The Sound of Bells

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Bremhill, Wiltshire, St. Martin, 6, 17-2-5 in E (after tuning)

Recorded: WAH 9/2/01, Ken Webb 24/3/01
Analysed: WAH 17/2/01

See here for a description of these bells prior to tuning. With the kind permission of both Ken Webb (Bremhill tower captain) and Whitechapel I was able to take recordings of the bells at the foundry both before and after tuning. The tuning done to most of the bells was considerable. As anticipated when I analysed them before tuning, the nominal of the second was left virtually untouched, so that the tenor nominal had to go down by 3/4 of a semitone. I understand that the bells were quite thick, so that there was plenty of metal to go at. Here are the retuned bells being rung at a wedding on 24th March 2001.

Bell Founder Tuning
1 R. Keene 1685 Whitechapel 2001
2 James Wells 1826 Whitechapel 2001
3 R. Keene 1688 Whitechapel 2001
4 Robert Wells 1770 Whitechapel 2001
5 A. Rudhall 1736 Whitechapel 2001
6 A. Rudhall 1736 Whitechapel 2001

Tuning of main partials

Tenor nominal: 664.8Hz (was 696.2Hz prior to tuning)

Bell Hum Prime Tierce Quint Nom'l S'quint O'nom.
1 -2308 -1228 -867 -406 887 676 1217
2 -2322 -1267 -890 -482 701 690 -
3 -2394 -1200 -882 -491 500 706 1268
4 -2403 -1197 -882 -512 388 697 1254
5 -2313 -1210 -886 -442 204 692 1247
6 -2320 -1201 -887 -494 0 700 1260

(The figures in this table are given in cents. For all partials except the nominal, the interval is given from the nominal of the bell. Intervals for the nominals are relative to that of the tenor. Pairs of values indicate a doublet. Frequencies for the quint are often not given, especially if inaudible.)

Intensity plots

I have included here before-and-after spectrums of all six bells to highlight the differences. As usual, the horizontal axis is cents, calculated from the nominal prior to tuning in both cases, so the extent to which the partials have moved can be seen:

Bremhill 1st before and after

Bremhill 2nd before and after

Bremhill 3rd before and after

Bremhill 4th before and after

Bremhill 5th before and after

Bremhill 6th before and after

Commentary - tuning of partials

The reason for wanting to analyse these bells before and after tuning was to investigate how partial intensities change on tuning. First, though, a description of the tonal qualities of the tuned bells.

Re the nominals, it is clear from the tuning chart above that these bells have been retuned in just temperament. The softer effect this gives is pleasing. The nominals appear to have been tuned particularly accurately, with a maximum deviation of four cents. The primes of the back four also have been tuned accurately - quite a success given the significant changes of pitch required. The primes of the trebles have been left, by accident or design, a little flat - not inappropriate in an old-style peal. The tierces also of the back five have been brought very close together. That of the treble has been left a little sharper, perhaps due to constraints in the original bell shape.

The hums of all the bells have been lowered considerably. In the case of three and four they have made it to the double octave (the fourth is now true-harmonic in all its low partials). The others could not be got down so far, due no doubt to the quality of the original material. However, the aural effect is of octave-hum mellowness. Here are recordings of the third before and after tuning. This bell (and the treble) had been fairly hacked about by a previous tuner with a file or cold chisel. I have not analysed doublets in the retuned bells here, but all have slowed very considerably and some have gone.


Commentary - spectra

In the spectrum diagrams above I have shown the bells before and after tuning on the same scale of cents, i.e. as cents from the untuned nominal. I've done this to show how the partials have changed in both frequency and intensity. All the recordings, except the sixth before tuning, were taken at the foundry on my video-recorder. The sixth before was recorded on a laptop while still in the tower. All bells (except the sixth before) were hit with the same clapper ball on a handle. I asked Nigel Taylor (Whitechapel's head tuner) to 'hit the bells where the clapper would'. The four, five and six were recorded standing on their crowns (or a headstock) before tuning, and hung on a crane via the central hole in the crown afterwards. One, two and three were recorded standing on the their crowns in both cases.

