[r-t] Bobs-only Stedman Triples

[Robert Bennett]

These peals were and are a great advance in ringing theory.
Andrew Johnson's peals have got us closer to something ringable by mere
mortals.
The 25 years might be history repeating itself: from J Noonan's peal of
1799 to Thurstans' peals also took a long time.

One question: have the *keys* to these compositions been published , i.e.
the device which links the equivalent of an even number of bob courses
together?
The magic blocks have been discussed, but do these later compositions
depend on something else?

-Robert Bennett

On Wed, Jan 22, 2020 at 8:48 PM Andrew Johnson <andrew_johnson at uk.ibm.com>
wrote:

> 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
>
>
>
>
>
> Unless stated otherwise above:
> IBM United Kingdom Limited - Registered in England and Wales with number
> 741598.
> Registered office: PO Box 41, North Harbour, Portsmouth, Hampshire PO6 3AU
>
>
> _______________________________________________
> ringing-theory mailing list
> ringing-theory at bellringers.org
> https://bellringers.org/listinfo/ringing-theory
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://bellringers.org/pipermail/ringing-theory/attachments/20200122/37855b8c/attachment.html>