Journal of Mathematics and Music, 2016 Vol. 10, No. 2, 127–148, http://dx.doi.org/10.1080/17459737.2016.1209588 Analysis of analysis: Using machine learning to evaluate the importance of music parameters for Schenkerian analysis Phillip B. Kirlin a ∗ and Jason Yust b a Department of Mathematics and Computer Science, Rhodes College, Memphis, USA; b School of Music, Boston University, Boston, USA (Received 16 November 2015; accepted 19 June 2016) While criteria for Schenkerian analysis have been much discussed, such discussions have generally not been informed by data. Kirlin [Kirlin, Phillip B., 2014 “A Probabilistic Model of Hierarchical Music Analysis.” Ph.D. thesis, University of Massachusetts Amherst] has begun to fill this vacuum with a corpus of textbook Schenkerian analyses encoded using data structures suggested byYust [Yust, Jason, 2006 “Formal Models of Prolongation.” Ph.D. thesis, University of Washington] and a machine learning algorithm based on this dataset that can produce analyses with a reasonable degree of accuracy. In this work, we examine what musical features (scale degree, harmony, metrical weight) are most significant in the performance of Kirlin’s algorithm. Keywords: Schenkerian analysis; machine learning; harmony; melody; rhythm; feature selection 2010 Mathematics Subject Classification: 68T05; 68T10 2012 Computing Classification Scheme: supervised learning; sound and music computing 1. Introduction Schenkerian analysis is widely understood as central to the theory of tonal music. Yet, many of the most prominent voices in the field emphasize its status as an expert practice rather than as a theory. Burstein (2011, 116), for instance, argues for preferring a Schenkerian analysis “not because it demonstrates features that are objectively or intersubjectively present in the passage, but rather because I believe it encourages a plausible yet stimulating and exciting way of per- ceiving and performing [the] passage.” Rothstein (1990, 298) explains an approach to Schenker pedagogy as follows. Analysis should lead to better hearing, better performing, and better thinking about music, not just to “correct” answers. [ ... ] I spend lots of class time—as much as possible—debating the merits of alternate readings: not pri- marily their conformance with the theory, though that is discussed where appropriate, but their relative plausibility as models of the composition being analyzed. Schachter (1990) illustrates alternative readings of many works and asserts that a full musical context is essential to evaluating them. Paring the music down to just aspects of harmony and voice leading, like “the endless formulas in white notes that disfigure so many harmony texts,” he claims, leaves the difference between competing interpretations undecidable. In publications *Corresponding author. Email: kirlinp@rhodes.edu © 2016 Informa UK Limited, trading as Taylor & Francis Group