[r-t] Proposed definition of a peal

[Don Morrison]

I may be mistaken, but I think those that have spoken to the issue of
Philip's proposal on this list are remarkably close to agreement on
the heart of what we're discussing. I think the issues that remain are
largely (a) details of wording, (b) how much needs to be codified in
legislative rules such as CCCBR Decisions, versus how much is mere
detail of record keeping mechanics, and (c) where to draw some line
when an otherwise desirable formalism proscribes certain potential
ringing constructs or behaviours.

I think there are really only a small number of things we seek to
define, albeit we have to reach closure on how to define them, and
that's non-trivial.

a) I think most of us agree that a peal is essentially just a true
   touch of length at least 5,000. The real issue is defining what
   "true" means, in the face of mixed stages, variable cover and
   multi-extent blocks.

b) Defining what we mean by a method.

This message is an attempt to address (a), leaving (b) for another
day.

Here's what I propose. What do you think?

------------------------------------------------------------

1) Change ringing is carried out by sounding a collection of bells
   repeatedly, in various orders. After any one bell, B, is sounded
   once, each of all the others must be sounded exactly once before B
   is sounded again.

2) A row is a sequence in which each bell is sounded exactly once. A
   piece of change ringing consists of a sequence of consecutive rows,
   each sounding of any of the bells during the piece of ringing being
   a part of exactly one of these rows.

3) Between some or all of the rows of a piece of change ringing the
   order of many of the bells will change. The number of bells that
   are changing between some of the rows is called the stage. It is
   an integer greater than or equal to 2, but less than or equal to
   the total number of bells being rung. Traditionally these stages
   are given names; for example the 6 bell stage is referred to as
   "minor".

4) If at some point during the ringing the stage is less than the
   total number of bells being rung, the bells that are not changing
   are called non-changing bells. The most common example of a
   non-changing bell is a bell ringing last in each row, which is
   called a covering bell.

5) At a stage S there are exactly S factorial different rows possible.
   The collection of all these rows is called the extent at stage S.

6) While most pieces of change ringing are rung entirely at one stage,
   some are rung of multiple stages. At any given point during a piece
   of change ringing the ringing is of a particular stage. The longest
   sequences of consecutive rows at the same stage, with the same
   bells, if any, serving as non-changing bells, are called stage
   fragments. The piece of change ringing is partitioned into a
   collection of non-overlapping stage fragments that collectively
   contain all the rows of the piece of change ringing.

7) A piece of change ringing, if all of one stage S, is called true is
   there is a non-negative integer N such that each of the rows in the
   extent at stage S occurs at least N times and no more than (N + 1)
   times.

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, then the overall piece of
   change ringing is called true.

9) A piece of change ringing that is not true, according to 7 or 8 as
   appropriate, is called false.

10) A peal is a piece of change ringing, during which all the bells
    being used sound in each row, that contains at least 5,000 rows,
    and that is true.

------------------------------------------------------------

Comments:

- As in all definitions there are words the meaning of which must be
  taken as already understood. Many of those so used in the above are
  certainly capable of generating arguments: What is a bell? What does
  it mean for a bell to sound? Is there a time limit to how long
  "during" could mean? However, these seem like the appropriate level
  to leave things not explicitly defined. And if people want to get
  fussed about such matters, they are orthogonal to the issues this
  definition seeks to address, and can easily be layered on.

- There are a couple of unattractive neologisms: non-changing bell and
  stage fragment. For most ringing they do not have to be understood
  or used. They are added only to deal with the otherwise awkward
  issues of mixed stage ringing. Folks that don't care about that can
  ignore both terms.

- The choice of the unattractive term non-changing bell instead of
  fixed bell is deliberate. Fixed bell is often used to mean something
  completely different in composition and conducting, and overloading
  the term could be confusing.

- Like the new terms, section (8) can be ignored by anyone that does
  not care about the issue of mixed stage ringing.

- While the mixed stage material is a little convoluted, I think
  everything else should be easy for the average ringer to
  understand.

- Things such as cylindrical are excluded from this definition of
  change ringing. While I personally would like to see it included, I
  believe my opinion on that point is a minority one. In practical
  terms leaving such things out is unlikely to cause lasting
  difficulty as such things are so difficult to ring they are unlikely
  to be practised even if legal. Again, this seems like a suitable, if
  perhaps slightly arbitrary, place to cut things off.

- Section (2) is primarily to ensure that rows are not viewed as
  overlapping, or that bells do not ring additional times between
  rows. Again I would personally not be horrified by allowing such
  things, but believe my opinion in this matter is a minority one. It
  seems prudent to exclude such things from the definition, as an
  appropriate compromise between my own possibly pathological level of
  inclusivity and what I perceive as the preferences of the majority.

- Section (10) prohibits bells being added or dropped during a peal.
  Again not something I'd personally object to, but I think I'm in the
  minority on that, and it seems an appropriate compromise.

- As I think everyone that has spoken up on the subject in this thread
  as said, variable cover is considered merely a special case of the
  higher stage. This implies a higher standard for truth in variable
  cover than fixed cover, but again I think this is a reasonable place
  to cut a compromise.

- There is ambiguity between whether a section of ringing is a single
  stage fragment at the higher stage, rung variable cover, or multiple
  stage fragments mixed together. It is really up to the band to
  declare which they are ringing. This ambiguity is no worse than many
  we happily accept today, such as "are we ringing Single Court Minor
  or are we ringing Original Minor?"

- Personally I'm not even so sure "truth" is all that important. I
  think I'd probably enjoy ringing (not calling though!) a peal of
  Stedman Triples that had queens, Whittingtons, back rounds and
  rounds each twelve times, once at each possible position in a
  division, than I would enjoy ringing in another performance of
  Dexter's No.2. But I believe I am in the minority, and that truth is
  Really Important to most of you. Hence, it is a strong part of this
  definition. (And yes, I work hard to try to ensure that all the
  compositions I publish on my web site are true!)

- Things that this definition does not exclude include
   - any number of covering, leading, or interior non-changing bells
   - bells staying put for longer than four consecutive blows
   - mixed stage multi-extent blocks
   - definitions of methods radically different than currently
     allowed, or even those covered by the Norwich Axioms
   - ringing a peal of doubles by ringing rounds 42 times, followed
     by the row 21354 42 times, followed by 23145 42 times, etc.
   - jump changes

- This definition is sufficiently broad that there are plenty of
  things that are allowed that I wouldn't personally want to ring in.
  A peal on 2 bells. A peal with 12 covers. The doubles described in
  the last point. But if someone else wants to, who are we to stop
  them? There are plenty of things that are legal today, and even are
  rung, that I'd certainly decline to ring myself.

- The Council's Decisions, and Philip's suggested replacement, contain
  additional rules regarding the conduct of peals. Things like "an
  error shall be corrected..." and so on. If desired, such additional
  rules can be added to this, as they are orthogonal to the issues
  this definition tries to address.

- I'm sure this is not perfect. I hope it is step in the right
  direction, hope you will agree and hope will help in polishing it.




-- 
Don Morrison <dfm at ringing.org>
"For the growing good of the world is partly dependent on unhistoric
acts; and that things are not so ill with you and me as they might
have been, is half owing to the number who have lived faithfully a
hidden life, and rest in unvisited tombs."  -- George Eliot, _Middlemarch_