Abstract
We investigate correlations among pitches in several songs and pieces of piano music. Real values of tones are mapped to positions within a one-dimensional walk. The structure of music, such as beat, measure and stanza, are reflected in the change of scaling exponents of the mean square fluctuation. Usually the pitches within one beat are nearly random, while nontrivial correlations are found within duration around a measure; for longer duration the mean square fluctuation is nearly flat, indicating exact 1/f power spectrum. Some interesting features are observed. Correlations are also studied by treating different tones as different symbols. This kind of correlation cannot reflect the structure of music, though long-range power-law is also discovered. Our results support the viewpoint that the fundamental principle of music is the balance between repetition and contrast.
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