Voice-Leading Transformation and Generative Theories of Tonal Structure

Abstract

[0.1.1] As the theories of Heinrich Schenker were gaining currency in the United States in the mid-twentieth century, Milton Babbitt observed that Schenker's theory of voice-leading levels was "strikingly similar to transformational grammars in linguistics" (1965, 60 Numerous generative approaches to explaining tonal structure and/or Schenker's theories have been proposed since Babbitt noted a resemblance between Schenker's analytical method and Chomskian generative grammars in 1965. One of the more challenging features of Schenker's theory to replicate in a generative system is the interaction of counterpoint and hierarchy. Many theorists, such as Lerdahl and Jackendoff, skirt the problem by developing non-contrapuntal systems, meaning ones that do not allow for layers with conflicting hierarchical descriptions.

Analysis of analysis: Using machine learning to evaluate the importance of music parameters for Schenkerian analysis

“…This hierarchy can be represented visually by the tree in Figure 2(a): this diagram illustrates the hierarchy of melodic intervals present in the composition and the various prolongations identified above. An equivalent representation, known as a maximal outerplanar graph, or MOP (Yust 2006(Yust , 2009(Yust , 2015, is shown in Figure 2(b). Binary trees of intervals and MOPs are duals of each other in that they represent identical sets of information, though the MOP representation is more succinct.…”

“…As with any complex human activity, the techniques of artificial intelligence may greatly advance our understanding of how Schenkerian analysis is performed and what kinds of implicit cognitive abilities and priorities support it. The present work builds upon the research of Kirlin (2014a;2015) which models Schenkerian analysis using machine learning techniques. By probing Kirlin's algorithm we address a question of deep interest to Schenkerian analysts and pedagogues: what role do different aspects of the music play in deliberating between possible analyses of the same musical passage?…”