[r-t] Calling positions and differential methods

[Don Morrison]

For treble dominated methods, particularly at even stages, it is usual to
notate all but the shortest compositions by citing the position of a fixed
bell, typically the tenor, at each call. For non-differential methods
without unusual features such as calls that affect more than one lead or
MEBs that have more than a plain courses worth of plain leads I think such
a scheme is guaranteed to work without ambiguity? Is that correct?

For differential methods this is no longer true. For example, consider the
fragment Wrong,Home applied to the unnamed differential little bob method
x1x45,2: it might mean 1.4, or 1.8, or 1.12.

A couple of further questions on this:

1) In the example above you can disambiguate the three possible callings if
you also supply the course heads (673254, 653724 and 623574, respectively).
Is this guaranteed to always be possible, or are there cases where two
different callings are both the same in terms both of the observation bell
position and of the course heads? I conjecture that there are, but I've not
successfully worked any out yet.

2) What about differentials where all the cycles are the same length, of
which three lead course royal methods are the most common example. If you
leave the observation bell fixed (that is, in its original cycle), then I
think this works the same as for non-differential methods. But it's not
clear to me that it continues to do so if you change which cycle it's in.
Is it possible to produce ambiguity in this case? I'm thinking not, but am
far from certain about that.

These points may also be relevant to a disagreement MBD and others have
voiced with the Central Council's lumping three lead course royal methods
and their ilk in with other differential methods that have hunt bells*. If
things like three lead royal methods are better behaved with respect to
ambiguity of composition description by calling position that might be
taken as a point in favor of not classifying them as differential; and
similarly if they are no better behaved it might be a point opposed.




* I'm sorry, I just can't bring myself to type that horrid neologism
"Differential Hunter". Oops, I just did.





-- 
Don Morrison <dfm at ringing.org>
"When you're a boy your life can be measured out as a series of
uncomfortable conversations reluctantly initiated by adults in an
effort to tell you things you either already know or really don't
want to know."       -- Ben Aaronovitch, _Moon Over Soho_
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