[r-t] Double Helix
Earisp at rsc.org
Tue Aug 23 12:11:38 UTC 2011
" 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 :-)
This communication (including any attachments) is intended for the use of the addressee only and may contain confidential, privileged or copyright material. It may not be relied upon or disclosed to any other person without the consent of the RSC. If you have received it in error, please contact us immediately. Any advice given by the RSC has been carefully formulated but is necessarily based on the information available, and the RSC cannot be held responsible for accuracy or completeness. In this respect, the RSC owes no duty of care and shall not be liable for any resulting damage or loss. The RSC acknowledges that a disclaimer cannot restrict liability at law for personal injury or death arising through a finding of negligence. The RSC does not warrant that its emails or attachments are Virus-free: Please rely on your own screening.
More information about the ringing-theory