Tuning the upper partials (was Olympic bell)

[oakcroft13]

George Dawson:
> Do I detect a hint here that Bill has worked out to control the higher partials in a bell, something that eluded even Andre Lehr??
Richard Offen:
> I don't know about Bill, but Whitechapel have been doing it with increasing levels of success, as demonstrated in the Olympic Bell, for the last 40 years or so!

Actually, it's the opposite of what George says, I am convinced that it is not possible to independently tune the rim or group-I partials. These are the partials which determine the strike note and make a big contribution to the overall timbre of a bell. I have analysed about 3,200 bronze and steel bells to date, with weights between 19kg and 36 tonnes, dates from 1258 to today, from 15 different countries, 100 different founders etc. In all these bells the frequencies of the rim partials relative to the nominal track strictly in proportion. I have also looked at a number of cases of before and after tuning figures, including some bells where a deliberate attempt was made to tune the upper partials, and all the rim partials move together.

In general, the thicker the bell (especially in the area of the soundbow), the closer the partials are together, and the thinner, the further they are apart, so as metal is taken out on the tuning machine the partials spread out following a strict rule of mathematical proportionality. I did some work with Robert Perrin a few years ago and we established theoretically why this law of proportionality might hold across all bells of normal shape. Lehr's tuning curves in his 1965 paper also help explain the phenomenon - nodes and antinodes for all the group-I partials are in the same place in the bell, so removing metal from any point affects them all.

The tierce is one of these group-I partials. However, the tierce can be controlled independently of the upper partials by making detailed changes to the shape of the soundbow - which is why both thick and thin bells can have exact minor-third tierces. Once the bell is moulded and cast, the tuner can't significantly change the relationship between tierce and nominal. 

The block of three partials between nominal and superquint are a different matter, their nodes and antinodes are not co-incident with those of the group-I partials. It is said by carilloneurs that these partials have an impact on bell timbre. They are difficult to uniquely identify from bell recordings and so far I have not attempted a similar analysis to see whether in practice the moulder (or tuner) has any independent control.

I have not discussed these issues in any detail with Whitechapel. However, if they are able to independently tune the group-I partials I shall be both surprised and impressed. The 7 upper partials of the Olympic bell I was able to measure lie on the theoretical curves.

Regards,

Bill H