A corpus analysis of common-practice themes shows that, when an intervallic pattern is repeated with one changed interval, the changed interval tends to be larger in the second instance of the pattern than in the first; the analysis also shows that the second instance of an intervallic pattern tends to contain more chromaticism than the first. An explanation is offered for these phenomena, using the theory of uniform information density. This theory states that communication is optimal when the density of information (the negative log of probability) maintains a consistent, moderate level. The repetition of a pattern of intervals is (in some circumstances, at least) highly probable; in some cases, the information density of such repetitions may be undesirably low. The composer can balance this low information by injecting a high-information (i.e., low-probability) element into the repetition such as a large interval or a chromatic note. A perceptual model is proposed, showing how the probabilities of intervals, scale degrees, and repetition might be calculated and combined.
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David Temperley; Information Flow and Repetition in Music. Journal of Music Theory 1 October 2014; 58 (2): 155–178. doi: https://doi.org/10.1215/00222909-2781759
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