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Fractal Dimensions and Entropies of Meragi Songs

机译:Meragi歌曲的分形尺寸和熵

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摘要

Melodies can be treated as time series systems with the pitches (or frequencies of the notes) representing the values in subsequent intervals. The pattern of a melody can be revealed in a scattering diagram where pitches represent vertices, and the directed pathways which connect the former pitches to the next ones signify the relations established during the performance. The pathways form a pattern which is called animal diagram (or lattice animal) in the vocabulary of graph theory. The slopes of pathways can be used to characterize an animal diagram and thus to characterize a melody; and the scattering diagram can be used to find out the fractal dimension. In addition, the entropy, the maximum entropy, and the negentropy (or the order) of melodies can be determined. The analysis of Meragi songs in terms of fractal dimension and entropy was carried out in this work. It was found out that there is not a correlation between the fractal dimension and the entropy; therefore, the fractal dimension and the entropy each characterizes different aspects of Meragi songs.
机译:旋律可以被视为与间距代表在随后的时间间隔的值的时间系列系统(或音符的频率)。旋律的模式可以在球场代表顶点的散点图显现,其中前者的间距连接到下那些定向途径意味着性能期间建立的关系。途径形成被称为在图论中的词汇动物图(或晶格动物)图案。途径的斜率可以被用于表征的动物图并因此表征旋律;和散射图可以用于找出分形维数。此外,旋律的熵,最大熵,和负熵(或顺序)可以被确定。的Meragi歌曲分形维数和熵方面的分析,在此工作的开展。据发现不存在分形维数和熵之间的相关性;因此,分形维数和熵每个表征的Meragi歌曲不同方面。

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