[r-t] Double Helix

[Philip Earis]

Simon Humphrey:
" I am amazed to learn that an extent of Double Helix Differential is possible"

As far as I'm aware, the whole design structure of Double Helix (a major differential consisting of a 3-cycle and a 5-cycle) is that in the 3-cycle, all 8*7*6 = 336 possible different arrangements of the 3 bells are included.

This being the case, rather than being remarkable it is arguably self-evident that a simple extent exists, along the lines of the arguments in the second part of your message.

Don't get me wrong, I am certainly excited by the extent.  Indeed, I have been discussing as much with Simon Melen in recent days... :-)

On the more general point, as you say such differentials lend themselves to producing extents. There are lots of rung 2-3 differentials on 5 bells with this property (120 change plain courses), and indeed one rung triples example - Upham Differential Triples (pealed in the early 1990s), but this isn't very neat.  

I am especially interested in using the differential approach to approximate to a different style of method, eg treble-dodging major [there are interesting analogies with the recent "un-principles" discussions here]  Given that differentials are the perfect extent building blocks, I think using them is more likely to yield a notable and neat extent of major than starting with conventional treble-dodging major and trying to force an extent out of it.

In the past few days, and linking in with Simons' (deliberate apostrophe) emails, I have been especially keen to see what is possible in these three areas:

1) 3-4 triples differentials to yield the extent.  With 1-2-3 ringing in every possible combination, there will be a 7*6*5 = 210 change course (ie 70 change divisions).  Method examples with pure triple changes and maximal symmetry would be very nice.

2) 1-3-4 major differentials.  With the 3-cycle ringing in every relative order *twice* in the course (once in each position with each parity), this gives a 8*7*6*2 = 672 change course, ie 224 change division.  This could lend itself nicely to the 1-cycle (treble) just treble-bobbing, leading to a "lead" that appears to be a whole asymmetric surprise method (penultimate row can be 12436587, with a 1458 leadend change gives you 14236857, which is handy), but which when taken as a course could have double symmetry, etc.  In other words, a sort of "fractal method".

3) Extents of Double Helix style (3-5) major differentials, involving splicing of different differential methods.

What can people produce?  Is there are good reason that could be a barrier to anything here?  

I'm salivating :-)



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