ajohnson1.github.io

More Bobs-only 10-part peals of Stedman Triples

Back in 1995 I discovered four irregular 10-part peals of Stedman Triples using just common bobs.

In 2012 I then found another 148 peals.

The number of bobs varies between 438 and 456 (compared to 438 & 441 for the previous 10-part peals). 15 of the peals are exact 2 parts. Some of the peals have at most 5 bobs in a row (compared to one run of 9 with the previous compositions). The peals can be arranged into 5 sets, with the peals within a set just differing in addition or removal of Q sets of bobs. The original 10-part peals form the sixth set. The peal we rang at Upham is an exact 2 part, with just 2 runs of 5 bobs in a row, 438 bobs in total, 5432167 at the half-way point, all 10-part ends with the reverse rounds rotations 3215467 etc. in the first half of the peal, and sizes of parts varying from 432 to 564 changes.

Runs of bobs in the Upham peal

Number of bobs in run	Instances of run	Total bobs
1	82	82
2	90	180
3	18	54
4	28	112
5	2	10
Totals	220	438

Runs of omits in the Upham peal

Number of omits in run	Instances of run	Total omits
1	118	118
2	54	108
3	22	66
4	20	80
5	6	30
Totals	220	402

Here is the full list of peals:

Bobs-only peals of Stedman Triples by Andrew Johnson 1-5 June 2012

152 peals, including the 4 original 10-part peals

The peals are labelled with the number of bobs and @ showing peals which have different sixes (even after rotation) - i.e. they are not the same after adding/removing Q sets of bobs.

Number of parts of each type in peal

Set	Peals	BCDELM	BsCsDsEsLsMs	FGHJK	FsGsHsJsKs
@1	4	10	0	0	0
@2	51	6	2	2	0
@3	48	2	4	4	0
@4	21	4	2	2	2
@5	15	2	2	2	4
@6	13	0	4	4	2

The component blocks

A=    PP---PPP--P-P----PPPP--P--P----PP-P--P-PP-
B=  A PPP--P--PP--P-PPPP--PP--P----PP-PP-P--P-
Bs= A --P--P--PP--P-PPPP--PP--P----PP-PP-P--P-
C1= A PPP--P--PP--P-PPPP-P-PPP-P--P-
Cs1=A --P--P--PP--P-PPPP-P-PPP-P--P-
C3= A PPP--P--PP--P-PPPP-P---PPP-P--P-
Cs3=A --P--P--PP--P-PPPP-P---PPP-P--P-
C5= A PPP--P--PP--P-PPPP-P-----PPP-P--P-
Cs5=A --P--P--PP--P-PPPP-P-----PPP-P--P-
C7= A PPP--P--PP--P-PPPP-P-------PPP-P--P-
Cs7=A --P--P--PP--P-PPPP-P-------PPP-P--P-
C9= A PPP--P--PP--P-PPPP-P---------PPP-P--P-
Cs9=A --P--P--PP--P-PPPP-P---------PPP-P--P-
D=  A PPP--P--PP--P-PPPP--PP--P----PPPPP--P----PP-PP-P--P-
Ds= A --P--P--PP--P-PPPP--PP--P----PPPPP--P----PP-PP-P--P-
E1= A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-PPP-P--P-
Es1=A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-PPP-P--P-
E3= A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---PPP-P--P-
Es3=A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---PPP-P--P-
E5= A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-----PPP-P--P-
Es5=A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-----PPP-P--P-
E7= A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-------PPP-P--P-
Es7=A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-------PPP-P--P-
E9= A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---------PPP-P--P-
Es9=A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---------PPP-P--P-
F=  A PP-----PPPPP---P-P--PP--P-PPPP--PP--P----PP-PP-P--P-
Fs= A -------PPPPP---P-P--PP--P-PPPP--PP--P----PP-PP-P--P-
G1= A PP-----PPPPP---P-P--PP--P-PPPP-P-PPP-P--P-
Gs1=A -------PPPPP---P-P--PP--P-PPPP-P-PPP-P--P-
G3= A PP-----PPPPP---P-P--PP--P-PPPP-P---PPP-P--P-
Gs3=A -------PPPPP---P-P--PP--P-PPPP-P---PPP-P--P-
G5= A PP-----PPPPP---P-P--PP--P-PPPP-P-----PPP-P--P-
Gs5=A -------PPPPP---P-P--PP--P-PPPP-P-----PPP-P--P-
G7= A PP-----PPPPP---P-P--PP--P-PPPP-P-------PPP-P--P-
Gs7=A -------PPPPP---P-P--PP--P-PPPP-P-------PPP-P--P-
G9= A PP-----PPPPP---P-P--PP--P-PPPP-P---------PPP-P--P-
Gs9=A -------PPPPP---P-P--PP--P-PPPP-P---------PPP-P--P-
H=  A PP-----PPPPP---P-P--PP--P-PPPP--PP--P----PPPPP--P----PP-PP-P--P-
Hs= A -------PPPPP---P-P--PP--P-PPPP--PP--P----PPPPP--P----PP-PP-P--P-
J1= A PP-----PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-PPP-P--P-
Js1=A -------PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-PPP-P--P-
J3= A PP-----PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---PPP-P--P-
Js3=A -------PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---PPP-P--P-
J5= A PP-----PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-----PPP-P--P-
Js5=A -------PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-----PPP-P--P-
J7= A PP-----PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-------PPP-P--P-
Js7=A -------PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P-------PPP-P--P-
J9= A PP-----PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---------PPP-P--P-
Js9=A -------PPPPP---P-P--PP--P-PPPP--PP---P-P--PP--P-PPPP-P---------PPP-P--P-
K=  A PP-----PP-PP-P--P-
Ks= A -------PP-PP-P--P-
L=  A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP--PP--P----PP-PP-P--P-
Ls= A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP--PP--P----PP-PP-P--P-
M=  A PPP--P--PP--P-PPPP--PP---P-P--PP--P-PPPP--PP--P----PPPPP--P----PP-PP-P--P-
Ms= A --P--P--PP--P-PPPP--PP---P-P--PP--P-PPPP--PP--P----PPPPP--P----PP-PP-P--P-

