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

We show that some of Bach’s pitch series can be considered as a stochastic process with scaling behaviour. Using the multifractal detrended fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analysed. In this view we find the 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 that the fat tail has more effect on the multifractality nature than long-range correlations.