Tuning of old-style rings

[oakcroft13]

The discussion below started on Ringing Chat but I am taking the 
liberty of posting my reply here as I think it is of general 
interest. The thread started with a post from Dave Sullivan about the 
peal of six at Broadhembury, Devon.

Dave Sullivan:
> . . . Broadhembury . . . completely-out-of-tune tenor . . .
> front 5 are old but the tenor is 1986 Taylor's! The front 5
> aren't all that bad. The tenor was cracked and replaced
> and IMHO sounds really weird (it sounds sharp).

M (who he?):
> . . . I have never noticed it being out of tune - I admit though
> that it is not a good bell (I think it was sympathetically
> tuned).

WAH:
Assuming that there is not some gross error in the tuning of the new 
bell, here is a possible explanation. It could be that both Dave and 
M are right . . .

I have rung on a number of old-style peals recently retuned where the 
trebles sounded clearly flat to me. On analysing these peals I have 
generally found that the nominals were spot on. Now, bellfounders 
will assume that the pitch of each bell (the note you hear when it 
rings) is half the nominal frequency, and that if the nominals are 
spot on the bells will sound 'in tune'. However, academic research on 
non-bell sounds suggests that if partial frequencies are not exact 
harmonics - such as is the case in old-style bells - the pitch is 
related in a complicated way to all the partial frequencies, not just 
to one of them. I have a theory, for instance, that if a bell has a 
loud flat prime it's pitch is lower than the half nominal. There are 
other more complicated instances I am investigating.

I have been discussing this phenomenon with Whitechapel (it was in 
bells they had retuned that I first noticed the effect). It became 
clear early in the discussion that the tuner at the foundry heard 
bells differently to me - he hears the nominal frequency, no doubt 
through practice of listening for it, I hear an overall impression of 
a different pitch. Therefore, we actually assign a slightly different 
note to the same bell. I am in the process of devising some 
experiments to test these effects on different listeners and try to 
come to some conclusion about them. I was beginning to think that 
there was something odd about my ears, and therefore I am most 
interested to hear of other people who hear the same effect.

(The most recent example I have experienced of this is Marychurch, 
Torquay, a Warner eight of 1877 retuned by Taylors in 1987 to which 
WBF added two trebles in 1989. The WBF trebles have octave primes and 
sharp hums, the original bells are old-style. Other examples are 
Wallingford and Southwold.) 

Bill H