[r-t] Brian Price Double Triples Methods

[Philip Earis]

Another of Brian Price's achievements was in triples principles. He has some very interesting results from his April 2002 paper "Triples Principles using the Group of order 168" (ie methods like Scientific triples, but with symmetry) which can be seen at: <http://www.ringing.info/bdp/triples-principles.html>



This was briefly discussed on this list in January 2009, with Eddie Martin also giving some background into his asymmetric methods (Martin's and Artistic Triples - see <http://bellringers.org/pipermail/ringing-theory_bellringers.net/2009-January/002778.html>)



In summary, Brian found there were 229 symmetric triples principles (consisting of single and double changes) of the Scientific type.



Of these, 23 of these are pure triples. Moreover, 5 of the 229 methods are double, of which two have the right structure to give an extent using simple substitute calls where only one call position is required for a peal:



&1.7.1.7.1.7.3.5.1.7.1.7.1.7.3,5 (very fluid and hunt-based - I suspect it would be quite tricky to ring)



&1.3.1.3.127.5.7.1.3.167.5.7.5.7.1,7





Ander Holroyd has produced a nice extent in one of Brian's other double methods:



5040 Unnamed Double Triples Principle

2 3 7  234567

-------------

s s s  563742

s s    476253

s s    527346

s s s  342675

-------------

6 part, omitting s half way and end



method = 3,&6.3.5.7.3.6.3.5.2.5.1.3.5.2.5 (3725614) single = 23 for final 6

http://ringing.org/main/pages/method?notation=6.3.5.7.3.6.3.5.2.5.1.3.5.2.5&pn-query=Display&stage=7&le=3

This would be very worthwhile to ring.

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