We present an in-depth analysis of the fractal nature of 21 classical music pieces previously shown to have scale-free properties. The musical pieces are represented as networks where the nodes are musical notes and respective durations, and the edges are its chronological sequence. The node degree distribution of these networks is analyzed, looking for self-similarity. This analysis is done in the full network, in its fractal dimensions, and its skeletons. The assortativeness of the pieces is also studied as a fractal property. We show that two-thirds of these networks are scale-invariant, i.e. scale-free in some dimension or their skeleton. In particular, two pieces were given attention because of their exceptional tendency for fractality.

中文翻译：

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古典音乐网络的自相似性

我们对先前显示具有无标度特性的 21 首古典音乐作品的分形性质进行了深入分析。音乐作品被表示为网络，其中节点是音符和相应的持续时间，边缘是其时间顺序。分析这些网络的节点度分布，寻找自相似性。这种分析是在整个网络、分形维数和骨架中完成的。碎片的分类也作为分形属性进行研究。我们表明，这些网络中有三分之二是尺度不变的，即在某些维度或其骨架上是无尺度的。特别是有两件作品因其分形的特殊倾向而受到关注。