We're spending Christmas and New Year in the Washington DC area, visiting Tina's family. Thanks to Tina's presidential blog, our presence was detected by Bryn and Leland Reimer and Myles Dakan, who are all coincidentally spending New Year nearby. They are based in Northampton, Massachusetts, so this was another "visiting bands" that took place on neutral territory.
We arranged to meet yesterday and planned to try two quarters, but in the end, the timing on the day limited us to one. We rang Cambridge Royal, followed by a short practice session with a course of Norwich Royal and a course of Stedman Caters.
The quarter was a good collaborative effort, not perfect but Cambridge usually holds together pretty well. Leland called a composition with half-lead singles to swap 7-8 for a course, followed by three homes. I rang 7-8 and I must confess that I didn't really like being swapped. Although the position is the same, the back-bell music is wrong. It was good to try it though. I think Change-Ringing on Handbells Volume 2 includes a suggestion of something similar with half-lead singles to swap 7-8 and standard singles to swap 3-4, which keeps everyone in their home positions throughout.
I then started thinking about peal compositions with half-lead singles. How many courses can we get by using standard singles at M and W to permute 2, 5 and 6 (keeping 5-6 in the 5-6 and 3-4 positions), standard singles at H to swap 3-4, and half-lead singles on 7-8? The starting point is this block, which gives six courses with all six permutations of 2, 5 and 6.
M W 23456 ----------- s 63452 s s 53426 s s 23465 ----------- Repeat.
The next step is to add singles at H, either as a pair in every course or equivalently one at the end and repeating:
M W H 23456
--------------
s s 63452
s 64352
s s s 53426
s 54326
s s s 23465
s 24365
--------------
Repeat.
This is false though, because Cambridge has B falseness, which means that reversing the coursing order of 23456 produces a false course. In more detail, the plain course and the course with coursing order 64235 have some rows in common.
OK, so the idea is a wash-out for Cambridge, but Yorkshire Royal doesn't have B falseness (Yorkshire Major does). So the composition above gives 12 courses of Yorkshire Royal. My idea was that doubling it by adding a pair of half-lead singles to every course would give 24 courses, which could be reduced to 14 for a peal by omitting five pairs of singles.
But it doesn't work! Among those 24 courses is the coursing order 098642357, i.e. reversing the coursing order of 2345678, and it turns out that this course is false against the plain course. The problem occurs when the tenor is becoming 3rd place bell:
1908765432 9107856342 1970583624 1907856342
At the treble's handstroke snap there's a roll-up on all the bells except the tenors, then the non-tenors pairs cross (sometimes this is a good conducting landmark), then the pairs hunt apart and dodge at the lead end back into adjacent positions to give the well-known row 1907856342. Now it's clear that swapping 7-8, 5-6 and 3-4 produces 1907856342 at the handstroke snap, repeating with the plain course.
The same thing happens in major, which is one occurrence (not the only one) of the B falseness in both Yorkshire and Cambridge:
17865432 71856342 17583624 17856342
Also it's the same in Cambridge Minor:
156432 516342 153624 156342
which means that calling two singles at H is false. I must have known this at some point, but had forgotten.
Back to the original question. The 12-course block above can't be extended by adding even one pair of half-lead singles, because the reversed coursing order on 23456 is already present in the block and additionally reversing 7-8 produces falseness.