[r-t] Ocean Finance Doubles

[Philip Earis]

Well done - a very nice 'decomposition'. 

Using the cyclic nature of the plain course to your advantage, allowing you to rotate through the necessary complimentary 'leads' to give an extent has a certain neatness.

So as well as your new "doubles king" status, I think you also now win the Ocean Finance prize. The actual prize is still to be determined - would ringing in a long peal at Victoria St suffice?


- original message -
Subject:	Re: [r-t] Ocean Finance Doubles
From:	Matthew Frye <matthew__100 at hotmail.com>
Date:		22/03/2008 1:10 am


The first thing i notice about this principle is the nature of the rows in a division:
12345 +
21354 +
12534 +
12543 -
15234 -
51243 -
 
And that the same pair of bells are together on the front for the first three changes (similarly on the back for the second three changes). A bit of working leads to the conclusion that if the extent includes the division from 12345 it must also include 21435 and no others with the 1 and 2 in 1-2 (or the 3 and 4 in 3-4). So an extent is not an assembly of mutually true courses as much as it's an assembly of true pairs of complimentary leads.
 
Looking at the composition you gave, it's basically in 2 sections (joined with 2 "A"s): we have a complete course at the end starting from 13254, and at the start we have a 3 lead block repeated 5 times the third lead of which (31524) is the complimentary lead for the 13254 lead. The permutation of the bells in the first section is 1>3>2>5>4, the same as the cyclic rotation for 13254 course, so this brings up the complimentary leads for the rest of the 13254 course. The other 2 leads in the first block have 12 and 15 on the front which translates to 2 bells ahead and 2 bells behind in the order of permutation so these will each bring up each others compimentary leads and include all the other pairs on the front not present in the 13254 course.
 
> From: pje24 at cantab.net> To: ringing-theory at bellringers.net> Date: Fri, 21 Mar 2008 23:56:08 +0000> Subject: [r-t] Ocean Finance Doubles> > This evening we rang an extent of a new asymmetric Doubles Principle - Ocean > Finance Doubles.> > There are six changes per division - the notation for a plain division is > +3.5.123.1.3.123> > To obtain an extent, there are two types of calls:> > T = 345 (instead of 123) at division end> A = 145 (instead of 123) at division end> > Composition:> TppTppTppTppTpAppppA> > Extents usually consist of an assembly of mutually true courses. This one > doesn't. So how does it "work"? > > > _______________________________________________> ringing-theory mailing list> ringing-theory at bellringers.net> http://bellringers.net/mailman/listinfo/ringing-theory_bellringers.net
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