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Binary Maths for Counting Bars

Here is an ingenious method of counting developed by young bassoonist and Oxford maths student, Ben Hopson. This uses binary* arithmetic, the number system at the heart of all computers.

The right-hand fingers are given numbers, thus:

   First finger:1

   Second finger: 2

   Third finger:4

   Fourth finger: 8

   Thumb:16

Each successive number is double the previous one. Use the index finger for one because it has to move the most. The sum of the fingers you have down represents the bar of rest you are in.

For example:

   1st down = 1

   1st up 2nd down = 2

   1st down 2nd down = 3

   1st up 2nd up 3rd down = 4

   1st down 2nd up Jrd down = 5

   1st up 2nd down 3rd down = 6

   1st down 2nd down 3rd down = 7

   1st up 2nd up 3rd up 4th down = 8

Next, the left-hand fingers are given these numbers:

   Thumb 32

   First finger 64

   Second finger 128

   Third finger 256

   Fourth finger 5 12

At first sight this looks unattractively complex. Yet it is not as difficult as it looks, and fits well with the tendency to group music in multiples and subdivisions of 32. Keep an open mind. Give yourself a few minutes to work it out. Ben Hopson states that it is easier to get used to than bassoon fingerings! He points out that having perfected the system, you can count to 3 1 on one hand, and 1 023 using both hands. At thirty bars-per-minute in common time that amounts to over half an hour of rests. That should be enough!

* Our normal counting system is decimal, that is, base ten. Binary maths, counting in base two, came to everyday attention in Britain when it began to be taught in schools in the late sixties and early seventies.

This report first appeared in Crescendo magazine, August 1998
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