I have recently been interested in the question of if one can fit 4 quarter peals of minor into a peal. Meaning can one find 4 true quarter peal compositions starting and ending in rounds which when rung in series give 7 extents. It turns out that this is trivial for plain minor. You can simply ring an extent 4 times over and insert 9 of the 12 different courses into each extent (say by using a pair of singles or an extra plain course) ensuring that each course is inserted 3 times.
The problem for treble dodging becomes harder as if one starts and ends each quarter at the lead end lengths must be a multiple of 24, however 1248 is just too short and 4 quarters of length 1272 gives 5088. However if you start 2 of the quarters at the snap and start the other 2 at the snap you have 2 quarters of length 1250 and 2 of length 1270. Then you can ring them in order 1250-1270-1250-1270 which starts and ends at the lead end and requires no "restarts". This means that you now need to include both in and out of course leads which creates issues of falseness. For most regular methods an extent requires that you either ring the entire extent in course or the entire extent out of course, with a few exceptions. However all these exceptions have one of Kent, Norwich or Oxford overwork, which is incompatible with our structure. This is due to the fact that the first 4 blows in the lead where you come round at the snap (124356) are the same as the first 4 blows of the lead starting 123456.
After thinking for a while I decided to try using Bogedone Delight Minor as the S_i underwork has very little out of course falseness, indeed each in course lead of Bogedone is false to only 5 out of course leads. (As an added bonus Bogedone is the old name for Bowdon where I used to ring regularly.) To me, the most natural approach to finding a compatible set of leads was to ring an extent (either in or out of course) in each of the quarters then split an out of course extents between each pair of a quarters of length 1250 and 1270. This then leaves one extent to insert, however this extent must be in course as all 4 of the quarters contain soe part of the lead 125364 (the lead where you come round at the snap). Even with the comparatively little out of course falseness of Bogedone this approach does not seem to work.
The idea which ended up working for me was that, roughly speaking you should ring the entire out of course extent (excepting the changes 125364 and 213546) in the 1270s and then ring every other lead in course, meaning that we ring 5 extents in course. Then in order for the quarters to be true all we need to do is in the 1250s have the in course extent plus 22 extra distinct in course leads then finishing with the out of course lead 125364. Then the 1270s contain every out of course lead plus 23 extra distinct in course leads, ensuring that 126543 (the in course lead containing 125364 and 213546) is included. This does not quite work as 126543 cannot be included in the extra leads in the 1250s, so 126543 can only appear 4 times. To fix this one can include 126543 twice in one of the 1270s, then remove the 4 other out of course leads false to this and include them in the 1250s. Note that any two of these 4 leads which have an in course lead false to them in common, other than 126543, must be in the same 1250. It ended up being beneficial to have 1 of them in one of the quarters and the other 3 in the other to minimise falseness and it was possible to find a true set of leads, in fact it gives a rather large class of choices.
So now comes the problem of joining up the leads into a composition, the possible sets of leads that I constructed certainly do not particularly lend themselves to being joined up. I believe that with my choice of possible leads it is probably impossible to do it with only common bobs and singles. I spent about a week and many sheets of A3 and eventually found some way of linking them up, though I had to use all 4 singles, as well as both 14 and 16 bobs. Needless to say the composition is not the most elegant one out there. I'm sure that there exists a "nicer" composition but I am not convinced that a "nice" composition exists.
1250 Bogedone Delight Minor Composed by Andrew M Roberts 23456 1 2 3 4 5 45623 – x 62345 – x 56423 – x 46325 – 25463 x – – 34256 – – – 63542 – – – 24653 – – s s x 53246 – – x – x 32546 – x x x x 25364 – c (2) x = 16 Bob; c = 1256 Single. Contains the in courses extent, 21 extra out of course leads, 1 out of course lead (136542), finishes with 2 blows of 125364.
1250 Bogedone Delight Minor Composed by Andrew M Roberts 23456 1 2 3 4 5 45623 x – 62345 x – 56423 – x 46325 – 42563 – 2 x 35426 – – – 46253 – – a a 63542 x a c – 52364 s b – x 25364 – s (2) x = 16 Bob; a = 1456 Single; b = 1236 Single; c = 1256 Single; Contains repeated rows without a call or change of method. Contains the in courses extent, 19 extra out of course leads, 3 out of course lead (124635, 135246 and 136425), finishes with 2 blows of 125364.
1270 Bogedone Delight Minor Composed by Andrew M Roberts (32456) 1 2 3 4 5 32456 a – c 45632 – a – c 24653 – a 25463 s s 54326 c b 64235 – – 56423 – – 34562 – x – x 63524 a x x – 45623 a – c a 23456 – c s (3) x = 16 Bob; a = 1456 Single; b = 1236 Single; c = 1256 Single; Start at the backstroke snap. Contains the out of course extent minus the four aforementioned leads (136542, 124635, 135246 and 136425) and 27 in course leads, all distinct except for 2 copies of 126543.
1270 Bogedone Delight Minor Composed by Andrew M Roberts (32456) 1 2 3 4 5 64253 – s – s 32645 c x a 63245 – 63425 s 24635 s – – 26543 a – 54362 c s – s 25643 a x c 32456 s – s 56234 b – – 23456 – (3) x = 16 Bob; a = 1456 Single; b = 1236 Single; c = 1256 Single; Start at the backstroke snap. Contains the out of course extent and 23 in course leads.
These 4 quarter peals cumulatively contain each change 7 times.
I am not aware of anybody else having thought about this problem before. It seems plausible that somebody may have rung a plain minor composition that works, either by design or accident but it seems rather unlikely that anybody has in a treble dodging method. Though of course ringing 8 extents satisfies the problem suboptimally. For minimus and singles the problem is trivial, though you perhaps want to ring a 5088 of minimus. This has been done before. For say plain doubles it isn't quite automatic as 42 does not divide by 4, to do it optimally all you need is a true 60 and a true 180 which combine for 240. 3*(BBH) for 180 and 3*F for 60 work for plain bob. It seems plausible that somebody has rung this before.