[r-t] Numbers
Philip Saddleton
pabs at cantab.net
Thu Dec 14 18:03:12 UTC 2006
Samuel M. Austin said on 14/12/2006 14:02:
> Afternoon, I've been thinking about extents of major with bells in their
> home position - some peals compositions have "6th the extent in 6ths" for
> example.
>
> I've tried to come up with a simple formula for this and this is what I've
> got.
>
> It may be completely wrong and it wouldn't surprise me if it is but here it
> is anyway and hope you don't mind looking at my working
>
> Aye
>
> Sam
>
>
> Extent with 7-8 together
>
> 40320 / 3 = 13440
>
> With 6,7,8 at home
>
> 40320 / (3 X 5) = 2688 - the 3 being the number 40320
> was divided by last time and the 5 the number of remaining
> bells
>
> With 5,6,7,8 at home
>
> 40320 / (15 x 4) = 672
>
> With 4,5,6,7,8 at home
>
> 40320 / (60 x 3) = 224
>
> With 3,4,5,6,7,8 at home
>
> 40320 / (180 x 2) = 112
>
> Also I have noticed that
>
> 112 X 2 = 224
> 224 X 3 = 672
> 672 x 4 = 2688
> 2688 x 5 = 13440
>
> but then the rule changes
>
> 13440 x 3 = 40320
>
But 13440 x 6 = 80640
7 can be in 6 positions relative to 8, but half of these are the reverse
of the other half, accounting for each row twice.
--
Regards
Philip
http://www.saddleton.freeuk.com/
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