巴赫《发明》音高中的长程相关性和多重分形性
Long-range correlation and multifractality in Bach's Inventions pitches
摘要：
我们表明，它可以被认为是一个随机过程的标度行为的巴赫音高系列。本文采用多重分形延迟涨落分析（MF-DFA）方法，对巴赫音高的频率序列进行了分析。在这个观点中，我们发现相同的二阶矩指数（双重轮廓后）的范围（1.7-1.8）在他的作品。原始序列的MF-DFA结果与混洗序列和替代序列的结果相比，我们可以区分由于长程相关性和广泛的概率密度函数的多重分形。最后确定了标度指数和奇异谱。我们得出结论，厚尾在其多重分形性质比长程相关性更有效。
英文摘要：
We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view we find same second moment exponents (after double profiling) in ranges (1.7-1.8) in his works. Comparing MF-DFA results of original series to those for shuffled and surrogate series we can distinguish multifractality due to long-range correlations and a broad probability density function. Finally we determine the scaling exponents and singularity spectrum. We conclude fat tail has more effect in its multifractality nature than long-range correlations.
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