Recently, Andrew Tibbetts and myself realised a much more elegant solution could be obtained. On ten bells, if rounds is transposed to queens, and the transposition repeated, then the 'magnificent six' rows are produced:
1234567890 (rounds) ---------- 1357924680 (queens) 1594837260 (reverse tittums) 1987654320 (reverse rounds) 1864297530 (reverse queens) 1627384950 (tittums) 1234567890 (rounds)
This transposition can be used as the basis for a six-part composition. Each part starts with a whole course, finishing with a single. There is then a 'turning course' used to get the required transposition. Andrew came up with the following:
s9 243567890 2,s3,s5,7,8,9,s12 357924680 (12 leads)
There are 21 leads per part, so with 6 parts this gives 2520 changes for Resurrection. The remaining changes are made up by using near-miss courses. Tibbetts' original complete composition is:
5040 Double Resurrection CB Royal - by Andrew Tibbetts (#6)
5 6 7 8 9 234567890
ss ss s ss 324
s s 243
(a) 357924680
ss s 375
(a) 594837260
s 549
(a) 987654320
6 ss s 978
(a) 864297530
ss s 846
(a) 627384950
s 672
(b) 432567890
s 423
s s 234567890
(a)=2,s3,s5,7,8,9,s12 (12 leads)
(b)=2,s3,s5,7,8,9,s11,s12 (12 leads)The same principle can be used to give a complete peal-composition (without the need of adding near-miss courses) for treble-dodging cyclic methods with the appropriate lead-head order.
The magnificent six can also be exploited, by using the half-peal six-part plan in resurrection, and using the other 2500 rows with 'conventional' music in a method like Bristol:
5000 Spliced Royal (2m) (PJE/AJWT)
234567890 (Resurrection)
s9 243567890
2,s3,s5,7,8,9,s12 357924680
A 594837260
A 987654320
A 864297530
A 627384950
A* 324567890
____________________________
M W H (Bristol)
- 43256
s 42356
-
- 34625
- s
- s
- 34256
- 23456
Contains 2500 each Bristol, Resurrection, atw.However, for maximus turning courses can be either arduous (for plain methods) or simply too long (treble-dodging methods). Following an email-exchange with Tibbetts, I think link-methods are the way forward.
Link methods originated in Birmingham to go between a 'conventional' coursing order and a course that produced cyclic music. However, they can be neatly used to quickly switch between the magnificent six courses in cyclic methods.
Perhaps the simplest such link method is the diferential hunter -18-36 on eight bells. It's elegant & right-place, and importantly very short. Two bells plain hunt in opposites, and the rest 'alliance-hunt'. The division-ends are:
24681357 (queens) 48372615 (reverse tittums) 87654321 (reverse rounds) 75318642 (reverse queens) 51627384 (tittums) 12345678 (rounds)
This is trivially extended to any even number of bells, eg for maximus -1T-30-58 = 24680T13579E. Unfortunately if this were to be used in a cyclic composition it would have a variable treble, which would greatly increase the complexity of the composition.
For a link method with the treble fixed, there are several possibilites. On ten bells, it's even possible to have a conventionally symmetric plain method which is the first leadhead as queens. -1-1-1-1-29, le 47 = 1357924680. Another ten-bell link method is the asymmetric -30-58 = 1246803579. This can be used to produce an interesting composition of Resurrection which exploits the magnificent six:
5904/5100 Spliced Royal (Resurrection & link - PJE from JEG from PJE) 1234567890 ------------- a 1924680357 a 1594837260 a 1654320987 a 1864297530 a 1384950627 a 1234567890 a = lp,8rp l = unnamed link method, +-30-58 r = double resurrection cyclic For 5904 call bbsbbs at part-ends For 5100 call bbsbb at part-ends then a whole course of DRCB with single home.
On 12 bells, the situation is a little more complicated if the treble is to be kept fixed. A perfectly regular six-part is difficult, because the rounds -> queens transposition involves ten steps (the magnificent six and four intermediates). A link that keeps the tenors fixed can get around this, such as -30-58 = 1246803579ET, with a few calls required to reach the full course-head.
Perhaps a more elegant solution is using a link that contains all ten of the transpositions, and only exploiting the magnificent six. A link method such as -3T-50-78 = 124680T3579E is ideal here, and a skeleton six-part composition is easily obtained:
3084 Spliced Maximus (Ascension & link) - PJE
1234567890ET
---------------
ls 126480T3579E
sh 124680T3579E
x 179E24680T35
lp=X3Tx50x78
ls=X3Tx50X3478
a=double ascension cyclic.
sh = { ap ap ap ap ap ap ap ap ap ap as }
x = { ap ap ap ap ap ap ap ap ap ap }
c1 = { ls sh x }
c2 = { lp lp ls sh x }
composition = { c1 c2 c1 c1 c2 c1 }
Of course, the 'magnificent six' link method idea can be used for conventional methods, possibly in conjunction with a cyclic link method. A final very interesting prototype, based on David Pipe's super cyclic six composition is given below. Pure cyclic methods are perhaps the most appropriate way to exploit this music, though.
5076 Spliced Maximus arr PJE from DJP Part = Slinky Deimos Phobos Maypole Ariel Zanussi Zanussi Ariel Maypole Phobos Deimos Composition = ===== 3 part cyclic link part 3 cyclic link 2 part 2 cyclic link part 3 cyclic link part cyclic link 3 part ===== cyclic link =X3Tx50x78