[r-t] Bobs-only Stedman Triples

Andrew Johnson andrew_johnson at uk.ibm.com
Wed Jan 22 07:47:41 GMT 2020

Twenty-five years ago, on 22 January 1995, the first peal of Stedman 
Triples using common bobs only was rung.

The composition https://complib.org/composition/10423 by Philip Saddleton 
and me has 579 bobs. Colin Wyld's compositions, which were composed first, 
but published and rung later, have 705 
https://complib.org/composition/21261 and 597 bobs.

These compositions are based on the magic blocks, which link the rows of 
10 B-blocks into 5 blocks, leaving 74 other B-blocks to be joined into a 
peal. There are 825 bobs (out of 840 positions) in these 79 blocks. By 
adding Q-sets of 3 omits we can link 3 blocks into 1, so 79 blocks to 1 
block for the peal requires at least 78 / 2 = 39 Q-sets or 39 x 3 = 117 
omits so 825 - 117 = 708 bobs. Colin's peal uses an extra Q-set to link 
everything, giving 705 bobs. With 3 B-blocks there are two places a Q-set 
can be placed to link them, so extra omits can be used, which allowed 
Colin to remove 108 bobs for his second peal. Philip carefully chose the 
B-blocks to allow further Q-set positions, reducing the bobs to 579.

It is possible to get a magic block composition with 708 bobs, as this 
arrangement shows: https://complib.org/composition/37705

Another question is the minimum bobs on this plan. In June 1995, Philip 
wrote (private communication) that he had found a peal with 576 bobs, 
though it wasn't published. Recently I looked and also found peals with 
576 bobs, for example https://complib.org/composition/59746 which is the 
fewest bobs I have found so far. I have found an arrangement of blocks 
with 90 Q-sets so conceivably 825 - 90 x 3 = 555 bobs, but they didn't 
link into a peal with that few bobs.

So the number of bobs for a magic block peal varies from 576 to 708. My 
10-part peals, including the 2012 exact 2-part variations have from 438 to 
456 bobs. My 3-part based peals from 2017 don't extend the range. The 
exact 3-parts have from 603 https://complib.org/composition/36006 to 639 
bobs. Some other 3-parts have from 606 (for example) 
https://complib.org/composition/60827 to 636 bobs. The irregular 3-parts 
have from 582 https://complib.org/composition/37434 to 705 
https://complib.org/composition/37446 bobs.

Recently I have discovered some more peals on a different plan, ranging 
from 561 https://complib.org/composition/60808 to 711 
https://complib.org/composition/60810 bobs. The first particularly might 
prove a challenge for the conductor.

Andrew Johnson

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