[r-t] Candidate definition #10

[Don Morrison]

On Wed, Aug 13, 2008 at 1:48 PM, Ted Steele <ted.steele at tesco.net> wrote:
> That's exactly my point. I know what you want to say, I just don't think
> these words say it. I think  that your wording factors it out
> completely. It's obviously not what you intend but it is what it says,
> to me at least. "One or more bells may ring in the same position in each
> and every row" means that, for example one bell, say the tenor may ring
> in the ultimate position in "each and every row" of the block. Thus no
> other bell may swap places with it because the tenor has got to be there
> for "each and every row". Whatever bell starts there has got to stay
> there for each and every row.

That is exactly my intention. If a block contains varying cover bells,
they are *not* non-changing bells.

Perhaps a concrete example would help.

We might ring a peal, on six bells, of doubles, minor, and variable
cover doubles. There are 16 blocks, as follows:

12 extents of Grandsire Doubles, all with the tenor covering. Each of
these extents is a block of stage 5, length 120, and with the tenor as a
non-changing bell. Each is true and complete.

1 extent of Cambridge Surprise Minor. This is a block of stage 6,
length 720, and with no non-changing bells. It is true and complete.

1 x 2160 of Cambridge Surprise Minor. This is a block of stage 6,
length 2160, and with no non-changing bells. It is true and complete,
containing every possible row three times.

1 block of Stedman Variable Cover Doubles. This is a block, of stage
6, and with no non-changing bells. If it is to be complete it must be
of length 720, or a multiple thereof. If it is of length 720 or
shorter, to be true each row, viewed as a six bell row, must be
distinct. In our hypothetical peal it is a 720, perhaps the one
attributed to Thomas Thurstans. It is true and complete.

1 59 of Grandsire Doubles, covered as usual by the tenor. It is a
block of stage 5, length 59, with the tenor as a non-changing bell. It
is true, but not complete.

The overall peal comprised of these 16 blocks is of length 5099.

Does that help clarify things?



-- 
Don Morrison <dfm at ringing.org>
"Granny lived her life via the back door. There were only three
times in your life when it was proper to come through the front
door, and you were carried every time."
                               -- Terry Pratchett, _Wyrd Sisters_