Sonification of Complex Data Sets: An Example from Basketball

Frances L. Van Scoy

Functions over the Same Domain

Next, let us draw in music a full circle. That is, we will present the two functions

f(t) = sqrt(k2 - t2) and g(t) = - sqrt(k2 - t2).

Figure 4 Graph of f(t) = sqrt(k2 -t2) and g(t) = sqrt(k2 -t2)

We now play two notes simultaneously, one representing the value of f(t) and one representing the value of g(t).

Music 5 Musical representation of graph of f(t) = sqrt(k2 -t2) and g(t) = sqrt(k2 -t2)

This works, to a certain extent, but has the disadvantage of producing sounds which are disharmonic.

Consider the pair of functions f(t) = t and g(t) = -t.

Figure 6 Graph of either f(t) = t and g(t) = -t or f(t) = abs(t) and g(t) = - abs(t)

These two functions can be represented by two chromatic scales, one ascending and one descending.

The resulting music has the same problem of that generated by the circle above of being unpleasant to the Western ear.

 

Music 6 Musical representation of graph of f(t) = t and g(t) = -t

It has another problem, however, in that the music is indistinguishable from that generated by the pair of functions

f(t) = abs(t)

and

g(t) = - abs(t).

Two possible solutions are choosing easily distinguished instruments for the two functions, or using pitch for one function and duration for the other.

For example, we might represent a relatively small value by a whole note and a relatively large value by eight eighth notes.

Simplifying the number of pitches for this example, we have two distinguishable melodies for f(t) = t, g(t) = -t and for f(t) = abs(t), g(t) = - abs(t).

Music 7 Musical representation using pitch and duration of ft) = t and g(t) = -t

Music 8 Musical Representation using Pitch and Duration of f(t) = abs(t )and g(t) = - abs(t)