[r-t] Stedman triples

[Philip Saddleton]

I don't disagree with most of Eddie's reasoning, but there is a little 
more work to be done...

Edward W Martin wrote:

>  
>
> In Caters and Cinques etc, I see no reason why all calls could not be 
> after say quick sixes. The composition would not be so convenient to 
> knit together but sufficient calling places do exist. However, Triples 
> is a different matter. As with Doubles the proof is in obtaining the 
> extent and like you, I do not know of any 5040 that has all calls 
> after say quick sixes. I’m fairly convinced that it can’t be had. My 
> reasoning (if mathematicians will forgive me) is as follows: I have 
> made what I think is a thorough search for all possible course 
> structures and I haven’t found one that fits this requirement. This 
> only leaves bobbed blocks (or compound blocks built up from bobbed 
> blocks). Blocks with consecutive bobs would fail the criterion, 
> therefore our building material would have to be something along the 
> lines of B P B P B P etc. But here, sooner or later we will need to 
> join otherwise excluded blocks. If we use common singles this will 
> invert the flow of changes and alter what on paper had been B P B P to 
> become P B P B.. So we not only need to design blocks P B PB etc but 
> also to design blocks to be excluded from the main comp and of the 
> nature B P B P This is asking a lot. I don’t know how to program a 
> computer but I think we paper & pencil boys would be overwhelmed. What 
> about a bobs only format? As I understand it this depends on the 
> sequence of omit slow, bob quick, bob slow bob quick, omit slow 
> followed by a tight bobbed block with bobs at both quick and slow. 
> These blocks can be plained away extensively as demonstrated by Messrs 
> Johnson and Saddleton but I don’t think that even they have shown any 
> likelihood of choosing bobs after only say quick sixes and this with 
> extensive computer searches traveling at the speed of light.
>
>
We could possibly have blocks containing bobs and singles, where because 
of the mixed nature of the sixes a single can shunt us into another part 
of a block rung the same way round - or alternatively use a set of 
part-ends that are both in and out of course, such as Thurstans' blocks.

> In triples I searched for course structures where singles made in 4-5 
> would be an integral part of the course structure but although I found 
> a few, I was disappointed in that I did away with the need for common 
> singles at the six end but still could not get away from the need for 
> bobs at the six end. This is understandable if you can follow my fuzzy 
> logic:
>
> If it is possible to set out the 5040 in 60 identically structured 
> courses then, each course must have 14 types of six. The requirement 
> is that all sixes MUST be plained at the parting and, allowing that we 
> may bob or single or whatever in the middle of a six, whatever we do, 
> each six-type must exist in two complementary halves. In short, for 
> building material what we need are 60 plain course structures that can 
> be cut and pasted at half six points. Unfortunately it has been 
> demonstrated that the 5040 cannot be set out in 60 true plain course 
> structures, therefore we are up the creek.
>  

Another possibility is that the two halves of a six occur in sixes of 
different types: suppose that the peal comes round with a call - we start

1234567
2135476
2314567

and so need to include somewhere

3215476
3124567
1325476

this could be the first half of a quick six, or the second half of a 
slow six. Thus showing that 60 plain courses don't exist is insufficient.


You could argue that pairs of bobs (or a bob that lasts seven changes) 
give a symmetrical lead. It is possible to join twin bob courses with 
calls at the half-six, so

5040 Stedman Triples (T Thurstans arr T Brook arr pabs)
1234567   2  3  4
-----------------
6354127   -  -    |A
234516    -  2  - |
-----------------
5123467    3A
-----------------
6325417   -  -  s |B

135246    -  2  - |
-----------------
4-part

p=3.1.7.3.1.3.1.3.7.1.3.1
b=3.1.5.3.1.3.1.3.5.1.3.1
s=3.1.7.3.1.347.1.3.7.1.3.1



-- 
Regards
Philip
http://www.saddleton.freeuk.com/