Appendix J. False Courseheads

1.

This appendix shows groupings of false courseheads. It is possible for one course of a method to contain one or more rows that also appear in another course of the same method. For example, the course of Cambridge Surprise Major that starts with 13245678 (which is referred to as this course's coursehead) contains the row 12345678 after the 2nd change of the 5th lead. The course with coursehead 13245678 is therefore false against the plain course.

Furthermore, it can be shown that courses that are false against a reference course (which is usually taken to be the plain course) occur in groups that are consistent across methods of the same type, such as methods with Plain Bob leadheads and one hunt bell, where the hunt bells have the same path.

The table below shows the falseness groupings of the 120 courses that comprise all the possible orderings of bells 2 to 6. These groupings apply to palindromic methods with an even stage of 8 or higher, with Plain Bob leadheads, and with a single hunt bell that follows a Treble Dodging path.

As the table only considers the possible orderings of bells 2 - 6 (the working bells), the remaining bells (the fixed bells) are removed from the table for conciseness. The treble (i.e. the hunt bell) is also removed. For example, coursehead 34265 is referring to 13426578 when considering Major, 1342657890 when considering Royal, and so on.

The table below is divided into courseheads that are "in-course" and courseheads that are "out-of-course". In-course courses are those that can be reached with bobs only (place notation 14 or 1[n-2]) when starting from rounds. Out-of-course courses are those that can only be reached with bobs plus an odd number of singles (1234 or 1[n-2][n-1][n]) when starting from rounds.

False coursehead groups that are designated below by uppercase letters (A to U) contain in-course false courseheads, and may also contain out-of-course false courseheads. Groups designated by lowercase letters (a to f) contain only out-of-course false courseheads.

2.
Group code
A
B
C
D
E
F
G
H
I
K
L
In-course
23456
24365
25634
32546
46253
32465
43265
45236
32654
56423
63542
53462
63425
54632
65324
65432
53624
26543 ) L1

42563 ) L2
36245 )
Out-of-course
[None]
25436
32456
23654
43256
42365
34265
53426
63452
24356
25364
24635
26345
24563
[None]
56243
62543
46523
36542
[None]
46352 ) K1
52346 )
64253 )
34526 )

64325 ) K2
54362 )
[None]

Group code
M
N
O
P
R
S
T
U
In-course
23564
23645
25463
26435
34562
62345
46325
54263
52643
36524
65243
46532
54326 ) P1
64352 )

56342 ) P2
64523 )
45623
56234
35642
62534
52364
34625
64235
45362
24536
25346
36452
43526
62453
26354
53246
24653
34256 ) U1
42356 )
43652 )
63254 )
52436 )
35426 )

35264 ) U2
42635 )
Out-of-course
[None]
62435 ) N1
53264 )
43625 )
35462 )

65234 ) N2
45632 )
52634 )
35624 )
63524
53642
56432
65423
[None]
[None]
[None]
32564
32645
46235
45263
[None]

Group code
a
b
c
d
e
f
In-course
[None]
[None]
[None]
[None]
[None]
[None]
Out-of-course
23465 ) a1

23546 ) a2
26453 )
26534
25643
35246
42536
42653
36254
34652
45326
62354
54236
36425
52463
43562
63245
54623
56324
65342
64532


3.

In Major, groups that include both in-course and out-of-course false courseheads always occur as complete groups. However, in Royal and above, in-course and out-of-course components of a group may occur independently. Therefore in the Methods Library, in-course and out-of-course groups are shown separated by a "/" for Royal and higher. For example, E/Bc indicates that the in-course false courseheads of group E, and the out-of-course false courseheads of groups B and c apply to the method (Royal or higher) in question.

A further consideration in Royal and higher is that certain of the groups defined above, K, L, N, P, U and a, can subdivide. The subdivisions, indicated by K1, K2, L1, L2, N1, N2, P1, P2, U1, U2, and a1, a2 are also shown in the table above. A Royal or higher method might therefore include U1 rather than U before the "/", or N2 rather than N after the "/".


4.

Example: Ibstock Surprise Royal has the following in the Methods Library:

FCHs
Ibstock
L1/BDK1c

The false courseheads associated with Ibstock are accordingly:

In-course: 26543

Out-of-course: 25436, 32456, 23654, 43256, 53426, 63452, 24356, 46352, 52346, 64253, 34526, 35246, 42536, 42653, 36254


5.

Methods without any in-course false courseheads are referred to as "cps", or clear proof scale. However, these methods will usually have out-of-course false courseheads. Bristol Surprise Major is an example of a cps method.


6.

A method that is false in the plain course will have false coursehead group A, usually in addition to other groups.