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We set out to perform a cluster analysis of harmonic structures (specifically, chord-to-chord transitions) in the McGill Billboard dataset, to determine whether there is evidence of multiple harmonic grammars and practices in the corpus, and if so, what the optimal division of songs, according to those harmonic grammars, is. We define optimal as providing meaningful, specific information about the harmonic practices of songs in the cluster, but being general enough to be used as a guide to songwriting and predictive listening. We test two hypotheses in our cluster analysis — first that 5–9 clusters would be optimal, based on the work of Walter Everett (2004), and second that 15 clusters would be optimal, based on a set of user-generated genre tags reported by Hendrik Schreiber (2015). We subjected the harmonic structures for each song in the corpus to a K-means cluster analysis. We conclude that the optimal clustering solution is likely to be within the 5–8 cluster range. We also propose that a map of cluster types emerging as the number of clusters increases from one to eight constitutes a greater aid to our understanding of how various harmonic practices, styles, and sub-styles comprise the McGill Billboard dataset.

The primary focus of this dissertation is a theoretical analysis of Steven Mackey’s piano concerto, Stumble to Grace, commissioned by the Los Angeles Philharmonic, New Jersey Symphony Orchestra, and St. Louis Symphony, and premiered in 2011. Inspired by his son “learning to become human,” the concerto moves through 5 stages (movements) that progress from awkward all-thumbs playing in the first stage—which represents an immature, childlike way of playing—to complex, mature counterpoint in the fifth stage, which represents the arrival as a fully mature, sophisticated human being. The motivation for this study comes out of the dearth of analytical study of Mackey’s music, despite its originality and growing reputation. Two questions are central to this study: 1) how does Stumble to Grace interact with and comment on the history of the concerto genre? and 2) how does Mackey create a musical syntax with his personal harmonic language? The primary method for the analysis of harmonic syntax is set-theory using Pitch-Class set notation. Edward Pearsall’s method of analyzing consonance and dissonance in atonal music is used, as well as Santa’s Modulo-7 approach to post-tonal diatonic music. The study will show that Stumble to Grace, like many concertos before it, invites the listener to consider the role of virtuosity in concert music, but in a new way: the concept of virtuosity is center-stage in the narrative of the piece. The narrative generates a progressive form, in which individual stages have returns to their opening material while the piece as a whole does not have returns or recapitulations (beyond structural pitch-class sets). The results of the analysis reveal (1) a motivic, thematic, and harmonic design interconnected by important pitch-class sets, (2) phrase-level harmonic syntax that is partially controlled by those sets, and (3) a theory of the logic of consonant and dissonant sonorities within the piece. It is my hope that this study not only furthers the understanding of Mackey’s music among theorists and composers, but also that conductors and concert programmers looking for connections to programmatic works about a life’s journey discover Stumble to Grace.

It seems clear, intuitively, that a concern for harmonic coherence would lead to the use of relatively compact, connected sets of points in harmonic space, where “connected” simply means that every element is adjacent to at least one other element in the set. How might such compactness be defined more precisely? I have been investigating an interesting algorithm in which sets of points are chosen, one by one, in somen-dimensional harmonic space, under the condition that each new point must have the smallest possible sum of harmonic distances to all points already in the set. That is, at each

Traditional harmonic analysis annotations can be represented in a computer model of a piece of music by plain text strings. But whenever automated processing like analysis, comparison or retrieval is intended, a formal definition is helpful. This should cover not only the syntactic structure, but also the semantics, i.e. the intended meaning, and thus adheres to the technique of mathematical remodelling of existing cultural phenomena. The resulting models can serve as a basis for automated processing, but also help to clarify the communication and discussion among humans substantially. This article proposes such a definition in four layers, which address different problems of encoding and communication: (a) relation of symbol sequences to staff positions, (b) combining functions, (c) chord roots, and (d) interval structure and voice leading. Only one of them is specific to functional (Riemannian) theory and can possibly be replaced to represent scale degree theory. The proposal is configurable to different interval specification methods and open to localisation. Syntax and semantics are defined by precise mathematical means, borrowed from computer science, and thus are unambiguously documented.

Heterofunctional Coordination (HC), in which conjuncts bear different grammatical functions (as in English What and when to eat to stay healthy ), is assumed to be solely multiclausal in Germanic languages, i.e., to be underlyingly a coordination of clauses. This is supposed to distinguish Germanic from Slavic, where monoclausal HC is also possible, in which the surface conjuncts are coordinated directly. In the case of German, this assumption has not been supported by any empirical studies. This paper offers two such studies—based on corpora and on acceptability judgement experiments—which, however, do not confirm the assumption that German HC is strictly multiclausal. In particular, numerous examples of monoclausal HC constructions may be found in German corpora, while judgement experiments show a great variability of acceptance rates of monoclausal HC in German and demonstrate that the acceptability of such constructions depends on various factors. As this variability does not seem to reflect processing effects, we conclude that a gradient (non-binary) grammaticality approach is needed to model German HC. While the focus of this paper is on deriving the right empirical generalizations, we also include an appendix containing a proof-of-concept sketch of such a gradient grammaticality analysis, which builds on Minimalist Gradient Harmonic Grammar and on ideas from Linear Optimality Theory and the Decathlon Model.

