Last week, I showed a first version of the animation of beating patterns. The application is more extensive now. You may find the new animation here (sorry it’s in Dutch).

You may control:
– the direction of the movements: for right or left-handed people
– the time: two, three or four beat
– the shape of the lower part of the movement: a circle, a straight line or something in between
– the distance between the beating points
– the placement of the last beat: in the middle (at the same spot as the first beat) or a little to the outside
– the speed of the movement
All controls may be combined. You may create more than a hundred different beating patterns.

In programming the animation, I tried to make the movements as objective as possible. I didn’t start from an ideal beating pattern, but instead I made assumptions about the movement and the shape followed from those.

The starting points for the animations the following:

• The beating points lie on the same height. If you read the books, you will find a lot of schemes in which this is not the case. The 1 is often made lower than the other beats. However, in the past fifty years or so, students are taught that the beating points should lie on the same height. The arguments for that are: a) Musicians have to be able to predict where the beating points lie and this is more difficult if the beating points lie on different heights. b) If you make the last beat high, you have little room left to make a subdivision on that beat.
• The movement between the beats are equal in length. With that the speed of beating is more or less constant. Thus, the distance to the left and the right is comparable to the height of the 1. One of the consequences of that choice is that the movement from 1 start to go to the right although the 2 is on the left. Without this, the movement from 1 to 2 would be too short.

For those who are interested below is explained the algorithm of the movements:

• The elementary movement of the beat is the bounce. This movement is comparable to that of a bouncing ball. Gravity pulls on the ball, upward the movement is unilaterally delayed, downward it is unilaterally accelerated. According to Newton:
x = ½ a t²

• In the animation the basic movement is the anchor movements. You will see this figure if you set the distance between the beating points to zero. The advantage of this movement is that it is clearly defined. In the anchor you make a vertical movement to 1, a movement to the left on 2 and a movement to the right on 3.
• In the anchor you are making a unilaterally accelerated movement. On the last beat you this is vertical. On the other beats it is slanted.
• In the anchor the maximum movement is 45 degree. The direction of the movement is clearly to be distinguished from the vertical movement for 1. And yet, the vertical component is clear enough so the beating point can be observed easily.
• In the anchor you might make the slanted movements over a part of a circle. In that case:
arc = ½ a t²

In that case the beats hardly get any accents, because the movements are fluid. The alternative is to move in straight lines. In that case the beating points are more accented, because you are making a corner. In the animation you have the possibility to choose an intermediate form as well, in between a circle and a straight line.

• as stated, the anchor is the basic movement of the animation. But in the beating technique it is convention to make the beats on different spots. In the four-beat pattern the 2 is on the left and the 3 on the right. To create such a pattern, on top of the anchor movement a second movement is made. This one is unilateral as well, resulting in a fluent movement.