than a tone out from the hum note . . . I have not got the sound of that discord that should have been an octave, out of my ears yet." It’s clear from the tuning figures above that the tenor hum is quite sharp. However, my recording of this bell demonstrates that the bell has a mellow, rosy tone. The explanation lies in the intensity of the various partials, shown in the spectral plot above. This plot shows that although the hum is very sharp it is very quiet. The prime, nominal and octave-nominal of this bell are quite close to octaves, and give it a nice ‘octavey’ sound because the hum can hardly be heard. The very strong tierce adds mellowness. The relative intensities of the partials are due mostly to the shape or profile of the bell but will also be affected by the clappering. Most of the back bells at Painswick have spectrums similar to the tenor (see the plot above of the back four), as do many modern true-harmonic bells. The hums, though sharp, are not really an issue.

In the trebles, the primes are quite flat, though the hums in these bells are quite near the double octave, low enough to fool the ear. Often, small bells with flat primes can ‘scream’ because the prime is so audible against the strike. The trebles at Painswick are not so bad in this respect. Their spectra are quite different from the tenors, with weak upper partials, strong nominals, and stronger hums. The real clue as to their sound in changes is shown by the plot below, demonstrating the changes in partial intensity over time for the treble of the ten.

Painswick third partial decays

The critical time in the above plot is the 200 milliseconds after the clapper strike. In changes, this is the time each bell can be heard before the next strikes. During this time, the nominal pre-dominates, and although the prime is quite loud, so is the near-double-octave hum. In small bells that ‘scream’ the prime is the dominant partial. When you listen to this bell (especially played against the tenor above) don't be fooled by it's tail - the extended sound - which sounds flat, with a prominent, seemingly sharp, hum. What you will hear in changes is only the first fraction of a second. Again, the rise and fall times and intensities of the partials may be influenced by clappering but are mostly due to the shape or profile of the bell.

So, what do we conclude from this analysis? Rudhalls did not have the knowledge or the tuning technology to tune accurately the prime and hum and hence produce true-harmonic bells. Despite this the primes in the back eight and the hums in several of the bells including the front two are really quite respectable, showing a good knowledge of design. Rudhalls have also used stretch to offset the flat primes in the trebles to make the peal as a whole sound in tune in changes, and in general the tuning of the nominals is well done. Rudhalls would have had no way to measure partial intensity, other than subjectively by listening to the bell. By rule of thumb and experience they must have developed different designs and profiles for bells, which they used in the Painswick peal to make the very best of what tuning capability they had.

Of course, there are more bells in the tower, giving a twelve and a light ten. A description of these bells appears on the next page.


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Last updated October 16, 2001. Site created by Bill Hibbert, Great Bookham, Surrey