[r-t] Quarter Peals of Treble Dodging Major

[Philip Earis]

Stephen Beckingham has created an interesting new website (http://bex280.x10.mx/), which he describes in an article published in this week’s Ringing World (page 123). 

He has essentially done a combinatorial search for musical (tenors-together bobs-only) quarter peal compositions of treble-dodging major methods, ranking them by their count of 4-bell runs from the front or back (internal runs are not included in the analysis).

The composition search used SMC32, with some script to run the different methods (both rung and unrung) through.

The top-scoring method, with 118 runs, is the double method Hat & Feathers Surprise (&-36-4-2.5.36.4.7-5-36-7,2).  Many of the top-scoring methods start –34-4-2 and hence generate runs from traditional run courses, though methods with awesome mega-tittums courses (like Muppet Show, and Superlative) also perform strongly.

Stephen understandably puts some restrictions on the unrung methods, to bring the search-space down.  One of these is to exclude methods with internal 7ths made...I’d like to see such methods included if possible, not least because the top-scoring (rung) method has this property.  Relaxing the restriction on tenors-together would also be interesting (I understand some new constraints might need to be introduced).

Incidentally, Richard Smith and I worked on an analogous exercise for the most musical 720 of minor methods a few years back – see http://www.cantabgold.net/users/pje24/music.html
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