乐谱中的多重标度行为和非线性特征
Multiple scaling behavior and nonlinear traits in music scores
摘要：
我们提出了一个统计分析的乐谱从不同的作曲家使用去趋势波动分析。我们发现不同的波动轮廓，对应于不同的自相关结构的音乐作品。此外，我们揭示了证据的存在下，非线性自相关估计的趋势波动分析的幅度序列，一个相应的研究适当的替代数据验证的结果。非线性相关的数量和性质因作曲家而异。最后，我们进行了一个简单的实验，以评估音乐替代件与原始音乐相比的愉悦性，发现非线性相关性可以在音乐作品的审美感知中发挥重要作用。
英文摘要：
We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear auto-correlations by estimating the detrended fluctuation analysis of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.
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