Fractal Music

Exercise 2 Fractality

By design, this composition is fractal with respect to duration.
Here is a table of the duration values. Remember that we started with a phrase consisting of eight quarter notes and repeated this phrase a total of six times.

Quarter note48
Dotted quarter note32
Whole note12

The smallest duration increment in our table is an eighth note (the difference between a quarter note and a dotted quarter note). If we wish to measure duration in whole units, we can multiply these values by eight:

Here is a log-log plot of this data. It demonstrates exactly what we would expect: a power law relation between the duration of notes and the number of notes of each duration.

Return to Exercise 2.