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[oakcroft13]

Bill:

> I have recently put together a very simple FREE Excel 
spreadsheet ...

Dickon:

> This is interesting, but it only gives the 12 chromatic
> pitches rather than the 21.

Yer pays yer money and yer takes yer choice . . .

Oh golly, where do I start. Of course we all know there are many many 
different tunings. 12 pitches in the octave, 21, 53 (which is 
actually one of the more interesting ones, as most of the normal 
temperaments are included), etc.

I actually put the spreadsheet together during a tea break at work to 
test an algorithm I was putting in a program. I always test my 
algorithms in Excel before coding them in C++. The objective was to 
deliver back an octave, note and error given a frequency. If this is 
the tenor of a peal we are talking about, it is perfectly valid to 
say that a bell is so many cents sharp or flat of a particular 
concert-pitch-equal-tempered note.

I am having a discussion with John Baldwin about the correctness of 
tenor notes in Dove, he asked that I check or supply the correct note 
of all the tenors I have measured exactly. To do this I need to 
choose some standard to measure them against and I think concert-
pitch-equal-tempered is the only valid standard. Whether to call a 
bell C# or Db in equal temperament is purely a matter of taste and 
preference, as they are the same frequency. To adopt some non-equal 
temperament immediately begs the question 'what is the keynote, i.e. 
what degree is this bell in some scale' to which, of course, there is 
no answer. Remember that founders, traditionally, often tuned down to 
the lowest pitch in the peal rather than to an absolute standard.

Once you start giving note names and errors for bells within a peal 
you are in a different position. Then of course there are quite valid 
differences in temperament and to judge a bell's tuning against equal 
temperament may lead you to make judgements about its tuning at 
variance with the intention of the tuner. But I would make three 
points which I think are of great importance:
* the acceptable tuning error in a reasonably well tuned bell may 
well approach the differences in frequency in the various temperaments
* the Doppler shift when a bell whizzes past your ear is not 
insignificant compared with differences in temperament
* the departure of a bell's pitch from the half nominal due to tuning 
of other partials may also be significant, though there is only 
anecdotal evidence of this to date.

And finally, the bell-tuning experiment of last week and this has 
given me some clear evidence on whether ringers can, or cannot, hear 
the differences in tuning between different temperaments. In bell 
tuning, ears is all we've got. If you can't hear it, it doesn't 
matter . . .

Bill H