From speech to songs via recital—A case of phase transition? A fractal study of Tagore’s work

This work explores the variation of scaling exponents in a song, recitation, and reading with the same lyrical content. Detrended Fluctuation Analysis (DFA) has been employed to find the long range temporal correlations (or the Hurst Exponent) present in each form of the auditory signal. Perceptually, it is known that the addition of rhythm and pitch, amplitude modulation distinguish between these different forms of audio signals, but the mathematical analogue of the same is still unknown. In this work, recordings were taken for 2 artists (1 male, 1 female) who were asked to read, recite and sing the entire lyrics of two (2) self chosen Tagore songs, each of which were later put to analysis. The rationale behind choosing Tagore’s works is because of its strong lexical content. It was seen that Hurst Exponent is found to be the lowest in case of reading while it maximizes in case of song implying that the amount of long range correlation increases consistently with addition of rhythmic content and pitch, amplitude modulation in the audio signals. With this work, we tried to establish a critical value of Hurst exponent, above/below which transformation occurs to other forms analogous to critical temperature in phase transition of matter.This work explores the variation of scaling exponents in a song, recitation, and reading with the same lyrical content. Detrended Fluctuation Analysis (DFA) has been employed to find the long range temporal correlations (or the Hurst Exponent) present in each form of the auditory signal. Perceptually, it is known that the addition of rhythm and pitch, amplitude modulation distinguish between these different forms of audio signals, but the mathematical analogue of the same is still unknown. In this work, recordings were taken for 2 artists (1 male, 1 female) who were asked to read, recite and sing the entire lyrics of two (2) self chosen Tagore songs, each of which were later put to analysis. The rationale behind choosing Tagore’s works is because of its strong lexical content. It was seen that Hurst Exponent is found to be the lowest in case of reading while it maximizes in case of song implying that the amount of long range correlation increases consistently with addition of rhythmic content and pitch, a...