Bill Hibbert bill at h...
Thu Jan 15 22:09:02 GMT 2004

David Sloman:

> It is probably a bit of a sauce to ask but
> what experimentation was carried out on the
> Leigh and Perrins bell?

For a summary of Perrin, Charnley and DePont's work see 
http://www.hibberts.co.uk/pandc.htm and associated pages. The actual 
paper runs to 21 pages (it's not on my website). The research 
comprised an absolutely exhaustive analysis of the vibrational modes 
of this particular bell, by stimulating it with a signal generator 
and probing all over the bell to identify nodes and antinodes. They 
identified 134 different modes of vibration, many of them split as 
doublets. They then built a computer model of the bell using finite 
element analysis, and adjusted the model until it produced the same 
modes of vibration, to confirm their understanding of the nature of 
each mode. These two pieces of work must both have been enormous 

Based on the analysis, they proposed a classification scheme for 
vibrational modes of bells which is utterly comprehensive, I don't 
believe there is anything more that could be said on the subject!

What they did not consider in their research was the significance in 
the heard sound of this multiplicity of modes. For instance, some of 
the modes are torsional, i.e. they involve the bell twisting about 
its vertical axis, and these modes radiate no sound into the air. 
What I did a couple of years ago is compare the P&C results with an 
actual recording of the bell and link the P&C classification scheme 
to what we hear when a bell rings.

This linking has been enormously useful to me because I now know the 
physical origin of each partial detected in a bell's sound. This 
provides an understanding of which modes are directly stimulated by 
the clapper blow, and which are 'sympathetic' vibrations (such as the 
quint) into which energy flows as the bell continues to vibrate. This 
was an essential step towards finally understanding the origin of the 
strike note. The partials I described as 'strike partials' in my 
recent RW article http://www.hibberts.co.uk/rwstrike.htm are those 
which Perrin et al identified as 'rim' partials, i.e. with an 
antinode at the soundbow, i.e. maximally stimulated by the clapper 

The work they did could also in principle be linked to Lehr's work on 
tuning - see http://www.hibberts.co.uk/lehr.htm which documents his 
experiments on how taking metal off at different points inside the 
bell affects the tuning of all the key partials. I am not aware that 
anyone has ever attemped this.

Saucy enough for you?

Bill H

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