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-course extent, 21 extra in-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-course extent, 19 extra in-course leads, 3 out-of-course leads (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 first two blows of 125364 and) the four aforementioned leads (136542, 124635, 135246 and 136425), 27 in-course leads which 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 (minus the first two blows of 125364) and 23 in-course leads.
These 4 quarter peals are all true quarter peals and cumulatively contain each change 7 times.