[r-t] Bobs-only Stedman Triples - 66 complete B-block peals

[Andrew Johnson]

66 complete B-block peals

I have found over 500 sets of round B-blocks which together with some B-blocks exactly cover the extent in an odd number [47 to 71] of round blocks where the sixes can be rearranged to give 66 complete B-blocks. Some of the sets of blocks are given below together with some peals.

47 round blocks, signature 39:2+53

2314567QS---------P-----P---------P----P---------P---P---------P--PP--------PPP*3(1)
6342571QS---------P--------P---------PP---------P--P----P-----P-----P*3(1)
https://complib.org/composition/85935 585 bobs, irregular 3-part
https://complib.org/composition/96222 594 bobs, 3-part
https://complib.org/composition/96220 591 bobs, 3-part

51 round blocks, signature 36:3+57

2314567QS---------P-----P---------P-----P---------P----P---------P---P---------P----P---------P-----P---------P----P---------P---P---------P----P---------P-----P---------P----P---------P---P--------P---------PP---------P--------P*1(1)
1742365QS-------PP--P-----P-PP--------PP-P---P----P-----P----P---P----P-----P----P---PPP-*1(1)
7146325QS---------PP---------P--------P---------PP---------P--------P*1(1)
https://complib.org/composition/78043 606 bobs

63  round blocks, signature 32:7+51

c 5040!63 
2314567QS---------P--------P---------PP------PP--------PPP---------PP------P-PP*1(1)
7521436QS---------PP----P-------P--P---------P--------P------P------P*1(1)
2541367QS--------P-------P---------P-P-------P---------P-P--P----P-P-*1(1)
2615437QS--------P--P--P---------P--PP-*1(1)
3546217QS--------PP--------PP*1(1)
3561247QS--------PP-P-------P*1(1)
2456317QS-------P-P-------P-P*1(1)
https://complib.org/composition/88097 612 bobs
https://complib.org/composition/91434 573 bobs

The 3-part peals make a change from the one-part peals. There are several types of 3-part peals:

Exact 3-parts: all the parts are called the same.

Other 3-parts:
Blocks which divide the extent into 3 identical parts. These are then linked with Q-sets of bobs or omits. For an easier peal it is best to use only 1 Q-set (or perhaps a second at a similar point in other parts). The sixes affected by the Q-set should be as close a possible to minimise the disruption. If the 3 identical parts are divided into ABCD at the Q-set points then peals of the form
ABC'CDAB'BCA'D
where ' is a bob or omit can sometimes be found. We should minimise the length of B and C.
So the peal links the parts like this (view in a fixed pitch font):
1234567: ABC
           /
1357246: ..CD
1357246: AB
          /
1526374: .BCD
1526374: A
          \
           \
1234567: ...D

A variation is
AB'B'BC'C'CDA'DA'D
which might be easier to call, at the expense of a longer first part and shorter second and third parts.

It might be possible to add extra Q-sets of omits to reduce the bob count, but the peal is then less regular.

Sometime the extent can be split into round blocks using a group of order 3, but not into 3 identical parts, but in 2,3,4,5.. sets of 3 identical parts. If there are an odd number of sets then it might be possible to find some Q-sets of bobs or omits to link everything together.

Irregular 3-parts
By bobbing all available Q-sets there might be whole B-blocks revealed as some of the sets. If complementary pairs of B-blocks are then available a free choice of 1 of the 6 possible pairs can be made, and that might give more Q-sets of omits to link everything together. The result is going to be a much less regular peal though.

With all these 3-part peals then by choosing an appropriate rotation/reversal a good part-end (either 1357246 or 3456127 etc.) can often be found.

To be continued.

Andrew Johnson