[r-t] 1536 Frog & Toad Major

[Philip Earis]

One of the most notable major compositions of recent years was successfully 
rung at the weekend: Prof. Ander Holroyd’s music-fest 1536 major containing 
all possible rows starting or finishing with a run of four or more 
consecutive bells (http://bb.ringingworld.co.uk/view.php?id=1014795)

Ander described the composition and its genesis in depth in a February 2015 
message to this list – see 
http://www.bellringers.org/pipermail/ringing-theory_bellringers.net/2015-February/005861.html.

As a quick summary, the composition is a stand-alone finely crafted work of 
genius that boils down to a 16-part with part ends being cyclic rotations of 
rounds and their reverses.

One way of describing the composition in terms of methods is in terms of 
splicing two rotationally-symmetric methods: Frog (a principle with 71 
changes per division) and Toad (a differential with 25 changes per 
division).  See Ander’s description at 
https://www.math.ubc.ca/~holroyd/comps/frogtoad8.txt and a .pdf of all rows 
(highlighting runs) at https://www.math.ubc.ca/~holroyd/runs.pdf.

Is this the best way of describing the composition?  I'd be very interested 
in seeing other partitions that anyone may feel are more natural.

In any case, it's a really great achievement to produce this (and indeed to 
score this - it's far from easy to learn and ring, but a very worthwhile 
challenge).  Especially given the accessible quarter-peal length I really 
hope some other bands will be up to the challenge of giving this a go.

Any more developments on this theme to report, Ander?


===
Frog Major:
-4-34.6.5.6-4-4.56.1.56.4-34-3.6.5-56.4.36-4.56.1.34.1.34.5-34.
56-4.56.1.56.1.34.5-36.5.34-4.3.6-56-5.34.1.34.5-5-3.4.3.56-5-1
l.e. 57628413
bob = 3

Toad Differential Major:
4-4-6.3.56.34.1.34-5.4-56.1.56.34.6.3-5-5.36
l.e. 13254876
bob = 6

       12345678
       --------
(F)   35426781
F     68751234
F     13284567
F_T_  64573218
F_TT_ 31248765
F_TT_ 86715432
F_TT_ 53462187
F_TT_ 28137654
F_TT_ 75684321
F_TT_ 42351876
F_TT_ 17826543
F_T_  46537812
F     71862345
F     24315678
F     57648123
F     82173456
(F)   12345678
       --------
Start and finish at the half-lead of Frog: 56-4.56.1...
===