# [r-t] Avon Double Cyclic Doubles

Philip Earis pje24 at cantab.net
Fri Jul 24 02:55:43 UTC 2015

```As highlighted on the Ringing Methods Facebook group, the Bathwick band have rung an extent of a new Doubles method, Avon Double Cyclic Doubles (3.4.3.4.3.2.3.2.3.2.3.4.3.2.3.2.3.4.3.4.3.4.3.2 = 23451) - http://bb.ringingworld.co.uk/view.php?id=472773.

The method is a principle with 24-change divisions, whose plain course produces the extent – always a nice property. The division (and also the half-division) has glide symmetry, an attractive property. The blue line is “clean”, consisting only of places, and the method is also cyclic. See http://ringing.org/main/pages/method?notation=3.4.3.4.3.2.3.2.3.2.3.4.3.2.3.2.3.4.3.4.3.4.3.2&pn-query=Display&stage=5&le= . All very interesting.

However, immediately apparent is the very strong similarity to Ander Holroyd’s beautiful double principle, Banana Doubles (3.2.3.2.3.4.3.4, http://ringing.org/main/pages/method?match=banana&name-query=Search), which has been discussed on this list before and which I highlighted in the “Compositions of the Decade” series (http://wiki.changeringing.co.uk/Compositions_of_the_Decade_2_-_Doubles).

Indeed, the Bathwick extent is simply the 120 of Banana Doubles, given from that link, also appearing on the list of plain course doubles extents Richard Smith produced at http://ex-parrot.com/~richard/doubles/extents/principles-2-blows.txt. Given it’s more concise nature and palindromic symmetry, I prefer Banana as a label here.

Perhaps one of the Bathwick band could tell us if the idea for “Avon Double Cyclic” came from these sources (nothing wrong with that), or if it was produced independently (and what the design motivation was if so)? I’m also interested if the 120 was rung and called as Banana Doubles, or as a plain course extent.

On the more general point, it is interesting to consider how a short doubles method can be converted into (or sometimes considered as) an extent.  There is of course centuries-old precedent for this, with doubles extents like Orpheus, Crambo and Tendring originating from a base of Stedman or Grandsire (see Richard’s Smith’s message to this list of October 2009 -http://bellringers.net/pipermail/ringing-theory_bellringers.net/2009-October/003061.html).

As well as Banana, there are several 8-change doubles principles with glide symmetry (number 2 on this list is related to the “Double Saturn” method I mentioned in my 2,4,6,8 doubles email earlier this week - http://bellringers.net/pipermail/ringing-theory_bellringers.net/2015-July/date.html):

3.2.3.2.3.4.3.4 41253 Banana Doubles
3.5.3.5.3.1.3.1 41253 Untitled Doubles
5.23.5.23.1.34.1.34 25134 Untitled Doubles
345.1.123.5.123.5.345.1 35214 Untitled Doubles
345.1.345.5.123.5.123.1 34251 Untitled Doubles

Looking at a list of double plain-course extents where every alternate change is a 3, we see the Banana / Avon Double (and rotation) is the only one with cyclic leadends:

3.1.3.2.3.2.3.4.3.5.3.2.3.5.3.4.3.4.3.2.3.1.3.4 54213 Untitled Doubles
3.1.3.2.3.4.3.4.3.5.3.2.3.5.3.4.3.2.3.2.3.1.3.4 45231 Untitled Doubles
3.1.3.5.3.2.3.1.3.5.3.2.3.5.3.1.3.4.3.5.3.1.3.4 53412 Untitled Doubles
3.1.3.5.3.4.3.1.3.5.3.2.3.5.3.1.3.2.3.5.3.1.3.4 43521 Untitled Doubles
3.2.3.1.3.2.3.5.3.4.3.4.3.4.3.5.3.4.3.1.3.2.3.2 45231 Untitled Doubles
3.2.3.1.3.4.3.5.3.4.3.4.3.4.3.5.3.2.3.1.3.2.3.2 54132 Untitled Doubles
3.2.3.2.3.2.3.4.3.4.3.2.3.4.3.4.3.4.3.2.3.2.3.4 34251 Untitled Doubles
3.2.3.2.3.4.3.4.3.4.3.2.3.4.3.4.3.2.3.2.3.2.3.4 51234 Untitled Doubles
3.2.3.4.3.2.3.2.3.4.3.4.3.4.3.2.3.4.3.4.3.2.3.2 35421 Untitled Doubles
3.2.3.4.3.4.3.2.3.4.3.4.3.4.3.2.3.2.3.4.3.2.3.2 53412 Untitled Doubles
3.4.3.2.3.2.3.4.3.2.3.2.3.2.3.4.3.4.3.2.3.4.3.4 45231 Untitled Doubles
3.4.3.2.3.4.3.4.3.2.3.2.3.2.3.4.3.2.3.2.3.4.3.4 54213 Untitled Doubles
3.4.3.4.3.2.3.2.3.2.3.4.3.2.3.2.3.4.3.4.3.4.3.2 23451 Avon Double Cyclic Doubles
3.4.3.4.3.4.3.2.3.2.3.4.3.2.3.2.3.2.3.4.3.4.3.2 51423 Untitled Doubles
3.4.3.5.3.2.3.1.3.2.3.2.3.2.3.1.3.4.3.5.3.4.3.4 43521 Untitled Doubles
3.4.3.5.3.4.3.1.3.2.3.2.3.2.3.1.3.2.3.5.3.4.3.4 53412 Untitled Doubles
3.5.3.1.3.2.3.5.3.1.3.4.3.1.3.5.3.4.3.1.3.5.3.2 54132 Untitled Doubles
3.5.3.1.3.4.3.5.3.1.3.4.3.1.3.5.3.2.3.1.3.5.3.2 45231 Untitled Doubles
3.5.3.4.3.2.3.2.3.1.3.4.3.1.3.2.3.4.3.4.3.5.3.2 53412 Ducklington Doubles
3.5.3.4.3.4.3.2.3.1.3.4.3.1.3.2.3.2.3.4.3.5.3.2 35421 Untitled Doubles

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