The Sound of Bells

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The Queen's Tower, Imperial College, Knightsbridge, 10, 38-1-15 in Db

Recorded: WAH 14/11/01
Analysed: WAH 14/11/01

This famous peal of ten hangs at the top of a tall, slender tower in the centre of London's museum district. They were cast by Taylors in 1892, as they were experimenting with true-harmonic tuning, which makes them of considerable archaelogical interest. A full description of bells and tower, together with a photograph of the tower, appears on Roger Bailey's website. Here is a recording of the ten bells being rung in rounds. It was taken from inside the tower, two floors above the bells, inside the base of the green copper dome visible in the picture. From this spot, the sound of the bells, the view of the whole of London, and the sway of the tower are all stupendous. My thanks to Roger Bailey for making me welcome when I visited the tower to record the bells.

Bell Founder Tuning
1 - 10 Taylors 1892 none since

Tuning of main partials

Tenor nominal: 553.6 Hz

Bell Hum Prime Tierce Quint Nom'l S'quint O'nom.
1 -2384 -1551 -922 - 1613 687 1223
2 -2369 -1480 -910 -465 1410 683 1222
3 -2330 -1437 -905 -390 1213 684 1223
4 -2235 -1437 -893 - 1111 680 1220
5 -2359 -1348 -906 -521 903 693 1240
6 -2314 -1311 -876 - 710 675 1213
7 -2351 -1231 -875 - 490 681 1225
8 -2355 -1251 -882 -491 404 683 1230
9 -2347 -1269 -883 - 187 686 1234
10 -2365 -1234 -868 -373 0 678 1218

(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. The links in the first column provide recordings of all the bells.)

Intensity plots

Analysis of these bells is only part complete. Here are intensity plots for the treble (chimed), the tenor (chimed) and the tenor (rung full circle). The chimed recordings were taken close to the bells, the full-circle recording was taken in the ringing room:

Imperial College treble

Imperial College tenor (chimed)

Imperial College tenor (full-circle)

Commentary

The tuning of nominals of this peal approximates to equal temperament, though the seventh and the ninth are a little flat, about 10 cents in each case. This is a minor discrepancy, within normal tuning margins, and not at all audible when the bells are rung together. The peal is tuned with stretch, of about 16 cents per octave. This is no doubt done to offset the flat primes in the trebles. It is interesting to compare these bells with Newcastle (a Taylor 10 of identical date and weight, with slightly less stretch). The pattern of the nominals in the back four of the two peals is tantalisingly similar. Is this co-incidence, or a feature of Taylor's tuning at this time? The discrepancies in both peals are in the opposite direction to those one would see if meantone or just tuning was intended. The plot below shows the differences in the nominal of each bell from equal temperament, together with a straight-line fit to the data.

Imperial College nominals

The other partials in these bells show clearly the changes Taylors were making in their tuning. The hums in all the bells are quite close to the double octave - much flatter than in old style bells - and especially in the trebles and tenors. The Imperial College hums are flatter than the Newcastle ones, the Newcastle tenor hum in particular being rather sharp, and this must contribute to the impression many people have that the Imperial bells are slightly the better. Detailed research in Taylor's records is indicated, to find out in what order the twenty bells were cast and tuned.

The primes in the Imperial bells however show the typical old-style trend of going quite flat in the trebles. If anything Imperial have flatter primes than Newcastle. Both of the Taylor peals have flatter primes than Stockport (a Mears ten of about the same date, though somewhat lighter). Dunham (a Taylor ten of 40 years earlier) have broadly similar primes in the trebles to the 1892 peals, though the tenor primes at Dunham are grossly sharp. Clearly, by 1892 Taylors had reasonable control over the tenor primes, but had not yet worked out how to scale their designs and tuning to achieve the same in the trebles.

There is more work to do on the analysis of these bells. However, the spectral plot of the treble is of considerable interest. This bell has a strong partial just 50 Hz above the nominal which can be clearly seen on the spectral plot above. I have spent some time trying to ascertain from my recording of this bell which of these two partials is actually the nominal. The second frequency could just possibly be a doublet, but this is highly unlikely, as these bells are relatively doublet free. The alternative explanation is that this is a rather flat eleventh (the 'secondary strike' partial). The intensity profile of these two partials over time is almost identical, with the higher frequency always slightly the quieter.

In an attempt to distinguish between these two partials I estimated the pitch of the treble, both when chimed alone and in changes, using the Pitcher program. The partial frequencies involved are 1405.5 Hz and 1450.5 Hz, giving pitches of about 703 Hz and 725.3 Hz respectively. For this bell, both in changes and rung alone, a pitch of 725 Hz feels too sharp. My best estimate of the pitch when chimed is 713 Hz. A pitch of 703 Hz feels too low for the bell on its own, but does not sound so bad in changes. This compromise value of 713 Hz is possibly an interpolation by the ear - beating between these partials at 45 beats per second will be hard to hear but might provide the compromise value. An alternative and less likely explanation is that the higher of the pair is actually the nominal, but the bell pitch is pulled down by the flat prime. Truly the pitch of bells is a fascinating subject!

This webpage will be updated as more analysis is completed.


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Last updated July 12, 2011. Site created by Bill Hibbert, Great Bookham, Surrey