Tonal functions—tonic, pre-dominant, and dominant—are a standard feature of North American music theory. The pre-dominant (PD) encompasses the largest number of chords, varying in quality and scale degrees; unlike the tonic and dominant functions, it is primarily defined by its syntactical role, preceding the arrival of the dominant. While Western harmony textbooks consistently organize PD chords according to a regulative syntax (e.g., IV goes to ii), they differ on its rationale and are rarely explicit about the repertoire(s) on which it is based. Furthermore, while the PD is thought to be an essential element of cadential closure, the role of PDs at various formal locations is underexplored, be it in textbooks or corpus studies. To facilitate exploration of these claims for future research, we analyzed all 22 sonata-allegro movements from the Mozart piano sonatas and generated a new dataset containing every occurrence of V (including the Cad6/4), the three chords preceding each V, and their formal location.

This article focuses on the right edge of nominal stems in Greek and aims to show that stem-final segments should be analyzed as distinct morphological constituents. Two types of such constituents are identified. On the one hand, stem endings such as -a(ð), -i(ð), and -a(t) have a predictable distribution, as they are found in nouns with specific morphosyntactic properties and stress patterns. On the other hand, stem endings like -o, -a, and -i cannot function as predictors of the morphosyntactic status of the noun, although they may convey information about its stress position. The distinction between the two constituent categories is captured through an analysis couched within Distributed Morphology. Specifically, it is proposed that stem endings of the first category function as nominalizer exponents, while those of the second category serve as exponents of a Theme node, which is inserted post-syntactically and bears no grammatical features. The allomorphic variation exhibited by these exponents is accounted for by means of a phonological analysis based on Gradient Harmonic Grammar. The proposed approach is shown to capture empirical generalizations that have been overlooked in traditional grammatical descriptions and theoretical analyses based on multiple stem allomorphs.

The fictional Dr. Strabismus sets out to write a new comprehensive theory of music. But music's tendency to deconstruct itself combined with the complexities of postmodernism doom him to failure. This is the parable that framesThe Sense of Music,a novel treatment of music theory that reinterprets the modern history of Western music in the terms of semiotics. Based on the assumption that music cannot be described without reference to its meaning, Raymond Monelle proposes that works of the Western classical tradition be analyzed in terms of temporality, subjectivity, and topic theory. Critical of the abstract analysis of musical scores, Monelle argues that the score does not reveal music'ssense.That sense--what a piece of music says and signifies--can be understood only with reference to history, culture, and the other arts. Thus, music is meaningful in that it signifies cultural temporalities and themes, from the traditional manly heroism of the hunt to military power to postmodern \"polyvocality.\" This theoretical innovation allows Monelle to describe how the Classical style of the eighteenth century--which he reads as a balance of lyric and progressive time--gave way to the Romantic need for emotional realism. He argues that irony and ambiguity subsequently eroded the domination of personal emotion in Western music as well as literature, killing the composer's subjectivity with that of the author. This leaves Dr. Strabismus suffering from the postmodern condition, and Raymond Monelle with an exciting, controversial new approach to understanding music and its history.

This paper describes the construction and analysis of a corpus of harmonic progressions from 12-bar blues forms included in the jazz repertoire collection The Real Book. A novel method of coding and analyzing such corpus data is developed, with a notion of “possible harmonic change” derived from the corpus and logit mixed-effects regression models that describe the difference between actually occurring harmonic events and possible but non-occurring ones in terms of various sets of theoretical constructs. Models using different sets of constructs are compared using the Bayesian Information Criterion, which assesses the accuracy and efficiency of each model. The principal results are that: (1) transitional probabilities are better modeled using root-motion and chord-frequency information than they are using pairs of individual chords; (2) transitional probabilities are better described using a mixture model intermediate in complexity between a bigram and full trigram model; and (3) the difference between occurring and non-occurring chords is more efficiently modeled with a hierarchical, recursive context-free grammar than it is as a Markov chain. The results have implications for theories of harmony, composition, and cognition more generally.

In this paper, I look at the distribution of case forms in Latvian prepositional constructions. Latvian prepositions assign either the genitive or the accusative case to their complements, primarily in an idiosyncratic manner. This pattern is disrupted in the plural, where all complements of prepositions show up invariably in the dative case. I investigate the nature of this unusual pattern and provide a post-syntactic account of the data, in which I claim that the observed asymmetry is the result of a cumulative effect in Latvian grammar: case may surface unfaithfully in configurations where marked combinations of case and number features occur in positions where certain case feature values are dispreferred to begin with. This effect arose diachronically as a repair mechanism after the language had lost one of its grammatical cases, the instrumental. This cumulative effect is captured using the framework of Harmonic Grammar. I also argue extensively against a purely syntactic account of the data.