多重分形音乐的计算方法
Computational approach to multifractal music
摘要：
在这项工作中，我们进行了分形分析的160件音乐属于六个不同的流派。我们发现，大多数碎片揭示的特征，使我们能够将它们归类为物理过程称为1/f（粉红色）噪声。然而，对于以肖邦作品为代表的古典音乐和一些比粉红噪音相关得多的爵士乐作品来说，情况并非如此。我们还进行了多重分形（MFDFA）分析这些音乐作品。我们发现，所有的作品揭示多重分形特性。流行音乐和摇滚音乐的多重分形结构最丰富。此外，多重分形特征的变化在流行音乐类型中最明显。这表明，从多重分形的角度来看，古典音乐和爵士音乐比最流行的音乐类型更加统一。
英文摘要：
In this work we perform a fractal analysis of 160 pieces of music belonging to six different genres. We show that the majority of the pieces reveal characteristics that allow us to classify them as physical processes called the 1/f (pink) noise. However, this is not true for classical music represented here by Frederic Chopin's works and for some jazz pieces that are much more correlated than the pink noise. We also perform a multifractal (MFDFA) analysis of these music pieces. We show that all the pieces reveal multifractal properties. The richest multifractal structures are observed for pop and rock music. Also the viariably of multifractal features is best visible for popular music genres. This can suggest that, from the multifractal perspective, classical and jazz music is much more uniform than pieces of the most popular genres of music.
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