Abstract
We show that music is represented by fluctuations away from the minimum path through statistical space. Our key idea is to envision music as the evolution of a non-equilibrium system and to construct probability distribution functions (PDFs) from musical instrument digital interface (MIDI) files of classical compositions. Classical music is then viewed through the lens of generalized position and velocity, based on the Fisher metric. Through these statistical tools we discuss a way to quantitatively discriminate between music and noise.
Highlights
Music plays an intricate part of human life
We show that using digitized music, through musical instrument digital interface (MIDI) files, classical compositions follow approximate power laws in a statistical space, despite mathematically having a time dependent exponent
L and J increase with time T as a power law, its index approaching unity in time for almost all compositions; (ii) J − L2 /T exhibits a power law ∝ T 1+m, where m signifies the deviation from the minimum path; (iii) By comparing musical compositions with results obtained from Gaussian white and colored noise, we show that music experiences the analogue of periodic forcing in statistical space while noise does not
Summary
Music plays an intricate part of human life. As a result there is a large body of work devoted to the analysis of music. We show that using digitized music, through musical instrument digital interface (MIDI) files, classical compositions follow approximate power laws in a statistical space, despite mathematically having a time dependent exponent. L and J increase with time T as a power law, its index approaching unity in time for almost all compositions; (ii) J − L2 /T exhibits a power law ∝ T 1+m , where m signifies the deviation from the minimum path; (iii) By comparing musical compositions with results obtained from Gaussian white and colored noise, we show that music experiences the analogue of periodic forcing in statistical space while noise does not. Meaning noise can be quantitatively differentiated from music through velocity in statistical space These results highlight the organization of music into “regularity” (an almost constant information flow) and deviations away from this constant flow.
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