Fractal Music

Duration Scaling

Scaling Plots

Here is a table of the durations and respective counts contained in each melody.

Based on the table, we can use the logs of the set of ordered pairs, {(1/8,16), (1/4,8), (1/2,4), (1,2)}, to generate a log-log plot of the musical data.

Because the resulting points lie on a straight line, we can assert that both melodies obey a power law distribution.

However, being that the examples are relatively short, we need to be careful about how we characterize their distribution of elements; each collection of notes represents too small a sample on which to make broad statistical generalizations. For the sake of argument, though, we can imagine each melody as part of a larger composition that continues in a similar fashion.

Return to Duration Scaling.

© 2004 Harlan Brothers