[r-t] Peals of Grandsire Triples without singles

[Robert Bennett]

Peals of Grandsire Triples without singles 

By using 5ths place bobs (Hics) as well as normal bobs, William Shipway
produced a peal of Grandsire with triple changes only (no doubles or
singles). His peal uses a composite Q set of (Bob, Hic) x 5, making a 10
course block. The other 62 courses can be joined to this with bobbed
Q-sets. Shipway cunningly used the bobbed Q-sets of Holt's 10-part to do
this. 

Jasper Snowdon in “Variation and Transposition” claimed that at least
5 Hics would be required, and that therefore only 5 should be allowed in a
peal composition! It is however possible to produce peals with only 2 Hics,
using a composite Q set of (Bob, Bob, Hic) x 2, making an 6-course block to
which the other 66 courses can be joined with bobbed Q sets.  

A Peal of Grandsire Triples 

using 119 bobs and 2 fifths place bobs (Hics)only: 

234567 

-462375 3 

-534762 1 

Hic576234 1 

-425376 1 

-764532 2 

-437625 3 

-564237 1 

-375426 2 

-263547 2 

-472356 2 

-634572 1 

-346572 4 

-463572 4 

-724356 2 

-567432 2 

-735624 3 

-527346 3 

-325674 5 

-463725 1 

-324657 3 

-763524 1 

-327645 3 

-623574 5 

-526437 5 

-265437 4 

-462753 5 

-374562 1 

-623457 2 

-426735 5 

-724563 5 

-637452 2 

-376452 4 

-473265 5 

-274536 5 

-362457 2 

-573246 2 

-625473 1 

-256473 4 

-452367 5 

-674235 2 

-526374 1 

-265374 4 

-572643 3 

-245736 3 

-742653 5 

-367542 1 

-423756 2 

-564372 2 

-235764 1 

-732456 5 

-567243 2 

-325467 1 

-563274 3 

-425763 1 

Hic476325 1 

-534276 1 

-765423 2 

-527634 3 

-735246 3 

-467523 2 

-724635 3 

-437256 3 

-234675 5 

-562734 1 

-235647 3 

-762435 1 

-237654 3 

-632475 5 

-436527 5 

-364527 4 

-563742 5 

-275463 1 

-632547 2 

-536724 5 

-735462 5 

-627543 2 

-276543 4 

-572364 5 

-265743 3 

-432576 2 

-534627 5 

-765234 1 

-657234 4 

-426357 1 

-264357 4 

-362745 5 

-623745 4 

-726534 5 

-527463 5 

-635742 2 

-736254 5 

-237465 5 

-762354 3 

-437562 1 

-624753 2 

-726345 5 

-327564 5 

-523476 5 

-425637 5 

-764325 1 

-647325 4 

-536247 1 

-365247 4 

-263754 5 

-632754 4 

-736425 5 

-367425 4 

-543267 1 

-675324 2 

-436275 1 

-364275 4 

-473652 3 

-354726 3 

-753642 5 

-267453 1 

-532746 2 

-465273 2 

-324765 1 

-723546 5 

-467352 2 

-234567 1 

Robert H.Bennett 

1992. 

Except for one Q set of 5 bobs, the peal is in two equal parts. 

I doubt that an exact two-part is possible, but a palindromic two part
like Holt's 10-part peal may be possible.  

A Peal of Grandsire Triples 

using 99 bobs and 2 fifths place bobs only: 

234567 

Hic263475 -3 

632475 -4 

756243 -2 

257364 -5 

642735 -2 

746523 -5 

237654 -2 

462537 -1 

564723 -5 

Hic563742 -5 

275463 -1 

472356 -5 

374625 -5 

673542 -5 

346725 -3 

743562 -5 

547236 -5 

245673 -5 

732564 -2 

457632 -1 

654273 -5 

256347 -5 

352764 -5 

753426 -5 

267345 -2 

532467 -1 

435726 -5 

734652 -5 

637245 -5 

236574 -5 

742653 -2 

257436 -3 

642357 -1 

576234 -2 

765234 -4 

347526 -2 

543672 -5 

435672 -4 

574326 -3 

375642 -5 

673254 -5 

356742 -3 

753264 -5 

647325 -2 

346572 -5 

543267 -5 

435267 -4 

234756 -5 

732645 -5 

457263 -2 

254376 -5 

472563 -3 

634257 -2 

346257 -4 

243765 -5 

742536 -5 

547623 -5 

645372 -5 

236745 -1 

452673 -2 

734265 -2 

237546 -5 

742365 -3 

267453 -3 

532746 -2 

735624 -5 

637452 -5 

756324 -3 

357462 -5 

243657 -1 

352476 -3 

453627 -5 

764253 -1 

537426 -2 

645237 -1 

536472 -3 

245736 -1 

362574 -2 

563427 -5 

635427 -4 

436752 -5 

654327 -3 

276435 -2 

352647 -2 

653724 -5 

756432 -5 

637524 -3 

246753 -2 

532674 -2 

465732 -1 

654732 -4 

436527 -3 

534762 -5 

735246 -5 

547362 -3 

345276 -5 

453276 -4 

254637 -5 

652743 -5 

436275 -2 

234567 -5 

Robert H.Bennett 

1995. 

The peal is an attempt to find the minimum number of bobs in this system.
I suspect however, that the minimum number of bobs required in this type
of composition with two Hics is about 95.
 
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