The most musical extent of minor | Ringing Homepage Email me |

What is the most musical possible 720 of minor? | ||

What is the most musical extent of minor? Obviously, giving individual rows a musical rank will not help when comparing different 720s. However, in different methods the rows will be ordered differently, and this can produce interesting musical differences. One musical effect I like in ringing is having runs of bells continuing from one row into another, handstroke to backstroke. In this case, a <n-run> is defined as being a run of n bells, which can be split accross adjacent hand/backstroke rows. There are therefore 12 possible <6-runs>, ie for symmetric treble-dodging methods: 123456 =1 H .....1 =1 B 234561 H ....12 =1 B 345621 H ...123 =1 B 456213 H ..1234 =1 B 5621.. H 612345 =1 B 621... and the six corresponding reverses.I contacted Richard Smith, who kindly generated a musical rank for the standard extent of all treble-dodging (778) and plain minor methods with regular lead-heads and no more than two consecutive blows in any position. Four different criteria were used to assess the music of the 720: <4-runs>, <5-runs>, <6-runs>, and wraps of rounds (forward <6-runs>). As expected, treble-dodging methods gave much higher scores than plain methods. Acting on a hunch, I also asked Richard to calculate the values if the extents were rung out of course (here starting 124356). The results for the top and bottom scoring methods for in-course 720s, as well as some standard methods, are summarised in the tables below: <4-runs> 67 Hertfordshire D &3-34.1-2-23-34-1,2 66 Langleybury S &34-3.4-2-23-2-1,6 66 Tollesbury D &3-34.1-2-23-2-5,2 65 Badgeworth TB &-34-1-5-1-2-1,6 65 Redbourn S &3-3.4-2-23-2-3,2 65 College Bob III S &-5-4-5-3-2-5,2 ... 57 Carlisle S &34-3.4-2-3-4-5,2 56 Cambridge S &-3-1-2-3-4-1,6 53 London S &3-3.4-2-3.4-4.3,2 52 Norwich S &-34-4-2-3-34-1,6 ... 44 Offenham D &-3-45-5-1-2-5,6 <5-runs> 25 Hertfordshire D &3-34.1-2-23-34-1,2 24 Untitled D &5-34.1-2-23-4-3,2 24 Untitled D &5-34.1-2-23-34-1,2 22 Langleybury S &34-3.4-2-23-2-1,6 22 Middlesex D &3-34.1-2-23-34-5,2 22 Tollesbury D &3-34.1-2-23-2-5,2 ... 19 London S &3-3.4-2-3.4-4.3,2 16 Carlisle S &34-3.4-2-3-4-5,2 15 Cambridge S &-3-1-2-3-4-1,6 15 Norwich S &-34-4-2-3-34-1,6 ... 11 Gresley D &-5-1-2-23-4-5,2 <6-runs> 09 Hertfordshire D &3-34.1-2-23-34-1,2 ... 07 London S &3-3.4-2-3.4-4.3,2 05 Carlisle S &34-3.4-2-3-4-5,2 04 Norwich S &-34-4-2-3-34-1,6 03 Cambridge S &-3-1-2-3-4-1,6 <Runs of rounds> 05 Letchworth S &5-3.4-2-23-34-3,2 05 Fincham S &3-5.4-2-23-2-3,2 05 Sandwich S &34-5.4-2-23-4-3,2 05 Untitled S &34-5.4-2-23-4-3,6 ... 03 London S &3-3.4-2-3.4-4.3,2 02 Carlisle S &34-3.4-2-3-4-5,2 02 Cambridge S &-3-1-2-3-4-1,6 01 Norwich S &-34-4-2-3-34-1,6 Interestingly, extents rung out of course tend to score higher on all the scales. No method has all six runs of rounds, but Buckland Brewer Delight (&-34-45-5-1-2-1,2) has five when rung out of course. It also manages 10 <6-runs>, 27 <5-runs> and 67 <4-runs>: higher than any extent rung in-course. Still higher for <4-runs> when out of course are Bingley Delight (&-3-45-5-1-4-1,6) with 71, and Fryerning Surprise (&-34-4-2-23-2-3,2) and Offenham Delight (&-3-45-5-1-2-5,6) with 70. As can be seen from the tables, Offenham is at the bottom of the list for extents rung in-course! Full details of all the methods can be found by downloading this Excel file (434kb). The 46 regular plain methods score considerably lower than treble-dodging methods. The maximum number of <6-runs> is 7, scored by St James Youths Exercise (&3.4-1-3,2) and Brentford (&34.1-1.34.1,2). |