[r-t] Spliced Treble Bob Minor Data Tables

Michael Foulds foulds at reaystreet.freeserve.co.uk
Sun Oct 3 15:48:06 UTC 2004

Richard Smith:-

 > For example, the tables in Michael Foulds
fourth book "Spliced Treble Bob Minor Data Tables" (except
the table of grid splices) can readily be generated in this

> (We can also generate the tables for five-lead splices that
are not course splices and two-lead splices that have been
omitted from this book.)

Just caught up with reading this - I hope I never said or implied that I'd
worked them out in my head!  The lead splicers and course splicers were
extracted simply by generating the rows and comparing them.  The 3-lead and
6-lead splicers were extracted by generating and comparing "patterns"
representing  the position of treble, fixed bell(s) and parity of a half
lead - as per the logic explained in book 2.  I'll come on to grid splices

I've done no formal maths since A-level (a very ong time ago!) so empathise
greatly with observations by Graham John, Richard Grimmett and others -
these procedures
were based on commonsense, logic, brute force and ignorance, and may be
lacking in elegance.   Also, I'm using the definitions and terminology I
used in the books, including the codes for lead end groups (consistent with
CC 1961 Collection)

With regard to splices omitted from the book, no 2-lead splices were
knowingly omitted, so if someone knows of some more, that's a cock up by me.
With regard to five lead splices, I was running out of space and energy,
don't really have enough grasp of the subject, and conscious that the reader
probably wouldn't be that interested  either.   The easy bit is finding
which methods contain the same 120 rows in 10 half-leads based on a lead
head set other than the plain course.  The hard bit is joining them together
into an extent.  I didn't want to include anything in the tables that
couldn't be arranged into an extent. Having mucked about for several hours
and got 9 examples, I got brassed off and called it a day.  Bear in mind the
tables on grid splices, 2-lead and 5-lead splices were an unadvertised bonus
not mentioned in the promotional material, so I didn't feel too bad about

One of the possibilities not covered in the book is that bob courses of
groups R, T and K/N produce the same lead head set, as do those of groups P,
U and H/L, so we can have "bob course splices", viz:-

  23456 Woodbine D
  52364 Neasden D
- 43526 Neasden D
- 65432 Neasden D
- 24653 Neasden D
- 36245 Neasden D
  52436 Woodbine D
  35264 Woodbine D
- 63425 Woodbine D
- 26543 Woodbine D
- 42356
 Repeat Twice

The reviewer seemed to take the view that even such information as had been
included on 5-lead splices was superfluous, so I felt justified in making a
conscious decision not to bother with it at all in "Treble Place Minor
Splicing Tables"

The table of Simple Grid Splices was generated similarly to those for 3-lead
and 6-lead splices, following the
logic of the "imaginary method" model (see books 2 and 3).    The "patterns"
are generated for non-crossing pairs
and non-pivot bells and compared with real methods in the appropriate lead
end groups to build the composite course.

For example (the one discussed in book 2), take London S. (lead end K).   To
build a composite course HKJKH, we compare first the patterns from the pair
25 (not of course a crossing pair in group K, but a crossing pair in group
H), and compare with those on pair 25 from real H methods.  We find a true
3-lead splice with Chelsea D.   Now compare the pattern generated by fixed
bell 4 in London (not the real pivot) with those in real J methods.  We find
a true 6-lead splice with Kelso S. (or Crowland D. et al).      Our grid is
Chelsea D (2 and 5 pb), London S (3 and 6 pb) and Kelso S. (4 pb).   Very
nice stuff to ring, too.

The table of Simple Grid Splices in the book contains all those found by
this procedure except:-

a)    "Parkerised" courses - those containing a mix of of 12 and 16 lead end
places were removed.

b)    Those requiring a mixture of regular and irregular methods were
removed.  All grid splices in the table use a composite course of three
regular or three irregular methods.  An example of a Simple Grid Splice
which works only with a mixture is Beighton S/ Bogedone D/ Cambridge S. -
there is no regular group G method which will replace Beighton S.

If you wanted a complete list of grid splices, you'd first have to define
what was going to be called a grid splice.   Take an extent of Wath D.
Clearly not a grid splice.   Now splice in 9 leads of Repton D.   Still not
a grid splice?   Now put in 6 leads of Earlsheaton TB.  Marginal?   Another
12 leads of Boston?  Must be a grid splice by now.  Where do you draw the
line? I've only included in the tables those which  are all regular or all

The procedure described above does not find those grid splices which are not
on individually true 3-lead and 6-lead splices.  I call these (after Ken
Lewis, Harold Chant) "complex grid splices".   Mostly, these have grids with
5-6 sections of X 1234 X, such as   Bourne S (3 and 5 pb), Ipswich S ( 2 and
4 pb) and Ely D (6pb) but there are several other possibilities.  In order
to find
these, I set up an array for each method with 10 columns for each possible
pair as crossing pair, 5 columns for each bell as pivot, and 12 rows for
each position of treble at + and - parity. The array elements contain the
positions of the bells in each row, so if 2nd pb is in 1st place and 3rd pb
is in 5th place at the -ve row with the treble in 4th place, then the
element for row "+4", column "23" is simply "15".   Row +1 is not actually
necessary as rounds is pretty much the same in any method.  With crossing
pairs, it doesn't matter which way around they are.

Finding the grid splices is now a matter of comparing the relevant columns
of methods in the appropriate lead end groups for each possible composite
course, and extracting those "perfect fits" where there is one bell in each
position in each row.  Here's an example of a complex grid splice with
composite course GHKHG.   The G method is Aspley D, 2 pb and 3 pb.   A
comparison of the "23" column of Aspley, with the "46" column of H method
Benhall TB shows no clashes, and a further comparison then with the pivot
"5" column of K method Antarctica D. gives a perfect fit, one bell (inc. the
treble) in each place at each row.

Parity           Aspley         Benhall         Antarctica
   &                    G                   H                     K
Treble          Pair 23         Pair 46             Pivot 5
+1                    23                   46                     5
-1                     23                   45                     6
+2                    14                   36                     5
-2                     14                   35                     6
+3                    14                   26                     5
-3                     24                   16                     5
+4                    13                   25                     6
-4                     23                   15                     6
+5                    12                    34                    6
-5                     12                    34                    6
+6                    12                    34                    5
-6                     12                    34                    5

- which gives us:-

  23456 Benhall TB
  56342 Aspley D
  64523 Aspley D
  42635 Benhall TB
- 23564 Antarctica D
- 45236 Benhall TB
  36524 Aspley D
  62345 Aspley D
  24653 Benhall TB
- 45362 Antarctica D
 Repeat Twice

I don't have the output from this procedure with me at present as it is on
my PC in Inverness.  If anyone wants a more complete table of grid splices,
including the complex ones, email me a request privately to
foulds at reaystreet.freeserve.co.uk including your postal address (it will be
hard copy) and I will deal with it next time I am there which will be about
3 or 4 weeks.  The output is in the form of splice cluster references and if
you haven't got the book(s) to look them up in you won't make much sense of
it - not a sales pitch, just a fact.  I don't expect the response to be
overwhelming and I can
afford half a dozen stamps.

Again, it doesn't include mixed/regular irregular grids, but the program can
be run again with the appropriate lead end codes in the input if anyone out
there particularly wants to know about them.  There aren't actually that
many complex
grids - my recollection is the list is about 25 to 30% longer than the table
printed in the book, through the addition of the complex grids, so most of
the stuff is in table 13 in the book anyway.

More information about the ringing-theory mailing list