Representation of Simple Functions

We initially began looking at ways to represent minute-by-minute scores from basketball games. We mapped each nonnegative integer between 0 and 108 to a note in the chromatic scale. That is, we had two functions f and g each with domain the integers between 0 and 40 and range the integers between 0 and 108. The value of f(t) corresponded to the score of one team when 40-t minutes of playing time in the game remained and g(t) to the score of the other team at that time.

For example, Music 2 shows the music generated this way from the first 10 minutes of the basketball game described later in this paper.

This approach has several disadvantages: nine octaves are required (beyond the range of a piano keyboard or other instrument), the two notes representing the current score of each team often are dissonant, and unless a different instrument is chosen for each team it is difficult to determine which team is ahead.

We then began looking at simpler functions.