# [r-t] Calling positions and differential methods

Alexander Holroyd holroyd at math.ubc.ca
Mon Jul 10 17:13:29 UTC 2017

```I'm not sure what conventions you want to assume when the observation
bell is affected by calls, so I'll stick to cases where it's not.

If by "course end" you mean a lead end when the _observation bell_ comes
back to its home position, then it seems clear that the answer to 1 is
yes.  In fact you do not need to know what the course end is, just that
there is one.  The sequence of calling positions just tells the
observation bell what to call, and it cannot ever wait a whole "course" in
the sense of its _own line_ between calls without having a course end.

If by "course end" you mean the lead end after number of leads for the
plain course to come round, then the answer is clearly no.  E.g. consider
the Royal method 67x (reverse plain hunt on front 6 and back 4), and the
call that substitutes 34 for x at the lead end.  Then the course

8ths.10ths 1654327890

has many possible interpretations.

Ander

On Mon, 10 Jul 2017, Don Morrison wrote:

> 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_
>
>
>
```