Compositions of the Decade 2000-2009 - 4 - Triples

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A Review by Philip Earis - continued

The 1990s was a landmark time for triples. The first peal of bobs-only Stedman in 1995 was of course notable, though Andrew Johnson’s 10-part construction later that year was the crowning compositional glory. The decade finished with the 1999 publication of Philip Saddleton’s composition collection for Stedman and Erin triples, summarizing progress to date. It can be seen at http://www.ringing.info/stedman.pdf.

So what has happened in the past 10 years? Has it been simply a case of tying up a few loose ends? Well, no, not really. Whereas the 1990s saw compositional progress in a few familiar and simple methods, this has been expanded in the past decade, leading to developments across an interesting range of methods.

A driving motivation remains of producing peals consisting of pure triple changes (ie only using the changes 1,3,5 and 7). It is true that the compositional challenge of bobs-only Erin triples remains unsolved - the likely suspects have invested quite a lot of time into the problem, so far without tangible success. However, a key theme of recent years has been the creation of interesting new triple-change compositions, as we shall see.

Triples composing is arguably the most mathematically-intense stage. Compositions are almost exclusively based around 5040 change extents – there is no room for the selectivity of higher stages, nor typically the flexibility offered by multi-extent blocks at lower stages. Things have to work for a good reason, and hence beauty and elegance are often evident.

The innovative new compositions I have selected below have come from a fairly small community of composers. The formidable triples-ringing strength of the Birmingham band has been very evident, and indeed a driver for many of the compositional developments.

1) Quick Six Triples – Philip Saddleton – Composition unrung (method first rung December 2004)

“Quick six” triples, as the name suggests, has 30-change divisions consisting of quick sixes. It was the winning touch in the “Triples Eisteddfod” in Birmingham in December 2004.

The notation is: 3.1.7.1.3.1.3.1.7.1.3.1.3.1.7.1.3.1.3.1.7.1.3.1.3.1.7.1.3.7

It's a beauty. Philip Saddleton, its creator, regards it “the most straightforward construction” of an extent of triples. And he’s a man who should know.

 5040 Quick Six Triples
123456 4 6 7 ---------------- 415263 - - - 642315 - - 465312 - 514623 - - 256314 - - 524316 - 351264 - - - 632451 - - 361452 - 153624 - - 216453 - - 321546 - - ---------------- Repeat

In Philip’s words:

“The coset graph for the Scientific group using these three place notations consists of five hexagons with other links and this Hamiltonian cycle is easily found. The blocks can be linked by replacing two quick sixes (the last two for the composition below) by two slow sixes, traversing the hexagons in reverse, and cunningly joining two blocks without introducing any false rows”

Who wouldn't love traversing hexagons in reverse? Whilst extremely tidy, my feeling remains that a call only acts on one row, meaning the composition would be better described as spliced.

In a similar concept, see also compositional choice “Artistic Triples” later in this article.

2) Titanic Triples – Alan Burbidge – January 2005

Titanic is sort of Stedman reduced – it consists of one row of right-hunting on three followed by one row of wrong-hunting on three. The notation for a division is simply 7.1.7.3 – this gives a course with two types of “six”.

The cinques was first pealed in 1987, but the past decade saw the first composition of an extent of Titanic Triples – a tour-de-force 3-part composition by Alan Burbidge. This is reproduced from the St Martin’s Guild website as below.

