[r-t] Pitman's 13440 change compositions
dfm at ringing.org
Wed Aug 9 18:53:39 UTC 2017
On Wed, Aug 9, 2017 at 2:23 PM, Philip Earis <pje24 at cantab.net> wrote:
> So for this #2 composition (unrung), the Sirilic musical analysis
> shows it has 12 5678s off the front and 12 8765s at the back, and 9
> 8765s off the front, more than would be expected in a "random"
> distribution of one third of the rows in the extent.
But, of course, it is far from a random distribution: the rows are selected
solely from tenors together leads of palindromic, treble single dodging
methods with Plain Bob lead heads. So, for example, all 120 rows of the
form 17000008 are impossible. I'm not certain, but I suspect the majority
of rows that are impossible or unlikely to appear are ones that are
conventionally viewed as unmusical, driving up the fortuitous appearance of
ones that do typically find favor. I suspect use of more "modern" methods
could probably easily improve things further, particularly off the front.
> The composition is also of course very far from being all the work,
> as the distribution below shows.
Again, exactly as might be predicted from the way it appears to have been
constructed. And as the number of methods goes up I would expect the number
of different place bells (as a fraction of those potentially available) the
front five get to ring would go down even further. I wonder if a smallish
number of methods, probably boringly similar above the treble, could be
assembled into an ATW composition on this plan by having two or more
different but complementary courses?
Don Morrison <dfm at ringing.org>
"Whenever you're called on to make up your mind, and you're hampered
by not having any, the best way to solve the dilemma, you'll find, is
simply by spinning a penny. No — not so that chance shall decide the
affair while you're passively standing there moping; but the moment
the penny is up in the air, you suddenly know what you're hoping."
-- Piet Hein, _Grooks_
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