The Sound of Bells

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Simulation of bell sounds

The previous page has details of the latest simulation I have put together. It also covers the way the simulation is done and why simulation is useful. This page describes a previous less successful attempt at the same thing. It shows some of the problems to be experienced and what can be learned from them.

For a presentation I gave in December 2001 to the London Branch of the Institute of Acoustics, I created a simulation of a Mears bell cast in 1859 (the third at Ranmore in Surrey) which gave reasonably satisfactory results. After the presentation I did more work on this simulation and the results are presented here. The recording on which I based the simulation was not good quality, which prompted me to repeat the work again on a better recording. The Ranmore bell is not true-harmonic. This was a deliberate choice as I have found it much more difficult to simulate old-style bells. (In a true-harmonic bell, a certain amount of confusion as to the octave of the sounds is permissible). The various parameters for each partial were initially estimated from a graph of the partial envelopes produced by wavanal. The values were repeatedly refined by creating a bell waveform, using Wavanal to find the partial envelopes, and comparing with the original bell waveform. It took about 15 cycles to produce the results presented here.

Not every partial present in the original recording is present in the simulation. Of course, all the loudest are there. I also made special efforts to include all the higher partials which contribute to generation of the strike note. I set the splash amplitude of these partials louder than the recording would suggest to compensate for the recorder limiting mentioned in the next paragraph.

I realised partway into the work that I had not chosen the best of recordings to simulate. My recording of the Ranmore bell (taken by chiming the bell with a video camera nearby) had been amplitude limited by the recorder. In the original recording, the envelope is flat for the first two seconds of the sound. In better recordings, the amplitude decays dramatically from a much higher maximum over this time. As I had already put work into the simulation I decided to persevere, though the results are disappointing. The eventual fit between the amplitude envelope of partials in the orginal sound and the recording is very good. Here is an example (the tierce) - 'org' is this partial in the original recording, 'sim' is the simulated version:

partial amplitudes compared

The final simulation, though not perfect, provided a good basis for further experiments.

The simulation, and experiments with it

Here is the simulated sound and here the original recording. Right-click on the following link to download the file ran3final.par used to create the simulation. This file can be loaded into wavanal using the 'read partials' button, and the simulated sound created using the 'create waveform' button, accepting the default values for the parameters.

Here are some examples of how the simulation can be modified to carry out experiments in the sound produced. In the first, I have edited the frequencies of hum, prime and tierce, and removed the doublets, to give a bell with true-harmonic tuning. In the next, I have further edited the frequency of the tierce to produce a major-third bell. And finally, here is the old-style simulation but with a gross doublet on the prime.

For better results than this, try the more recent simulation.


Last updated January 26, 2002. Site created by Bill Hibbert, Great Bookham, Surrey