 5040 Titanic Triples
1234567 A B C 4352167 - - - 2534167 - B6 - 4315267 - - - 5123467 - - - 3241567 - - - 1423567 - B6 - 3254167 - - - 4523167 - B6 - 3215467 - - - 5142367 - - - 2415367 - B6 - 5134267 - - - 4321567 - - - 1253467 - - - 3542167 - C* 2453167 - B6 - - B6 3521467 B6* - 1245367 - - - 5432167 - - - 2314567 - - - 3 times 7th unaffected 6th sub observation
Can be transposed for 1/2 observations with normal start. 1 unaffected, 2 sub observation
Standard A S8, S13 B S1, 3, S7, S8, S12 C 3, S5, S6, S7, S10, 12, 13
Variations B6 S1, 3, 6, S7, S8, S12 B6* S3, 6, S7, S8, S12 C* S1, S3, S5, S6, S7, S10, 12, 13
- denotes standard course
861 calls (255 bobs, 606 singles)

3) “In course doubles” Triples - Andrew Johnson – October 2006 / November 2009 (Unrung)

Building on his Doubles “composition of the decade”, where he produced a very neat in-course 120 of doubles with each row occurring once at each stroke, Andrew Johnson has extended the concept to produce a lovely true triples extent.

The triples principle takes the same notation as the doubles, replacing two “5s” in the notation with “7s”. This thus becomes the first triples principle with 24-change divisions, and very nice it is too.

e.g. 1.3.5.1.3.5.1.3.7.3.5.3.1.3.5.1.3.5.1.3.7.3.1.3

The principle results in an extent in B-blocks, where a B-block is one of these 120 change courses.

 5040 Unnamed Triples
1 2 3 4 5 6 7 8 9 0 ------------------- - - - - - - - - | - - - - - - - - | - - - - - - - |A - - - - - - - - | - - - - - - - - | - - - - -  : | ------------------- 5A - - - - - - - - - - - - - - - - - - - - - - - - - - s - - - - - - - - - - - - - - - - - - - - - - - s - - -  : ------------------- method = 1.3.5.1.3.5.1.3.7.3.5.3.1.3.5.1.3.5.1.3.7.3.1.3 bob = 5 replacing 7 single = 345 replacing 7
 5040 (Different) Unnamed Triples
2314567 1 2 3 4 5 6 7 8 9 0 1 2 3 4 ----------------------------------- 2341576 s - - - - - - 6231754 s - - - - - - - - - 4627315 - - - - - - - - - - - - 1563427 - - - - - - - - - - 3154627 - - - - - - - - - - - 5642371 -  : ----------------------------------- 7564132 - - - - - - - - - - | 2751643 - - - - - - - - - - - - | 4376251 - - - - - - - - - - |A 6432751 - - - - - - - - - - - | 3725614 -  : | ----------------------------------- 2314567 5A ----------------------------------- method = 3.1.7.3.1.5.3.1.3.1.3.5.3.1.7.3.1.5.3.1.3.5.3.5 bob = 5 replacing 7 single = 34567 replacing 7

In Andrew’s words, “The starts of the second method is chosen so the starts for bells in the plain course is close to Stedman in feel - with quick and slow work. I'm not sure why I chose the starts/rotation of the first - possibly for 46s or 567s in the plain course. 567 singles don't work well as you rapidly run false. The methods are asymmetric so in general you need in-course singles to avoid having to ring methods backwards. If you single in B-blocks then you can have out of course singles (c.f. Grandsire ?)”

Andrew also feels there’s scope for compositional improvement (principally more consecutive plain leads) – watch this space…

4) 5040 Artistic Triples – Eddie Martin – Rung June 2009

Eddie’s description of this new pure triples extent tells you all you need to know:

“To be truly artistic, a method along the lines of 'Scientific Triples' really ought to be able to get 5040 in pure triple changes. What is needed is a direct shunt from one lead block to another, without involving any other lead blocks. I’ve looked at various possibilities & the only one that I can find is to substitute two consecutive quick sixes for two consecutive slow ones. (This will work in ‘Quick six Triples except for being two slow in lieu of two quick!) So I looked for something a bit more challenging than ‘quick six triples’ & came up with the following:

