[r-t] Grandsire Dixonoid Triples

[Philip Earis]

I like both the "Dixonoid" concept (where the position of one or more particular bells triggers a change in the notation), and the "helixoid" differential concept (where a subset of bells ring in every combination of places in the row relative to each other, making an extent fairly easy to obtain).

On seven bells the two concepts can combine very neatly and clearly.  In the simplest triples dixonoid, if all bells plain hunt but with 5ths being made the handstroke after bells 1, 2 or 3 lead, then you get a miraculous course of 210 changes which comprises every possible order of 1,2 and 3 in the row.  An extent composition is straightforward (though remains unrung - we've lost it a couple of times, including once near the end) - further details are on Ander Holroyd's website or at <http://www.bellringers.org/pipermail/ringing-theory_bellringers.net/2010-September/003643.html>

In that same 2010 message, I introduced another simple triples Dixonoid, which either has a Grandsire flavour or is a simple extension of Dixon's Bob minor, depending on how you look at it.  The rules are simply that all bells plain hunt, but with 3rds made the handstroke after the treble leads, and 5ths made the handstroke after bells 2 or 3 lead. The plain course is 420 changes, with bells 1, 2 and 3 appearing in every relative order twice (they come home after 210 changes, bringing up the row 1237654). 

See the line (grid) at:

<http://www.boojum.org.uk/cgi-bin/line.pl?bells=7&pn=3.1.5.1.5.1.7.1.7.1.3.1.7.1.7.1.7.1.5.1.5.1.7.1.7.1.7.1.3.1.7.1.7.1.5.1.5.1.7.1.7.1.7.1.7.1.3.1.5.1.7.1.5.1.7.1.7.1.5.1.7.1.3.1.7.1.7.1.7.1.5.1.7.1.5.1.7.1.3.1.5.1.7.1.7.1.5.1.7.1.7.1.7.1.3.1.5.1.7.1.7.1.7.1.5.1.7.1.3.1.7.1.7.1.5.1.7.1.7.1.7.1.5.1.3.1.7.1.5.1.7.1.5.1.3.1.7.1.5.1.5.1.7.1.3.1.7.1.7.1.7.1.7.1.5.1.5.1.3.1.7.1.5.1.7.1.7.1.3.1.7.1.7.1.5.1.7.1.5.1.7.1.7.1.5.1.3.1.7.1.5.1.7.1.7.1.3.1.5.1.7.1.7.1.7.1.7.1.5.1&qs=Grid&lines=1&line=4&line1=b&line1c=red&line2=b&line2b=23&line3=b&line3b=4567&line3c=black&line4=n&action.x=1>


Ander has now happily produced a few very simple compositions of this Grandsire Dixonoid Triples, which I think would be fun and worthwhile to ring:

bob = 5 for 3
double (D) = 34567 for 3
calling positions are when 1 leads (30 per course)

2 17
----
D
-  2
3  -
----
2 part


2 17
----
D
-
D
-  -
----
3 part


2  8  23   1234567
------------------
   D  D       6745
D     D       5647
   D  D       4756
D     D       6457
   D  D       5764
       D     325467
------------------
repeat

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