Long-range correlation and multifractality in Bach's Inventions pitches

Details Long-range correlation and multifractality in Bach's Inventions pitches Long-range correlation and multifractality in Bach's Inventions pitches

2007-04-05

arxiv.org/abs/0704.0726v2

J. Stat. Mech. P04012 (2007)

Physics

Data Analysis, Statistics and Probability

18 page, 6 figures, to appear in JSTAT

Scientific paper

10.1088/1742-5468/2007/04/P04012

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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