 Plain = 7.1.7.1.7.3.7.3.7.1.3.1.7.3.7.3.1.3.1.3.7.3.1.3.1.3.7.1.7.1  gives  5671234 
 x = 7.1.7.1.7.3.7.3.7.1.3.1.7.3.7.1.3.1.3.1.7.1.3.1.3.1.7.1.7.1  gives  5641327"
5040 Artistic Triples
1234567 3 5 6 --------------------- 6521347 x x x 3512647 x 5641327 x x -------------- 2563147 x x 1536247 x 5243167 x x -------------- 6125437 x x x 4152637 x 1635427 x x -------------- 2164537 x x 5146237 x 3215467 x x x --------------------- 6423157 x x x 1432657 x 4653127 x x -------------- 2461357 x x 3416257 x 4251367 x x -------------- 6324517 x x x 5342617 x 3614527 x x -------------- 2365417 x x 4356217 x 1234567 x x x ----------------------

The composition was rung in hand by the Birmingham band in June 2009, building on their prior achievement of ringing the first peal on Scientific in hand the previous November.

In a development based on Scientific triples on a slightly different tangent, in April 2009 Colin Wyld used Scientific as the starting point for a composition of spliced, adding its reverse (1.7.1.7.1.7.1.5.1.5.1.7.1.7.1.7.1.7.1.5.7.1.7.1.5.1.7.1.3.7, “New Scientific”) into the mix.

Whenever a double (place notation is 347 replacing the final 7ths place) is called there is a change of method and whenever there is a change of method there must be a double. He produced a regular 7-part composition:

S, 2N, 3S, N, 4S, 2N, 5S, N, 2S, 3N (there is a call at the part end so that the next part can start with Scientific) Part end 5362714

He described things more fully at http://www.bellringers.org/pipermail/ringing-theory_bellringers.net/2009-April/002964.html.

Intriguing, Colin left the Fermat-esque comment at the end of his post,

“…I have produced two more compositions based on combinations of 12 lead, 4 lead, 3 lead and 2 lead splices. I haven't worked out the specific arrangements but there is the potential for 40+ methods. The second has no calls except changes of method and triple changes throughout. I will submit these when I can get the formatting sorted out”

I am still waiting for these new compositions to appear – they would surely have made this article if published.

5) 21-part Stedman Triples - Richard Grimmett – November 2004

Richard generated a list of 13778 compositions of Stedman triples that have a 21-part structure. These can be seen at: http://www.smgcbr.org/ringing/composition/stedman7/21part/sted21coll.htm.

The compositions make use of two similar blocks – one that cyclically rotates through the bells, whilst the other rotates through the rounds -> queens -> tittums transition.

This idea is very nice, and a direct analogue of the 54-part peals of Caters developed by me and Ander Holroyd in early 2003. In fact, looking at Richard’s website, it looks like Brian Price got there with Stedman triples compositions on this plan even earlier.

Nevertheless, a nice development. The first composition in Richard’s collection, which has a maximum of 3 consecutive calls, is given as an illustrative example:

 5040 Stedman Triples
 Contains 351 calls. 231 bobs, 120 singles.
2314567 1 2 3 4 5 6 7 8 9 10 ------------------------------------- 2361574 s - - | 4231576 - s - - |A 7264531 - - | 5216374 s - s - - - | ------------------------------------- 7156342 s s - - | 2716354 - s s - - |B 5742316 - - | 3764152 s - s - - - | ------------------------------------- 7431526 5B 5732461 A 6143572 6B 5647123 A 2314567 6B -------------------------------------

6) Innovative original triples – Ander Holroyd (peal attempted 2007)

Continuing the theme of Dixonoid compositions, Ander Holroyd has a very clever extent of original triples. All bells plain hunt, with a silent handstroke bob (5 in the notation instead of 7) made after bells 1,2 or 3 lead. This gives a course of 210 changes, with a simple extent resulting from ringing the 24 courses of this. The different courses are obtained with omits and doubles (34567) – the only slight shame being a “pure“ triples extent cannot be produced.

