[r-t] Spliced Cinques & Max

[Richard Smith]

Stephen Penney wrote:

> C.2: Peals consisting of extents and/or round blocks shall only be called
> Spliced if each extent or round block is spliced.
>
> So the example Richard gave of a peal of minor stating and ending with the
> same method would not be called "spliced", as it contains round blocks
> which aren't.

Nope.  (D)C.2 needs reading in conjunction with (D)B.2:

| Peals of Minimus, Doubles, Minor and Triples [...] shall 
| consist of at least 5040 changes rung in any combination 
| of the following, each starting from rounds:-
| 
| (a) Extents, in which each of the possible rows at that 
| stage occurs once and only once.
|
| (b) Round blocks of two or more extents in which each of 
| the possible rows at that stage occurs the same number of 
| times.

I would certainly interpret this to mean that the peal had 
to be made up exclusively of extents and/or MEBs (round 
blocks per (D)C.2(b)).  There's still a bit of ambiguity 
here.  For example, the decisions don't say that extents and 
MEBs can't overlap, or that all of the component rows for an 
extent or MEB occur consecutively.  But I think we can 
safely assume that was the intention.

So, the peal must be divisible into extents and MEBs, and 
the MEBs must start and end with rounds.  This makes it 
trivial to check algorithmically whether the rows of a peal 
conform to (D)C.2 without understanding anything about the 
peal.  Look at each batch of n! rows in turn.  If they're 
not mutually true or next row is not rounds, call them part 
of an MEB that hasn't yet finished and add the rows to those 
from the next batch of n!.  Otherwise, call the rows an 
extent (if there are n!) or an MEB and start afresh with the 
next n! rows.  If you reach the end of peal while in an 
unfinished MEB, call the touch false.

However, this does not provide the only way of dividing a 
peal into extents and MEBs.  Nothing in the decisions state 
that when partitioning the peal into extents and MEBs 
you have to choose the largest possible number of extents 
and MEBs.  So, under the current decisions, there's nothing 
to stop you from calling the whole peal a single MEB even if 
it happens also to be describable as seven extents.  And 
then, even one change of method (pace MBD) is sufficient to 
make the peal spliced.

RAS