The peals

438 @1 B C3 C1 C3 D B C9 D D D
438 @1 B D C3 C1 C3 B D D D C9
438 @2 ( C1 C3 D Ds G3 ) *2
438 @2 ( Cs1 C3 H D C3 ) *2
438 @2 C1 C1 C1 G1 Ds H D C9 D Cs1
441 @1 B C1 B D B C7 D B C9 D
441 @1 B C1 B D C9 B D C7 B D
441 @2 B C1 B Cs1 C3 G1 Ds H D C9
441 @2 B C1 B Ds G7 D Ds G3 C1 C3
441 @2 Bs C1 F H D C9 D Cs1 C1 C3
441 @2 Bs D C7 F H C3 C1 C3 Cs1 D
441 @2 C1 C1 K D Cs1 D Ds H C9 E3
441 @2 C1 C3 Cs9 H D M C1 K D Cs1
441 @2 C1 G1 Ds K C1 M D C9 D Cs3
441 @2 Cs1 C3 K C3 H D M D C3 Cs5
441 @3 C1 G1 Cs1 D Cs1 G1 Ds G7 H Cs1
441 @3 Cs1 C3 H Cs1 D Ds G3 Cs1 G3 G1
444 @2 ( B C1 B Ds G7 ) *2
444 @2 ( B Cs1 B C7 H ) *2
444 @2 ( C1 K D Cs7 M ) *2
444 @2 ( C7 D E1 Ds K ) *2
444 @2 B C1 B Cs1 D Ds H C9 E5 K
444 @2 B C9 D Bs B Ds F G3 C1 C3
444 @2 B C9 D Cs3 C1 G3 M B Ds K
444 @2 B Cs1 C3 F H D C9 B C3 Bs
444 @2 B Cs1 C3 K B C3 Cs9 H D M
444 @2 B Cs5 Cs1 B M D C7 K C3 H
444 @2 Bs C1 F K C1 M D C9 D Cs5
444 @2 Bs C9 E3 C1 C3 D Ds F K D
444 @2 Bs D C7 K C1 L H C7 Cs1 D
444 @2 Bs D M C3 C1 C3 Cs9 F K D
444 @2 C1 K D Cs5 Cs9 K C1 M D M
444 @2 C3 K C9 Cs3 D M D E1 Ds K
444 @3 B Cs1 G3 G1 Cs1 B Ds G7 H Cs1
444 @3 Bs Cs1 C3 G1 Ds G7 F G1 Cs1 D
444 @3 Bs Cs1 D Cs1 F G7 H Cs1 C1 G3
444 @3 C1 G1 Es1 Ds G9 D Cs1 K H Cs1
444 @3 C1 J7 H Cs3 Cs1 D Cs1 G1 Ds K
444 @3 C1 K D Cs1 G1 Ds J1 Cs9 H Cs1
444 @3 C1 K D Cs1 H Cs7 J3 Cs1 H Cs1
444 @3 Cs1 C3 K G7 D Ds G1 Es1 Ds G1
444 @3 Cs1 D Ds J1 Cs5 Cs1 G3 K C3 H
444 @4 C1 C1 K C9 Gs1 Hs H E1 Ds Cs1
444 @4 C1 C3 Gs1 Hs K C7 H E1 Ds Cs1
444 @4 C1 K C3 Cs1 C3 Cs5 Gs1 Hs H M
444 @4 Cs1 C3 Cs3 H M C3 Gs1 Hs K C3
444 @5 ( C1 G3 Gs1 Hs Cs1 ) *2
444 @5 ( Cs1 C3 Gs1 Hs G1 ) *2
444 @5 C1 G1 Cs1 C3 Gs1 Hs G3 Gs1 Hs Cs1
447 @2 B Bs B Cs1 B C9 B C7 F H
447 @2 B Bs B Ds F G7 B C9 B C1
447 @2 B Bs C1 F K B C9 D Cs7 M
447 @2 B Bs C9 E7 D Ds F K B C1
447 @2 B Bs D C7 K C9 Cs1 B L H
447 @2 B Bs D C9 B L G1 Ds K C7
447 @2 B Cs5 Cs9 K C3 K B M D M
447 @2 B Cs9 K B M C1 K D Cs7 M
447 @2 B Ds K B E5 K C9 Cs3 D M
447 @2 B Ds K B E9 D E1 Ds K C7
447 @2 Bs C1 K D Cs7 M C9 L K D
447 @2 Bs D E1 Ds K C7 D L K C9
447 @2 Bs D M C7 Cs9 K C1 L K D
447 @2 Bs D M D L K C3 K C9 Cs5
447 @3 B Cs1 G3 J7 H Cs3 Cs1 B Ds K
447 @3 B Cs1 G3 K B Ds J1 Cs9 H Cs1