 5040 Triples
54 89 1234567 -------------- 1 1 7546 D 1327456 2 (1) 4765 -------------- 6 part (1) in parts 1,3,5 only

(See http://www.math.ubc.ca/~holroyd/comps/o7.txt for more)

In November 2009 Alan Burbidge produced an extent he describes as “Variable treble Grandsire triples”. Here, the “calls” reset the notation to the beginning of a lead of Grandsire triples, with a new treble.

Alan has produced both a 10-part and a 7-part composition – as with the Holroyd composition, both of these (and indeed any composition on this plan) need special singles.

Whilst I’m sure it is interesting to ring, I feel this concept feels a bit more contrived and perhaps lacks the clever design framework of the Holroyd approach. I might be missing something.

Alan is currently writing an article for the Ringing World about the composition, and so on request I haven’t reproduced the composition in this article.

7) Stedman Triples without adjacent calls - Eddie Martin – November 2009

I think all rung Stedman triples compositions have adjacent calls – clearly with twin-bob and B-block compositions this is a rather fundamental property.

Eddie Martin has produced a very simple 10-part composition that avoids adjacent calls completely. It’s arguably the quickest ever Stedman triples composition to learn. The only drawback in the third type of call used, which disrupts the frontwork:

 5040 Stedman Triples
Each course called 1s 5s 8s 10s 12* 12* = bob if marked ‘-‘ or places 12567 if marked “x” 2314567 - 2461357 - 2156437 - 2635147 x 6534217 x 5431627 -* 5123467 10 part
Ring x instead of bob marked * in parts 3 and 8

Eddie has produced other examples of compositions without adjacent calls which just have two types of call (though these also have the 12567 call)

8) Erin Triples - Eddie Martin - June 2006

A very neat 5-part composition of Erin Triples. Whilst there are exact 5- and 10- part compositions of Erin by Andrew Johnson in Philip Saddleton’s 1999 collection, Eddie’s exudes appeal to me, again due to the elegant regularity of the courses

 1234567
 ----------------------------
 3562417  s2 s4  (24 changes)
 4356217  A  B
 2435617  A  B
 6243517  A  B
 5624317  A  B
 4627153  A  B*
 5123467  A* B
 ----------------------------
 5-part
A (84 changes) = 3 5 s7 9 11 s14 A*(72 changes) = 1 3 s5 7 9 s12 B (84 changes) = 5 s7 9 s14 B*(72 changes) = 5 s7 9 s12

9) Stedman triples composition that is symmetric about calls – Philip Saddleton – December 2004

Another characteristic of Stedman triples (and Stedman at higher stages, but not doubles) is that it is a rare example of method which is not symmetric about the (traditional) calls.

Philip Saddleton countered my assertion with the argument that pairs of bobs give a symmetrical lead. To produce an extent, he joined twin bob courses with calls at the half-six:

 5040 Stedman Triples (T Thurstans arr T Brook arr PABS)
1234567 2 3 4 ----------------- 6354127 - - |A 234516 - 2 - | ----------------- 5123467 3A ----------------- 6325417 - - s |B 135246 - 2 - | ----------------- 4-part
p=3.1.7.3.1.3.1.3.7.1.3.1 b=3.1.5.3.1.3.1.3.5.1.3.1 s=3.1.7.3.1.347.1.3.7.1.3.1

10) 10080 Triples – (Stedman - Rod Pipe – attempted December 2008; Erin – Philip Saddleton – rung August 2005)

Rod Pipe has produced a 7-part 10080 of Stedman triples with each row occurring once at handstroke and once at backstroke.

