[r-t] Monster extent of triples

Robert Bennett rbennett at woosh.co.nz
Tue Oct 7 01:13:27 UTC 2014

	It would be interesting to start from another peal of pure triples
and use the same sort of process. 

	Possible peals: 

	(1) Shipway's 5 part of Grandsire Triples or any others using bobs
and hics only; 

	(2) Peals of spliced Grandsire and Oxford Bob Triples; 

	(3) peal of Grandsire Triples with Holt's singles such as Holt's
10part. The Holt's singles could be treated as a discontinuity to
start with, and removed before the end. 

	(4) Could also do the same process, but include double changes as
well as triples 


	On the question of the memory effect, I would suspect that there was
one. To be sure, will need to have several monster peals, preferably
starting from different types of peals (2 part, 3 part, 5 part as well
as different starting methods). 

It may be that there are only a relatively small number of these
monster peals. In that case they will have more of their own
character, and less of where they were derived from, but they should
still show some. 

	Robert Bennett.

----- Original Message -----
  From:"Philip Earis" 
To:ringing-theory at bellringers.net
Sent:Mon, 6 Oct 2014 13:42:37 +0530
Subject:[r-t] Monster extent of triples
In this week's Ringing World (page 1027) there is a very interesting
showcasing an exciting new extent of pure triples. The article (by
N. Steyn", who is reputed to share a computer terminal with a
four-in-hand ringer from the Midlands) explains the creation of a new,

seemingly structureless, one-part composition of triples.

The starting point for the new extent was Andrew Johnson's 10-part of 
bobs-only Stedman. This was run through an algorithm to repeatedly
chop and 
rearrange it until a completely new extent emerged.

The algorithm took a random change in the base extent, and then
swapped the 
next change for one of the other two possible changes (eg 3.1 could
3.5 or 3.7). The choice of which change to insert was heavily weighted
equalise the occurrence of 1s, 3s 5s and 7s throughout the
composition. The 
algorithm then reversed all the changes between the original (randomly

chosen) starting point and an occurrence of the newly-chosen change.
produces a sequence of 5040 changes with a discontinuity...multiple 
applications of the algorithm led to the discontinuity disappearing
producing a true and fiendish new extent.

The place-notation for "Frankie's" new extent is copied below. It
would of 
course be a very significant (though I feel and hope achievable)
to ring this It feels like an appropriate challenge for the ringing
prizes" I proposed a while back.

Anyway, I have some questions:

1) Each change (ie 1, 3, 5 and 7) appears 1260 times in the new 
composition.The frequency of occurrences of the 12 possible 2-change

1.3 454
1.5 363
1.7 443
3.1 429
3.5 449
3.7 382
5.1 374
5.3 451
5.7 435
7.1 456 (457 if comp rotated)
7.3 355
7.5 448

Please can somebody also produce a similar table showing the frequency
the 108 possible 4-change blocks, and also all possible 6-, 8- change

2) What is the longest string of notation that appears
4,5,6,7,8,9,10,11 and 
12 (or more) times?

3) Who can come up with interesting results by applying the algorithm
existing extents on 5 or 6 bells?

4) Is there ever a "memory effect", ie how (if at all) can the choice
starting extent influence the "monster" chopped up extent produced?

Place notation for the new monster triples extent:

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