[r-t] Singles in treble-dodging minor

Richard Smith richard at ex-parrot.com
Thu Sep 23 12:57:14 UTC 2004

Philip Saddleton wrote:

> An alternative way of looking at it is to construct a dual "method" with
> the same rows as the original, but with each pair of rows in a half-lead
> with the treble in a given place interchanged. The nature of the rows
> when starting from an out of course lead head will match those of the
> original starting from an in-course lead head.

That's a good way of thinking about it -- I'd not thought of
it like that before.

> Or, turning it on its head, a similar analysis to Richard's can be used
> to determine whether two methods can be spliced in-course.

Yes.  I've been using this type of analysis for quite a
while to determine how methods splice with each other
in-course.  I've found it the most convenient way of getting
a computer to determine a complete list of splices between
pairs of methods.  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.)

Or, we can use the same idea to generate the splicing
information between pairs of methods, one rung in-course,
one out-of-course.  As this is not something I have seen
printed before, I have included these tables for the
"regular" 147 TDMMs.  (Note these tables only include one of
a family of lead splices -- for instance Westminster is
included whilst Allendale is not.  Similarly, only one lead
end variant is included.)

A.  Out-of-course 3-lead splices

  23 Westminster S    24 Pontefract D
  or Disley D         or Sandiacre S

  24 Rochester TB     23 Cotswold TB

  23 Morning S. TB    24 Tewkesbury D

  34 Morning S. TB    34 Trinity S. TB

  26 Duke of N. RB    26 Trinity S. TB
                      or Quantock TB

  46 Evening S. D     36 Pontefract D

  45 Disley D         35 Trinity S. TB

  26 Conisboro' D     26 Caernarvon D

  45 Burnaby D        36 Southwark D

  36 Ipswich S        45 Cunecastre S

  45 York S           36 London S

  45 Durham S         36 Wells S

In many of these splices, the fixed bells for the splice
(the numbers given next to the methods) are also the bells
affected by the singles.  Another observation is that, with
all of these splices, if 3rds place bell is a fixed bell
in-course, then 4ths place bell is the fixed bell
out-of-course, and vice versa.  (In the final four splices
between the Cambridge and London overworks, the same is true
of 5ths and 6ths place bells.)

In a seconds place method, a standard 1234 single swaps the
bells in 3-4, which is precisely the right effect to take
counter to swapping of the bells in 3-4 either side of the
single.  That said, not all of these can be made to work.
The Morning Star / Trinity Sunday 3-lead splice on 34 is an
example of this.  The splice defines six in-course lead
heads/ends that must be removed from the composition, and a
second, out-of-course set of six lead heads/ends that must
be added.

  Removed    Added

   23456     24356
   53462     54362
   63425     64325
   24365     23465
   54326     53426
   64352     63452

Now we have a problem.  In each case, a plain applied to any
of the added lead heads/ends goes to another added lead
head/end, and a 1234 single goes to a removed lead end.
This means that it is not possible to get to or from the
added leads without visiting a removed lead.  (Bobs can only
delay the problem, not remove it.)  This means that the A0
splice is useless.

In other cases, the 1234 single has the right effect.  For
instance, this composition of Rochester and Cotswold.

  720 Spliced Treble Bob Minor (2m)

    123456 Rc
  s 146235 C1 C1            Rc = Rochester TB
  s 136524 Rc Rc Rc         C1 = Cotswold TB
  s 126453 C1
  s 162534 Rc Rc Rc          s = 1234

  Twice repeated

Sixth place methods, whether rung with 1456, 1236
or 1234 singles, are not as easy -- so far I've been
unable to make any work.

The splices between the Cambridge and London backworks are
best suited to a 1236 single as this affects the bells in
3-4 and 5-6.  For example,

  720  Spliced Surprise Minor (4m)

    123456 Yo
  s 132456 Lo               Yo = York S
  s 146532 Yo Yo Yo Du      Du = Durham S
  s 152346 We               Lo = London S
  s 136452 Yo Du            We = Wells S
  s 156324 We
    ------                   s = 1236
  s 134256

  Twice repeated

The only composition I can recall seeing that uses one of
these out-of-course 3-lead splices is one in Composition
502(?), I think by Roger Bailey.  (I don't have my copy of
Comp. 502 to hand.)  It went something like this.

  720 Spliced Surprise Minor (6m)

    123456 No No
  - 164235 No               No = Norwich S
  - 126435 No Bo Ws         Bo = Bourne S
  - 135426 Ad               Hu = Hull S
  - 135264 Ws               Ws = Westminster S
  s 153642 Sa               Ad = Allendale S
  s 162534 Hu               Sa = Sandiacre S
    134256                   s = 1234

  Twice repeated.

B.  Out-of-course 6-lead splices

  3  Lightfoot S      4  Caernarvon D
                      or Alnwick S

  3  Wearmouth S      4  Warwick D
                      or Newcastle S

  4  Duke of N. TB    3  Berwyn TB
  or Conisboro' D     or Barham D
  or British S.P. TB  or Berkeley D
  or Wilmslow D       or Mendip TB
  or Dunedin D        or Peveril D
                      or Chelsea D

  5  Old Oxford D     5  Old Oxford D
  or Bamborough S     or Bamborough S

  5  Pontefract D     5  Pontefract D

  6  Westminster S    6  Westminster S

  6  Morning S. TB    6  Morning S. TB

This list includes the "self-splices" mentioned in the
previous email (that is, the five families of methods that
splice out-of-course with themselves):  Old Oxford,
Westminster, Bamborough, Morning Star and Pontefract.

  720 Spliced Surprise Minor (2m)

    123456 Lf
  s 153642 Ak               Lf = Lightfoot S
  s 124653 Lf Lf Lf Lf      Ak = Alnwick S
  s 135624 Ak
  s 142635 Lf Lf Lf          s = 1234
  - 142356

C.  Out-of-course 5-lead splices

     Duke of N. TB          Kent TB
  or Morning Star TB

     Kirkstall D            Combermere D

These 5-lead splices are fairly difficult to make work.
This is because even when the leads on one side of the
single are a course, those on the other side are not.  I
tried briefly to produce a worthwhile composition using them
but failed.

D.  Out-of-course lead splices

  Oxford TB           Kent TB

This lead splice between Kent and Oxford is particularly
interesting as it allows a touch of lead-end-spliced Kent
and Oxford to be produced:

  720 Spliced Treble Bob Minor (2m)

    123456 Kt Kt
  s 164253 Ox               Kt = Kent TB
  s 126435 Kt Kt            Ox = Oxford TB
  s 154236 Ox Ox
  s 162534 Kt Kt Kt          s = 1456

  Twice repeated.

(Don Morrison's web page has a very similar composition by
Glenn Taylor.  His has a better method balance, but requires
both bobs and 1236 singles.)  (By ringing Kt for Ox and vice
versa, each part has a whole courses of Oxford, allowing its
course splices, Sandal etc., to be added.)


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