[r-t] multi-peal extent of major
Alexander Holroyd
holroyd at math.ubc.ca
Mon Dec 7 22:22:21 UTC 2009
Since (e.g.) the 8 rows formed by swapping the pairs
12(34)(56)(78)
form a group, one could even start with a regular 8-part extent having
these as part ends. Then the resulting 8 5041's would have identical
callings, except for the extra change at the beginning and end of each
one.
Getting something worth ringing (sensible method, some reasonable music in
each peal,...) on this plan might be a bit more challenging, though.
Ander
On Mon, 7 Dec 2009, Alan Andrews wrote:
> Frank Blagrove composed a set that did this although, from memory, there
> would have been more repeated rows. I used to have hard copies but they are
> tucked away now in a box somewhere. No doubt they are online somewhere...
>
> Cheers,
> Alan
>
>
>
> On 7 Dec 2009, at 21:38, Philip Saddleton wrote:
>
>> I recall an article in the RW a few years ago discussing a set of eight
>> peals of PB Major which between them contained all the rows, with only the
>> plain course repeated. I can't remember whether these had been rung, or if
>> it was merely a theoretical exercise.
>>
>> There are certainly enough ways to get in and out of rounds without
>> repetition. Here's a plan:
>>
>> Consider pairs of changes which, combined, are equivalent to place notation
>> 'x'. There are seven of these, i.e. place notations
>>
>> 1234 5678
>> 1256 3478
>> 1278 3456
>> 12 345678
>> 34 125678
>> 56 123478
>> 78 123456
>>
>> Given a right-place plain method, take any one of these pairs, and find the
>> lead containing the two rows given by rounds transposed by these PNs, e.g.
>>
>> 12435687
>> 12345678 1256
>> 21346578 3478
>>
>> This gives a way of smuggling rounds into a different lead in each case,
>> providing it is not a second's place or group M method (take Double
>> Norwich, for instance). Along with the lead starting from rounds this gives
>> eight separate leads. Then find a way of partitioning the extent into
>> mutually true blocks each containing one of these leads. Eight 5040s, seven
>> of which have an extra row inserted so that you can start and finish with
>> rounds.
>>
>> --
>> Regards
>> Philip
>>
>> Frederick Karl Kepner DuPuy said on 07/12/2009 19:49:
>>> I'm probably not the first one to think about all this, though. What
>>> conclusions have been reached on the question before? Has it ever
>>> actually been done?
>>
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