Abstract
In the field of music composition, creating polyphony is relatively one of the most difficult parts. Among them, the basis of multivoice polyphonic composition is two-part counterpoint. The main purpose of this paper is, through the computer technology, conducting a series of studies on “Two-Part Inventions” of Bach, a Baroque polyphony master. Based on digitalization, visualization and mathematical methods, data mining algorithm has been applied to identify bipartite characteristics and rules of counterpoint polyphony. We hope that the conclusions drawn from the article could be applied to the digital creation of polyphony.
Highlights
Fractal geometry originated in the nineteenth century
Fractal sets are the geometry of chaos
Studies show that global context has an effect on music perception [5]
Summary
Various types of patterns and rules are available in music works, the audience’s understandings on music can be expressed in a formalized way through a series of rules [1, 2]. These rules enables the audience to generate hearing expectation, which exists in different dimensions such as melody, rhythm, and harmony, and produces different patterns and pieces on the basis of constant changes in basic elements [1, 2]. Fractal sets are the geometry of chaos. It is an important branch in modern mathematics
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