[r-t] Proposed definition of a peal

[Iain Anderson]

Mark Davies wrote:

> RAS writes,
> 
> > 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 is incomplete, then the overall piece of
> >    change ringing is called true.
> 
> Yes, I think this is the same as Don's and Iain's definition
> [...]
> 
> 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.