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

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.Comment: 18 page, 6 figures, to appear in JSTA

Pitch Perception of Complex Sounds: Nonlinearity Revisited

The ability of the auditory system to perceive the fundamental frequency of a sound even when this frequency is removed from the stimulus is an interesting phenomenon related to the pitch of complex sounds. This capability is known as "residue" or "virtual pitch" perception and was first reported last century in the pioneering work of Seebeck. It is residue perception that allows one to listen to music with small transistor radios, which in general have a very poor and sometimes negligible response to low frequencies. The first attempt, due to Helmholtz, to explain the residue as a nonlinear effect in the ear considered it to originate from difference combination tones. However, later experiments have shown that the residue does not coincide with a difference combination tone. These results and the fact that dichotically presented signals also elicit residue perception have led to nonlinear theories being gradually abandoned in favour of central processor models. In this paper we use r..