447 @3 B Cs1 H Cs1 B Cs1 H Cs7 J5 K
447 @3 B Ds G1 Cs1 B Ds G1 Es5 K G7
447 @3 Bs Cs1 C3 F G7 F G3 Bs Cs1 D
447 @3 Bs Cs1 C3 G1 Ds J1 Cs9 F K D
447 @3 Bs Cs1 C3 H Cs7 J3 Cs1 F K D
447 @3 Bs Cs1 C3 K F G1 Es1 Ds G9 D
447 @3 Bs Cs1 D Cs1 F K C1 J7 H Cs5
447 @3 Bs Cs5 Cs1 F J5 K C3 H Cs1 D
447 @3 Bs Cs9 H Cs1 C1 K D Cs1 F J3
447 @3 Bs Ls G1 Cs1 C3 K G7 D Ds G3
447 @3 Bs Ls G9 D Cs1 K H Cs1 C1 G3
447 @3 C1 J9 D Cs1 K H Cs3 Es1 Ds K
447 @3 C3 K G7 D Ds J1 Cs3 Es1 Ds K
447 @3 Cs1 D Ds J1 Es3 K C9 Cs1 K H
447 @3 Cs1 D Ds J1 Es5 K G1 Ds K C7
447 @4 Bs C1 K C9 Gs1 Hs H L Cs1 C3
447 @4 Bs C3 Gs1 Hs K C7 H L Cs1 C3
447 @4 Bs E3 C1 C1 K C9 Gs1 Hs F Ds
447 @4 Bs E3 C1 C3 Gs1 Hs K C7 F Ds
447 @4 C1 C3 Fs K C9 Fs H E1 Ds Cs1
447 @4 C1 M E1 Ds Cs3 K C9 Gs1 Hs K
447 @4 C1 M E1 Ds Cs5 Gs1 Hs K C7 K
447 @4 Cs1 C3 Cs5 Fs H M C3 Fs K C3
447 @5 C1 G3 Fs Cs1 C3 Fs G3 Gs1 Hs Cs1
447 @5 C1 J3 Gs1 Hs Cs3 Cs1 C3 Gs1 Hs K
447 @5 C1 J3 Gs1 Hs Cs5 Gs1 Hs Cs1 C1 K
447 @5 C1 K C3 Gs1 Hs J1 Cs5 Gs1 Hs Cs1
447 @5 Cs1 C3 Fs G1 Cs1 C3 Gs1 Hs G3 Fs
447 @5 Cs1 C3 Gs1 Hs K C3 Gs1 Hs J1 Cs3
447 @6 Cs1 G1 Cs1 H Cs3 Gs1 Js5 K G1 Ds
447 @6 Cs1 G3 Cs1 K H Cs1 H Cs3 Gs1 Js3
450 @2 ( B Cs9 K B M ) *2
450 @2 ( B Ds K B E9 ) *2
450 @2 ( Bs C9 L K D ) *2
450 @2 ( Bs D L K C9 ) *2
450 @2 B Bs B Cs9 F K B C9 B M
450 @2 B Bs B Ds K B C9 B L G9
450 @2 B Bs C9 L F K B C9 D Bs
450 @2 B Bs D C9 B L F K C9 Bs
450 @2 B Cs9 K B M C9 L K D Bs
450 @2 B Ds K B E9 D L K C9 Bs
450 @3 B Bs Cs9 H Cs1 B Cs1 F J5 K
450 @3 B Bs Ls G1 Cs1 B Ds G7 K G7
450 @3 B Cs1 K H Cs3 Es3 J9 B Ds K
450 @3 B Ds J1 Cs3 Es5 K G7 B Ds K
450 @3 B Ds J1 Es5 K G9 Cs1 B Ds K
450 @3 Bs Cs1 C3 F J3 Bs Cs9 F K D
450 @3 Bs Cs1 C3 K F G3 Bs Ls G9 D
450 @3 Bs Cs1 D Ds J1 Es5 K F K C9
450 @3 Bs Cs3 Es1 Ds K C3 K F J9 D
450 @3 Bs Ls J5 K C9 Cs1 K H Cs1 D
450 @3 Bs Ls J7 K G1 Ds K C7 Cs1 D
450 @3 Bs Ls K C1 J9 D Cs1 K H Cs5
450 @3 Bs Ls K C3 K G7 D Ds J1 Cs5
450 @4 Bs C3 Fs K C9 Fs H L Cs1 C3
450 @4 Bs E3 C1 C3 Fs K C9 Fs F Ds
450 @4 Bs E5 K C9 Gs1 Hs K C1 L Ds
450 @4 Bs E7 Gs1 Hs K C7 K C1 L Ds
450 @4 Bs M L Cs3 K C9 Gs1 Hs K C3
450 @4 Bs M L Cs5 Gs1 Hs K C7 K C3
450 @4 C1 M E1 Ds Cs5 Fs K C9 Fs K
450 @5 ( Cs1 C3 Fs G3 Fs ) *2
450 @5 C1 J3 Gs1 Hs Cs5 Fs Cs1 C3 Fs K
