A Probabilistic Model of Hierarchical Music Analysis

In a nutshell, this dissertation is about supervised machine learning of Schenkerian analysis. I describe a probabilistic model of Schenkerian music analysis, and illustrate how to use the model to analyze new music. Humans judge the algorithmically-produced analyses to be, on average, about one letter grade (A-B-C-D-F) below corresponding analyses done by a professional.

Abstract: Schenkerian music theory supposes that Western tonal compositions can be viewed as hierarchies of musical objects. The process of Schenkerian analysis reveals this hierarchy by identifying connections between notes or chords of a composition that illustrate both the small- and large-scale construction of the music. We present a new probabilistic model of this variety of music analysis, details of how the parameters of the model can be learned from a corpus, an algorithm for deriving the most probable analysis for a given piece of music, and both quantitative and human-based evaluations of the algorithm's performance. In addition, we describe the creation of the corpus, the first publicly available data set to contain both musical excerpts and corresponding computer-readable Schenkerian analyses. Combining this corpus with the probabilistic model gives us the first completely data-driven computational approach to hierarchical music analysis.

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For anyone planning on printing this (wishful thinking, perhaps), note that Appendix A is very long and may not be worth the trees.

Please cite as: Phillip B. Kirlin. A Probabilistic Model of Hierarchical Music Analysis. PhD thesis, University of Massachusetts Amherst, February 2014.

Machine-readable Schenkerian analyses

The data for this work consists of 41 musical excerpts of common practice period music. All excerpts are for a keyboard instrument and are in a major key. Please cite the dissertation if you use any of these data. Download all data: (.tar.gz) (.zip)

These data constitute a superset of the data used in an earlier paper.

Each piece of music has a MusicXML file that contains the notes of the excerpt, and an analysis file with the Schenkerian analysis of the excerpt. The analyses mainly list the prolongations present in the music. Each prolongation is in the form X (Y) Z where X and Z are lists of notes that are prolonged by the notes in Y. One of X and Z may be absent. The notes in X, Y, and Z are given so that they may be easily located in the MusicXML file. Each note is specified with a measure number, pitch, octave, and occurrence. For instance, 4f#5-2 specifies the second occurrence of the F# in the fifth octave (using scientific pitch notation) of the fourth measure.

mozart1Piano Sonata 11 in A major, K. 331, I, mm. 1-8
mozart2Piano Sonata 13 in B-flat major, K. 333, III, mm. 1-8
mozart3Piano Sonata 16 in C major, K. 545, III, mm. 1-8
mozart4Six Variations on an Allegretto, K. Anh. 137, mm. 1-8
mozart5Piano Sonata 7 in C major, K. 309, I, mm. 1-8
mozart6Piano Sonata 13 in B-flat major, K. 333, I, mm. 1-4
mozart77 Variations in D major on "Willem van Nassau," K. 25, mm. 1-6
mozart8Twelve Variations on "Ah vous dirai-je, Maman," K. 265, Var. 1, mm. 23-32
mozart912 Variations in E-flat major on "La belle Francoise," K. 353, Theme, mm. 1-3
mozart10Minuet in F for Keyboard, K. 5, mm. 1-4
mozart118 Minuets, K. 315, No. 1, Trio, mm. 1-8
mozart1212 Minuets, K. 103, No. 4, Trio, mm. 15-16
mozart1312 Minuets, K. 103, No. 3, Trio mm. 7-8,
mozart14Untitled from the London Sketchbook, K. 15a, No. 1, mm. 12-14
mozart159 Variations in C major on "Lison dormait," K. 264, Theme, mm. 5-8
mozart1612 Minuets, K. 103, No. 12, Trio, mm. 13-16
mozart1712 Minuets, K. 103, No. 1, Trio, mm. 1-8
mozart18Piece in F for Keyboard, K. 33B, mm. 7-12
schubert1Impromptu in B-flat major, Op. 142, No. 3, mm. 1-8
schubert2Impromptu in G-flat major, Op. 90, No. 3, mm. 1-8
schubert3Impromptu in A-flat major, Op. 142, No. 2, mm. 1-8
schubert4Wanderer's Nachtlied, Op. 4, No. 3, mm. 1-3
handel1Trio Sonata in B-flat major, Gavotte, mm. 1-4
haydn1Divertimento in B-flat major, Hob. 11/46, II, mm. 1-8
haydn2Piano Sonata in C major, Hob. XVI/35, I, mm. 1-8
haydn3 Twelve Minuets, Hob. IX/11, Minuet No. 3, mm. 1-8
haydn4 Piano Sonata in G major, Hob. XVI/39, I, mm. 1-2
haydn5 Hob. XVII/3, Variation I, mm. 19-20
haydn6 Hob. I/85, Trio, mm. 39-42
haydn7 Hob. I/85, Menuetto, mm. 1-8
bach1Minuet in G major, BWV Anh. 114, mm. 1-16
bach2Chorale 233, Werde munter, mein Gemute, mm. 1-4
bach3Chorale 317 (BWV 156), Herr, wie du willt, so schicks mit mir, mm. 1-5
beethoven1Seven Variations on a Theme by P. Winter, WoO 75, Variation 1, mm.1-8
beethoven2Seven Variations on a Theme by P. Winter, WoO 75, Theme, mm. 1-8
beethoven3Ninth Symphony, Ode to Joy theme from finale (8 measures)
beethoven4Piano Sonata in F minor, Op. 2, No. 1, Trio, mm. 1-4
beethoven5Seven Variations on God Save the King, Theme, mm. 1-6
chopin1Mazurka, Op. 17, No. 1, mm. 1-4
chopin2Grande Valse Brilliante, Op. 18, mm. 5-12
clementi1Sonatina for Piano, Op. 38, No. 1, mm. 1-2