Appendix E. False Courseheads
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.
Groups A to U and a to f also include tenors-split members that are not shown in these tables. There are 3 additional groups, X, Y and Z, that only have tenors-split members and do not have any tenors-together members. As these tables only show tenors-together members, groups X, Y and Z show below as not having any members.
42563 ) L2
64325 ) K2
56342 ) P2
35264 ) U2
65234 ) N2
23546 ) a2
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 "/".
Example: Ibstock Surprise Royal has the following in the Methods Library:
The false courseheads associated with Ibstock are accordingly:
Out-of-course: 25436, 32456, 23654, 43256, 53426, 63452, 24356, 46352, 52346, 64253, 34526, 35246, 42536, 42653, 36254
Example: A composition might be advertised as being 'true to BDEKacdefYZ'. A band is considering using this composition to ring Othorpe Surprise Major. The CC Methods Library shows that the false coursehead groups for Othorpe are BDXY. Because Othorpe has group X falseness but the composition does not include X in the list of groups that it is true to, this composition will be false if used with Othorpe.
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.
A method that is false in the plain course will have false coursehead group A, usually in addition to other groups.