We elaborate Alfred Schutz's theory of musical communication empirically. Our technique for analysing musical communication aligns Schutz's sociological theory with the mathematics of anticipatory systems. Music, we argue, can be considered as an anticipatory system that articulates through its diachronic unfolding, fundamental symmetries which can be traced back to its initial moments. Following Bohm and Dubois, we argue that these symmetries are present in fractal structures that gradually increase in definition as the music progresses. Critically, we focus on the role of redundancy in this process of providing increasing definition. By analysing the entropy of musical data, we show how graphs of relative entropies can be produced from which a fractal is constructed. In arguing that coherence in music can be established through the alignment of self-similar patterns, the connection between Dubois's anticipatory systems and Schutz's characterization of the dimensions of musical communication shows how redundancy underlies musical coherence.

中文翻译：

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音乐传播中的冗余：舒茨“一起制作音乐”的操作化

我们根据经验详细阐述了阿尔弗雷德舒茨的音乐传播理论。我们分析音乐传播的技术将舒茨的社会学理论与预期系统的数学相结合。我们认为，音乐可以被视为一种预期系统，它通过其历时展开的基本对称性来表达，这些基本对称性可以追溯到其最初的时刻。继 Bohm 和 Dubois 之后，我们认为这些对称性存在于分形结构中，随着音乐的进行，这些对称性在定义上逐渐增加。至关重要的是，我们关注冗余在提供不断增加的定义的过程中的作用。通过分析音乐数据的熵，我们展示了如何生成相对熵图，从而构建分形。