[r-t] Wraps in Minor

[Matthew Frye]

I think that any 2880 (with each row at each treble position) will have
the same number of wraps of rounds/back rounds/any arbitary row
beginning with the treble (though not any other bell?) and also the
same number of 5-runs or less. I believe that a 1440 would not automatically share this property.



It's a bit late to go into detail, but I'll give an outline: If you
take any run of 6 consecutive strikes (across a handstroke-backstroke),
it must either consist of all 6 distinct bells or the first and last
bells are the same (and one is omitted). Either way, if you take any
one location (6 places long) in a lead (ie. 4ths place of 4th change to
3rds place of the 5th change) and have the treble fixed, you have 120
different posibilities for that position in the lead and you must ring
all of them in a 2880 (this bit is critical and could probably do with
a slightly more rigourus proof, but not at 1:30AM).

Note that this does not give you every 6 bell change appearing at every
wrap position, as many of the positions in the lead will be prevented
by the first and last bells being the same. But every 5 bell
combination will show up (twice?) in every wrap position.

eg. Back rounds can (and in a 2880, will) appear as a wrap at any
Handstroke-backstroke where the treble in moving up or staying in the
same position, as per the example given by Phil.



I think that my original conclusions follow quite easily from this. In
a 1440, you are not guaranteed every possibility in every position, so
my reasoning does not hold, there is simply too much variation.




I hope that made sense, I may elaborate further tomorrow.


From: Earisp at rsc.org
To: ringing-theory at bellringers.net
Date: Wed, 29 Jul 2009 16:15:34 +0100
Subject: [r-t] Wraps in Minor





















A musical effect that is very nice is when there is a “wrap”
of music from the handstroke to backstroke.  For example:

 

213654 (handstroke)

321645 (backstroke)

 

As has been discussed before on here, the number of wraps in
a standard extent of minor changes significantly depending on the method being
rung.  For minor, I summarised lots of the results on my website at http://www.cantabgold.net/users/pje24/music.html

 

Now a noted handbell ringer from Scotland (for the sake of anonymity
let’s call him “Mr T”) has recently been reading that page,
and posed the following conjectures:

 

“If one was to ring a 1,440 of each of the treble
dodging minor methods (TDMMs), with each row once at handstroke and once at
backstroke, would every TDMM produce the same number of wraps, or would some methods
be better than others? Would the result be different for a 2,880 with each row
rung once at each possible treble position?”

 

Elegant solutions are requested.

 

 

 

 

 






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