# [r-t] Proposed definition of a peal

Richard Smith richard at ex-parrot.com
Fri Aug 8 11:50:58 UTC 2008

```Iain Anderson wrote (quoting MBD):

> > Consider for instance a peal of "Singles and Triples".
> > The composition consists of two extents on three bells,
> > so these changes are rung twice in the peal:
> >
> > 1234567
> > 2134567
> > 2314567
> > 3214567
> > 3124567
> > 1324567
> >
> > The remainder of the peal is a true Triples touch of
> > 5028 changes.
> >
> > Doesn't that look absolutely awful? It's really a false
> > 5040 with six changes repeated. I do not do not do not
> > like it at all!
>
> I think this example separates my definition from that of
> DFM and RAS.  With the recursive defintion you have to
> true extent's worth of rows from the set and re-apply the
> truth test on the remaining rows.  (If you can't do this,
> it's false.) Since you can't extract a full 5040 of
> triples, since there are 6 rows missing, it would be
> false. Now if you rang a 5034 of triples that was mutually
> true against the singles, that would be a "true" 5046.

A good point.  But do we want to change the definition of
'true' to prevent such things?  For example, if I ring a
10,096 of major and triples comprising two ordinary peal
compositions, a 5040 of triples and a 5056 of major, rung
back to back, is this 'true'?  Under my/DFM's definition, it
is; under yours, it is not.

If we want such a peal to be considered false, we can fix my
version of Don's 8th definition to read:

8) A piece of change ringing, if of multiple stages, is
called true as follows. All the stage fragments
contained in the piece of change ringing that are of
the same stage with the same non-changing bells, are
grouped together, and tested for truth as for a single
stage. If all such groupings are true, and at
most one, which must be of the lowest stage present, is
incomplete, then the overall piece of change ringing is
called true.

I.e. I've inserted "which must be of the lowest stage
present" into the definition.  This renders the triples,
quoted above, false; it also renders the mixed major and
triples false.

(And for the sake of completeness -- no pun intended -- we
are complete, the overall piece of change ringing is called
complete".)

Note that there is still a choice of which stage fragment
grouping can be incomplete because there is not necessarily
a unique lowest stage grouping -- the lowest stage groupings
may differ by the non-changing bells.

RAS

```