Are the melodies fractal?

So then, can both be considered fractal with respect to note duration?

No. Though they contain an identical distribution of durations, the first example (above) simply states the sorted set of values, starting with the second longest duration, proceeding to the shortest, and then wrapping back around to the longest. Furthermore, each measure contains only a single duration value. There is no suggestion of a distribution of elements sufficiently heterogenous that a given sub-region might contain, on average, roughly the same distribution as the whole piece. |

The second example, by contrast, is a far more convincing. With the exception of measures 4 and 8, which are filled by whole notes, each measure contains some combination of different duration values. |

Return to Duration Scaling.

© 2004 Harlan Brothers