Looking first at the treble; nominal, tierce (and superquint) have been flattened, the hum has been flattened considerably and the prime left almost untouched. The intensities have remained almost unchanged, execept the nominal which is a little weaker. One should not read too much into this, due to differences in damping of crown vibrations against the floor and in the way the bell was struck. What is clear is that the overall shape of the profile has not changed at all - strong hum and tierce, little or no upper partials. The nominal of this bell was dropped from 1153.8 Hz to 1109.5 Hz (68 cents).

The second was the bell least tuned. From the chart, one can see that the nominal, tierce and prime were barely touched, the hum lowered a little. Again, the overall shape of the spectrum has hardly changed, though the hum and prime have become rather louder and the tierce weaker. The nominal of the bell only changed from 998.6 Hz to 996 Hz (4.5 cents), most of the tuning on this bell was done on the hum.

The third (which prior to tuning was arguably the worst sounding bell in the tower) has been tuned in a similar way to the treble - nominal, tierce and prime dropped somewhat and hum flattened considerably. There were some higher partials before which are little less evident now, and the hum has strengthened, but yet again the overall shape of the spectrum has survived. The nominal in this bell was lowered from 901.7 Hz to 887 Hz (28 cents).

The story for the fourth is a repeat of that for the front three. The tierce has weakened a little, and the scatter of lower intensity high partials has remained. The nominal of this bell was lowered from 869.5 Hz to 831.5 Hz (77 cents). The front four bells all had similar intensity profiles before tuning and these have fundamentally been preserved.

The fifth had a very different intensity profile prior to tuning - lots of high frequency partials with the superquint and octave nominal practically as loud as the tierce and nominal. One can see how the partials have been moved by the tuning process but the number and intensity of the high partials is still present. This gives the bell after tuning a bright, brassy tone which taken with the true-harmonic partials is quite pleasant. The strength of the octave nominal and superquint is likely to be moderated when the bell is bolted up to a headstock. See Perrin's paper on bell mounting, especially section 5, for some research in this area. Before tuning this bell was arguably the second worst toned in the tower. It's nominal was tuned down from 775.3 Hz to 747.5 Hz (63 cents).

Coming now to the tenor, this is the only bell whose intensity profile has changed significantly. It's clear from the spectrum plot that the nominal and tierce have been flattened, the prime is almost unchanged, and the hum was flattened considerably. The prime is almost unchanged in frequency. In the retuned bell, energy has moved away from the lower partials and nominal and into the higher partials. The superquint is now by far the strongest partial in this bell, and there are many other higher partials (including one 160 cents above the nominal which is not so strongly present in bells of normal profile). The nominal of the tenor was lowered from 696.2 Hz to 664.5 Hz (81 cents) and one can speculate that the amount of metal removed on tuning has significantly changed the physical profile of the bell. Again, bolting the bell to a headstock may subdue the higher partials. The bell after tuning has a bright, harmonious sound and in changes it sounds good.

Summary and conclusions

The main objective of this investigation, which was to investigate how intensity profiles change when bells are tuned, was successfully met. The intensity profiles of the front five bells stayed fundamentally the same, despite considerable differences in the tuning of the various partials. This was true despite the fact that the fifth had a rather different profile both before and after tuning than the front four. This suggests that the timbre of a bell, due one supposes to it's physical shape and the composition of its metal, is preserved under normal conditions of tuning. This in turn suggests limits to the improvement that can be made to a 'bad' bell even if its partials are brought into true-harmonic alignment, and that conversely, bells with true-harmonic partials and poor timbre are quite possible.

I cannot explain the effect seen in the tenor, where the intensity profile changed considerably on tuning, other than to suggest that the extent of the changes and the amount of metal removed brought about some fundamental change in the physical shape of the bell. But then, if there was nothing left to explain, life would be very dull!


Last updated May 17, 2001. Site created by Bill Hibbert, Great Bookham, Surrey