 2314567
 3425167 -
 3451276 S
 4132567 S
 4125367 -
 1543267 -
 1536472
 5617324
 5673124 -
 6351742 S
 6314527
 3462175
 3427651
 4736251 -
 4762351 -
 7245613
 7256413 -
 2674513 -
 2645731 S
 6523417
 6534217 -
 5462371 S
 5427613
 4756213 -
 4762531 S
 7243615
 7236415 -
 2674315 -
 2643751 S
 6325417
 6354217 -
 3461572
 3415672 -
 4537126
 4571362 S
 5143762 -
 5136427
 1652374
 1623574 -
 6315274 -
 6352147 S
 3261547 -
 3215647 -
 2534176
 2547361
 5723416 S
 5734216 -
 7452316 -
 7421563
 4176235
 4162753 S
 1245637
 1256473 S
 2614573 -
 2647135
 6723451
 6734215 S
 7462315 -
 7421653
 4175236
 4152763 S
 1247563 -
 1276435
 2614735 -
 2643157
 6321475 S
 6317254
 3762145 S
 3721645 -
 7136254 S
 7165342
 1573642 -
 1534726
 5412367
 5423167 -
 4356271
 4367512
 3745621 S
 3756412 S
 7631524
 7615324 -
 6573142 S
 6534721
 5462317
 5423671 S
 4356217 S
 4362571 S
 3247615
 3276451 S
 2634751 -
 2645317
 6521473
 6514273 -
 5467132
 5473621
 4356712 S
 4367521 S
 3745612 S
 3751426
 7132564
 7125364 -
 1576243
 1562743 -
 5217643 -
 5276134 S
 2653741
 2637514 S
 6725314 -
 6751243
 7162543 -
 7124635
 1476253 S
 1465732
 4517623 S
 4576132 S
 5643721
 5632417
 6254317 -
 6241573
 2167435
 2174635 -
 1423756
 1437265 S
 4712365 –
 4726153*
7645231 7652431 - 6273514 6235714 - 2567341 S 2574613 5421736 5417236 - 4752163 S 4726531 7643215 7632415 - 6274351 S 6245713 2567431 S 2573614 5321746 5317246 - 3752146 - 3721564 S 7136245 7164352 1473652 - 1436752 - 4617325 S 4673125 - 6341725 - 6312457 3265174 3251674 - 2136547 S 2164375 1423675 - 1437256 4712356 - 4725163 7541236 S 7512436 - 5274136 - 5243761 2357416 S 2374516 - 3421765 3417256 S 4732156 - 4725361 7543216 S 7532416 - 5274316 - 5241763 2157463 - 2174563 - 1426735 1463257 4315672 4356127 S 3641527 - 3612475 6237154 6271354 - 2163754 - 2137645 S 1726354 S 1763254 - 7315642 7354126 3471562 S 3415762 - 4536127 4562371 5247613 5271436 2153764 2137564 - 1726345 1763245 - 7314652 7346152 - 3671425 S 3612754 6237145 S 6271345 - 2163745 - 2134657 1426357 - 1465273 4517632 4576123 S 5641732 S 5617423 S 6752134 6723541 7365241 - 7354612 3471526 3415726 - 4537162 S 4576321 5643712 S 5637421 S 6754312 S 6741523 7162435 7124653 S 1476235 S 1463752 4315627 4352176 3247561 3276415 2634715 - 2647351 S 6725413 6751234

Philip Saddleton also produced a 10080 of bobs-only Erin Triples that was rung in August 2005

 10080 Erin Triples
1234567 ------- 4561732 a | | 1365247 b | | 6243517 c |X | 1435267 d | | 6251437 e | | 5432167 c | | ------- | 2165734 a | |A 5361427 b | | 5423176 f | | 4631275 2g | | 5627413 h |Y | 4312576 j | | 3625174 2g | | 4617352 h | | 4512367 k | | ------- 1234567 4A ------- 2154367 Y |B 3451267 X | ------- 1234567 4B -------
a = 2.4.5.8.10.11.12 (12) b = 1.6.8.9.12 (12) c = 2.4.5.6.7.9 (9) d = 2.4.5.6.7 (8) e = 3.4.5.6.8 (8) f = 5.6.8 (9) g = 1.3.4.5.6.8 (9) h = 1.4.5.7.12 (12) j = 1.2.3.5.8.9.11 (12) k = 1.2.3 (5)

See Also