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

## TL;DR

This paper analyzes Bach's pitch series as stochastic processes exhibiting multifractality, revealing that fat-tailed distributions contribute more to multifractality than long-range correlations.

## Contribution

It applies multifractal detrended fluctuation analysis to Bach's pitch series, distinguishing effects of correlations and distribution shape on multifractality.

## Key findings

- Bach's pitch series show consistent second moment exponents (1.7-1.8).
- Multifractality mainly arises from fat-tailed distributions, not long-range correlations.
- Scaling exponents and singularity spectra characterize the multifractal nature.

## Abstract

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.