David Temperley

A corpus analysis of rock harmony

In this study, we report a corpus analysis of rock harmony. As a corpus, we used Rolling Stone magazines list of the ‘500 Greatest Songs of All Time’; we took the 20 top-ranked songs from each decade (the 1950s through the 1990s), creating a set of 100 songs. Both authors analysed all 100 songs by hand, using conventional Roman numeral symbols. Agreement between the two sets of analyses was over 90 per cent. The analyses were encoded using a recursive notation, similar to a context-free grammar, allowing repeating sections to be encoded succinctly. The aggregate data was then subjected to a variety of statistical analyses. We examined the frequency of different chords and chord transitions. The results showed that IV is the most common chord after I and is especially common preceding the tonic. Other results concern the frequency of different root motions, patterns of co-occurrence between chords, and changes in harmonic practice across time.

Do Grammars Minimize Dependency Length

A well-established principle of language is that there is a preference for closely related words to be close together in the sentence. This can be expressed as a preference for dependency length minimization (DLM). In this study, we explore quantitatively the degree to which natural languages reflect DLM. We extract the dependencies from natural language text and reorder the words in such a way as to minimize dependency length. Comparing the original text with these optimal linearizations (and also with random linearizations) reveals the degree to which natural language minimizes dependency length. Tests on English data show that English shows a strong effect of DLM, with dependency length much closer to optimal than to random; the optimal English grammar also has many specific features in common with English. In German, too, dependency length is significantly less than random, but the effect is much weaker than in English. We conclude by speculating about some possible reasons for this difference between English and German.

Syncopation in rock: a perceptual perspective

While study of the social and cultural aspects of popular music has been flourishing for some time, it is only in the last few years that serious efforts have been made to analyse the music itself: what Allan Moore has called ‘the primary text’ (1993, p. 1). These efforts include general studies of styles and genres (Moore, 1993; Bowman, 1995); studies of specific aspects of popular styles such as harmony and improvisation (Winkler 1978; Moore 1992, 1995; Walser 1992), as well as more intensive analyses of individual songs (Tagg 1982; Hawkins 1992). In this paper I will investigate syncopation, a phenomenon of great importance in many genres of popular music and particularly in rock.

Bayesian Models of Musical Structure and Cognition

This paper explores the application of Bayesian probabilistic modeling to issues of music cognition and music theory. The main concern is with the problem of key-finding: the process of inferring the key from a pattern of notes. The Bayesian perspective leads to a simple, elegant, and highly effective model of this process; the same approach can also be extended to other aspects of music perception, such as metrical structure and melodic structure. Bayesian modeling also relates in interesting ways to a number of other musical issues, including musical tension, ambiguity, expectation, and the quantitative description of styles and stylistic differences.

A Unified Probabilistic Model for Polyphonic Music Analysis

Abstract This article presents a probabilistic model of polyphonic music analysis. Taking a note pattern as input, the model combines three aspects of symbolic music analysis—metrical analysis, harmonic analysis, and stream segregation—into a single process, allowing it to capture the complex interactions between these structures. The model also yields an estimate of the probability of the note pattern itself; this has implications for the modelling of music transcription. I begin by describing the generative process that is assumed and the analytical process that is used to infer metrical, harmonic, and stream structures from a note pattern. I then present some tests of the model on metrical analysis and harmonic analysis, and discuss ongoing work to integrate the model into a transcription system.

Statistical Analysis of Harmony and Melody in Rock Music

Abstract We present a corpus of harmonic analyses and melodic transcriptions of rock songs. After explaining the creation and notation of the corpus, we present results of some explorations of the corpus data. We begin by considering the overall distribution of scale-degrees in rock. We then address the issue of key-finding: how the key of a rock song can be identified from harmonic and melodic information. Considering both the distribution of melodic scale-degrees and the distribution of chords (roots), as well as the metrical placement of chords, leads to good key-finding performance. Finally, we discuss how songs within the corpus might be categorized with regard to their pitch organization. Statistical categorization methods point to a clustering of songs that resembles the major/minor distinction in common-practice music, though with some important differences.

The melodic-harmonic ‘divorce’ in rock

Several authors have observed that rock music sometimes features a kind of independence or ‘divorce’ between melody and harmony. In this article, I examine this phenomenon more systematically than has been done in the past. A good indicator of melodic-harmonic divorce is cases where non-chord-tones in the melody do not resolve by step. I argue that this does occur frequently in rock ‐ often with respect to the local harmony, and sometimes with respect to the underlying tonic harmony as well. This melodic-harmonic ‘divorce’ tends to occur in rather specific circumstances: usually in pentatonically based melodies, and in verses rather than choruses. Such situations could be said to reflect a ‘stratified’ pitch organisation. A particularly common situation is where the verse of a song features stratified organisation, followed by a chorus which shifts to a ‘unified’ organisation in which both melody and accompaniment are regulated by the harmonic structure.

A Bayesian Approach to Key-Finding

The key-profile model (originally proposed by Krumhansl and Schmuckler, and modified by Temperley) has proven to be a highly successful approach to key-finding. It appears that the key-profile model can be reinterpreted, with a few small modifications, as a Bayesian probabilistic model. This move sheds interesting light on a number of issues, including the psychological motivation for the key-profile model, other aspects of musical cognition such as metrical analysis, and issues such as ambiguity and expectation.

Dependency-length minimization in natural and artificial languages∗

Abstract A wide range of evidence points to a preference for syntactic structures in which dependencies are short. Here we examine the question: what kinds of dependency configurations minimize dependency length? We consider two well-established principles of dependency-length minimization; that dependencies should be consistently right-branching or left-branching, and that shorter dependent phrases should be closer to the head. We also add a third, novel, principle; that some “opposite-branching” of one-word phrases is desirable. In a series of computational experiments, using unordered dependency trees gathered from written English, we examine the effect of these three principles on dependency length, and show that all three contribute significantly to dependency-length reduction. Finally, we present what appears to be the optimal “grammar” for dependency-length minimization.

Distributional Stress Regularity: A Corpus Study

The regularity of stress patterns in a language depends on distributional stress regularity, which arises from the pattern of stressed and unstressed syllables, and durational stress regularity, which arises from the timing of syllables. Here we focus on distributional regularity, which depends on three factors. Lexical stress patterning refers to normal stress patterns within words; interlexical stress patterning refers to patterns that arise from word combinations; and contextual stress patterning refers to adjustments in normal lexical stress patterns (such as the well-known phenomenon of ‘stress clash avoidance–. A corpus study was done to assess the effect of these three factors on distributional stress regularity in conversational and formal spoken English, by comparing the degree of stress regularity in stress-annotated corpus data to randomly manipulated versions of the data and to ‘citation-form–stress patterns drawn from a phonetic dictionary. The results show that both lexical and interlexical patterning contribute significantly to stress regularity in English; contextual stress patterning does not, and in fact significantly reduces regularity in comparison to citation-form stress patterns.