The Sound of Bells

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London, St. Paul's Cathedral, 12, 61-2-12 in Bb

Recorded: WAH 18/7/00
Analysed: WAH 11/1/01

These bells are a complete Taylor twelve of 1878, one of the most famous peals of bells in the world. They have not been tuned since installation, though they have just been rehung. The architecture of the tower is such as to get the best from the bells, which are hung a short distance below large openings in the tower walls with reasonable space above them. Here is a recording, taken from the street, of the bells being set at the end of a half-muffled quarter peal on 18/7/00.

The individual recordings on which this analysis is based were made from the ringing room with the bells rung full circle, and as a result are not of the very best quality. As a result it was sometimes difficult to be certain about the existence of doublets.

Bell Founder Tuning
1 - 12 Taylor 1878 None since then

Tuning of main partials

Tenor nominal: 465.9Hz.

Bell Hum Prime Tierce Quint Nom'l S'quint O'nom.
1 -2235 -1438
-1427
-882 - 1971
1974
662 -1177
2 -2229 -1419
-1412
-883 - 1727 678 1205
3 -2241 -1364
-1354
-871 - 1631 662 1188
4 -2259 -1368 -879 - 1423 680 1215
5 -2298 -1360 -893
-886
- 1237 682 1227
6 -2279 -1285 -870 - 1106 674
678
1220
7 -2289 -1298 -879
-872
- 897 675 1224
8 -2298 -1206 -866 -398 709 686 1224
9 -2301 -1278 -882
-873
- 527
536
677 1225
10 -2240 -1236 -865
-846
-411 412 669 1206
11 -2339 -1262 -896 -464 215 692 1248
12 -2356 -1256
-1246
-887 -517 0 689 1241

(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. Pairs of values indicate a doublet. Frequencies for the quint are often not given, especially if inaudible.)

Intensity plots

Here are all twelve bells plotted on the same chart to give an overview of the tuning:

London, St. Paul's Cathedral

and here is the tenor:

London, St. Paul's Tenor

Commentary

I ought to say, at the start, that the observations made below are points of detail, and are not meant as slights on such a fine peal of bells.

The nominals of these bells are of some interest. Here is a plot of them showing the difference in cents of the nominal of each bell from equal temperament.

St. Paul's Nominals

It is clear both from this graph and the tuning figures above that the treble is very sharp, and the seventh is somewhat flat. Between treble and tenor there is stretch of no less than 3/4 of a semitone, and in the octave between 5th and tenor the stretch is 37 cents or 1/3 of a semitone. This is a considerable stretch. As ever with stretch, two factors are of note. First, the stretch in the 5th at 37 cents is very comparable with the sharpness in the octave nominal in the tenor at 41 cents. Secondly, the primes flatten considerably as the bells get smaller, which may offset the sharpness of the nominals. As explained elsewhere, which of these two explanations for octave stretch is the correct one is not yet clear.

The other interesting thing about nominals is the tuning of the middle bells, especially 6, 7 and 8. It's clear from the diagram that the seventh is the flattest bell in the tower. Sharpening bells on the tuning machine is not easy, and it looks as if the tuner has 'shaded' the nominals of the bells either side to accommodate the 7th.

In the intensity plot above showing all the bells, several points are worthy of note. First, the tierces are very compatible across the peal, and were obviously carefully tuned. No bell has much in the way of a quint. The hums also are well controlled, though not quite as closely as the tierces. The primes get steadily flatter in the smaller bells, as already noted, presumably because the smaller bells have a thicker profile to give them power. One might guess from the scatter that Taylors were not tuning primes separately at this time. Most of the bells have quiet partials above the nominal, the tenth being a notable exception in this regard.

One could analyse all the bells in some detail, but I have chosen to look at the tenor, both because in many ways tonally it is the most important in the peal, and also because it is a remarkably good bell. Looking first at the intensity profile, all partials above the nominal are well subdued. The nominal is very strong, giving the bell a very clear sound. There is some trace of partials at 400 and 1700 cents that could give rise to a secondary strike, but fortunately they are quiet enough not to do so in this bell. There is a slight doublet on the prime which can be just heard in the recording above after the tenor has set.

Turning now to the exact tuning of the partials, the tenor hum (and also that of the 11th) are very close to the second octave below the nominal. The primes of both bells are only a little below the octave. And the superquint and octave nominal have begun to move up from their positions in old-style bells towards the higher position one sees in modern Taylor bells. This bell was cast 17 years before Simpson published his first paper. Does it show the results of research by Taylors, pre-Simpson, into the profiles and tuning of the best bells on the continent?


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Last updated January 12, 2001. Site created by Bill Hibbert, Great Bookham, Surrey