[r-t] Lead-based methods [was ...

[John Harrison]

In article <000201d0235a$c7a51ce0$56ef56a0$@changeringing.co.uk>,
   Graham John <graham at changeringing.co.uk> wrote:

> I define a method as a specification of a sequence of changes. That can
> include:-

> Methods made up of an  unvarying sequence of changes i.e. statically
> defined by a sequence of place notation.

> and...

> Methods where the changes are determined by rules based upon the
> position of bells in the previous row(s) i.e. dynamically defined or
> Dixonoids.

That's a good definition, and I was surprised that others didn't pick up my
suggestion of static v dynamic structure yesterday.  However, it prompts
further thoughts.

There are three ways to determine what change to ring next:

1 - Derive it as the next change from the static definition.

2 - Generate it on the fly from a rule(s) applied to the previous row.

3 - Respond to a call.

Note that in (2) there is a default static structure as well as a rule.
For example Dixons has a defaul place notation X 1 and the rule is only
applied to alternate changes.  The 1 may be replaced but not the X.

Other Dixonoids might have longer default place notation.  (For example on
might be based on Forward:  34 X 34 . 1).  Others might havethe rule(s)
apply at more than one point in the default place notation.  (MBD's
example of St Simons / St Martins for example.)

Re (3) conventional wisdom says that calls are not part of the method, but
is that axiomatic?  For ringers of Doubles variations the call certainly
does constitute part of it, and for any normal ringer a variation is a type
of method.

But suppose you do declare that anything called is not part of the method
then logically you have a problem with a silent & non-conducted peal
because nothing is called so everything must be part of the method.  If you
consider the standard extent of XYZ Minor the band doesn't need to memorise
the position of the exceptional changes because they are rule based (on the
position of 5, 6 for Surprise and 2, 5, 6 for Plain methods), with the
default place notation of XYZ.

NB - I am not suggesting that a silent standard 720 of a method is a
different method, just pointing out a wrinkle in the definition.

-- 
John Harrison
Website http://jaharrison.me.uk