[r-t] Proposed definition of a peal

[Richard Smith]

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 
> start with the highest stage. -> 3) Otherwise remove a 
> 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 
should probably add "If, additionally, all such groupings 
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