450 @5 C1 K C3 Fs J3 Fs Cs5 Gs1 Hs Cs1
450 @5 Cs1 C3 Fs K C3 Gs1 Hs J1 Cs5 Fs
450 @5 Cs1 C3 Gs1 Hs K C3 Fs J3 Fs Cs3
450 @6 ( Cs1 K H Cs3 Js3 ) *2
450 @6 Bs Cs1 H Cs3 Gs1 Js5 K F Cs1 G3
450 @6 Bs Cs3 Gs1 Js5 K G3 G1 Cs1 F Ds
450 @6 Cs1 K G9 Gs1 Js1 Es1 Ds Cs1 K H
450 @6 Cs1 K H Cs3 Js1 Cs3 Js5 K G1 Ds
453 @3 B Bs Cs3 Es5 K F J9 B Ds K
453 @3 B Bs Ls J7 K G9 Cs1 B Ds K
453 @3 B Bs Ls K B Cs1 K H Cs7 J9
453 @3 B Bs Ls K B Ds J1 Cs9 K G7
453 @3 Bs Cs1 D Bs Ls J7 K F K C9
453 @3 Bs Cs5 Bs Ls K C3 K F J9 D
453 @4 Bs E7 Fs K C9 Fs K C1 L Ds
453 @4 Bs M L Cs5 Fs K C9 Fs K C3
453 @5 Cs1 C3 Fs K C3 Fs J3 Fs Cs5 Fs
453 @6 Bs Cs1 K G9 Gs1 Js1 Es3 K F Ds
453 @6 Bs Cs3 Js1 Cs3 Js5 K G3 K F Ds
453 @6 Bs Cs3 Js5 K F Cs1 K H Cs3 Js3
453 @6 Bs Ls Cs1 K H Cs1 K G9 Gs1 Js3
456 @3 B Bs Cs9 K F J9 B Bs Ls K
456 @6 ( Bs Cs3 Js5 K F ) *2
456 @6 Bs Cs1 K G9 Gs1 Js5 K F Bs Ls

How it works

From Philip Saddleton: Ringing Theory, June 2012

At about the same time as Andrew Johnson produced his famous bobs-only 10-part, he discovered a way of splitting the rows into five identical two-part blocks but could not join them without singles (Nigel Newton independently discovered the same block). Andrew says that he pointed out at the time that this block was very similar to the 10-part peal (containing only two sixes per part that do not appear in the 10-part). I must have missed this, or I am sure I would have looked into it further.

Anyway, 17 years later Andrew has found that by mixing together the two blocks more bobs-only peals can be found. The peal we rang this evening has one additional linkage which is quite complex: adding a pair of bobs jumps from one half of the peal to the other but introduces a false six. The corresponding six is got by bobbing two elements of a Q-set and omitting a bob. The attached sheet attempts to show how it all works:

• corresponding sixes from different parts are on the same row
• the sixes introduced by teh twin-bob linkage are highlighted in orange
• the part q-sets are yellow
• the omits are green
• other linking q-sets of omits are yellow

Using this and another twin bob linkage, Andrew now has 148 new compositions.

PABS