[r-t] Fwd: Re: Wraps [was Quarter Peals of Treble Dodging Major]

[Mark Davies]

Yes sorry Philip, counting wraps is tricky, and can be done in different 
ways:

1. Counting the total number of unique (handstroke,backstroke) pairs, of 
which there are quite a lot, is perhaps not useful, due to inevitable 
falseness. (If you allow falseness, you can repeat one exactly, anyway!)

2. The "traditional" way of listing wraps (Graham's diagram, which gives 
us 10 on Minor) is good in general, but not all of these wraps may be 
available if you have (e.g.) a fixed treble structure.

3. When counting for a fixed structure, you have to remember to knock 
out not only those wraps which cannot be reached, but also those which 
could be reached but would be false (otherwise we are back in case 1).

So looking at a treble-dodging path, out of the 10 total wraps, one is 
directly knocked out by the treble path restriction:

   xxxx12
   345612

And a further two are removed because they cannot be rung within a TD 
extent without falseness:

   456123    546123    465123
   456213    456213    456213  (only one choice here)

That leaves 7, assuming you can actually squeeze both of these in:

   561234    651234
   56xxxx    56xxxx

In theory that is possible with two sections like this:

   652134       652143
   561234 56    651234 12
   562143 12    562134 56
   651243 56    561243 12

I don't fancy your chances with the rest of the composition though!

MBD