[r-t] Stedman triples

[Edward W Martin]

----- Original Message ----- 
From: "Philip Earis" <pje24 at cantab.net>
To: "ringing theory" <ringing-theory at bellringers.net>
Sent: Sunday, December 05, 2004 5:36 PM
Subject: [r-t] Stedman triples


>I really enjoyed the article in this week's RW about Stedman triples.  I 
> hope the weekend's Eisteddfod was sucessful, as I'm sure it will have been. 
> I was sorry not to have been there. Perhaps Clarrie can inform us what 
> method 'won' the Eistedfodd, and what else was presented?
> 
> Contrary to what some people think, I believe Stedman triples is a decent 
> method.  It's just on higher numbers that Stedman is a bland disappointment. 
> Anyway, I've three comments/challenges for Stedman triples composers...
> 
> 1) One negative point about Stedman is, I feel, that it is not really one 
> method, but instead two methods spliced together (ie Erin and Bastow).  To 
> support this, I would say that no compositions exist (as far as I am aware 
> on any number of bells) without half-lead calls.  Is it possible for a 
> composition (of triples) to have calls only at the end of either quick or 
> slow sixes?
> 

I haven’t had the opportunity to read about the Eisteddfod and do wish I could have been there to witness it all I’m not a mathematician but if you’ll bear with me I’ll try and give you something of what I have experienced in trying to compose Stedman Triples
 

I don’t think that this is at all a negative point.  By ignoring the principle and insisting that the Central Council definitions should be adhered to then I can see where you might be coming from and (ignoring the principle) it is a valid point of view. However, in Tintinnalogia we are told that change ringing began with the sixes (which I infer to mean that on 3 bells they rang plain hunt both forward and back). When extended to higher numbers, but still retaining the idea of plain hunting on 3 and double dodging above, when we consider 5 bells, neither continuous forward nor continuous backward hunting is a method (in the original usage of the word) for obtaining the extent. However, as Stedman discovered, if you follow the principle of alternating the two then this principle IS in fact a method of obtaining the extent!  His instructions for obtaining a 120 were to call a single anywhere you like so long as it switches the work of only two bells, then call this same single 60 changes later.



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.


> 2) Following on from that point, is a composition possible which has no 
> consecutive calls?


I have discovered several course structures, which initially do not have consecutive calls, however calls needed to link these courses either haven’t worked or have resulted in consecutive calls. I did discover one course structure that had no consecutive calls: all singles except for a special (nasty Holts type single) A 5040 of this is possible and it uses only the two types of call, but the Holts singles really put me off So, if you don’t mind nasty Holt’s singles, then YES it is possible


> 3) Another draw-back is that the method is not traditionally symmetric about 
> a call being made.  Do any compositions exist which counter this, ie which 
> contain calls only in the middle of a six (doubles-style calls)? 


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. 

Eddie Martin
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