Upper partials (was Berlin Freedom Bell)

[Bill Hibbert]

I have now found a better recording of this bell (less birdsong, more 
bell!) and it matches the G&J tuning figures; I was wrong to doubt 
their forks. The hum is 46 cents flat and the prime 33 cents flat.

RO:
> I well remember Wally Spragett telling me of his adventures tuning
this bell ... would have been a rather expensive mistake had the bell
needed recasting like the Wannermaker Bell a few decades earlier!

Richard, you should write your memories down, they are a fascinating 
insight into the historic activities of bellfounders.

> It was one of G & J's early ventures into serious upper
partial tuning

I have just completed an analysis of the upper partials of 1,800+ 
bells. For bells of 'western' shape it proves conclusively that the 
frequencies of all the 'rim' partials above the nominal (that create 
the strike note and determine the timbre of the bell) are related, so 
that tuning one tunes them all. André Lehr was aware of the link 
between superquint and octave nominal, but the relationship between the 
rest of the partials is I think a new discovery. It holds across 
casting dates spanning 750 years and nominals spanning five octaves. 
Remarkably, steel bells also fit the model exactly; the analysis shows 
that Naylor Vickers bells are far too thin and that had they been cast 
to the same thickness as bronze bells they would have sounded like them.

The set of three minor partials between nominal and superquint can be 
tuned independently (their effect on timbre is limited) but the major 
partials above the nominal can't be seperately tuned; sadly Wally was 
on a wild-goose chase.

Bill H