Towards a Cognitively Based Quantification of Metrical Dissonance

Metrical dissonance is a powerful tool for creating and manipulating musical tension. The relative extent of tension can be more or less acute depending (in part) on the type of dissonance used and moving among those dissonance types can contribute to the shape of a musical work. This chapter sets out a model for quantifying relative dissonance that incorporates experimentally substantiated principles of cognitive science. A supplementary webpage [**html page] provides an interactive guide for testing out these ideas, and a further online supplement [**URL—included in the main text as Section \ref{sec:online}] provides mathematical formalizations for the principles discussed. We begin with a basic model of metre where a metrical position’s weight is given simply by the number of pulse levels coinciding there. This alone enables a telling categorization of displacement dissonances for simple metres and a first sense of the relative differences between them. These arbitrary weighting ‘values’ are then refined on the basis of tempo and pulse salience. This provides a more subtle set of gradations that reflect the cognitive experience of metre somewhat better while still retaining a clear sense of the simple principles that govern relative dissonance. Additionally, this chapter sees the model applied in a brief, illustrative analysis and in a preliminary extension to ‘mixed’ metres (5s, 7s,…). This sheds light on known problems such as the relative stability of mixed metres in different rotations, and suggests a new way of thinking about mixed metres’ relative susceptibility to metrical dissonance.

Danses Fantastiques

Much of Tchaikovsky's music for the ballets Sleeping Beauty and Nutcracker exhibits what Harald Krebs calls metrical dissonance: the juxtaposition or superimposition of noncoincident pulses and rhythmic patterns. This article shows how the dances of the composer's collaborators, Enrico Cecchetti, Antonietta Dell'Era, Lev Ivanov, and Marius Petipa, respond to and participate in these metrical dissonances. The first part of the article defines metrical dissonance, the processes that transform it, and the related but distinct phenomenon of metric type. The second part presents four choreomusical analyses that draw on archival dance notation and videos of present-day performances.

Response to Lynn Cavanagh

Krebs's unusual monograph demonstrates that the writing of pure music theory remains an essential enterprise—particularly in the relatively neglected rhythmic domain—but only if the reader undertakes active reading and has prior knowledge of how the music goes. Within the monograph, perpetuation of the image of the misunderstood and suffering artist as a clue to the extramusical meaning Schumann associated with metrical dissonance leads to biased results. This essay's supplementary analysis of the first movement of Schumann's Symphony No. 3, informed by the history of ideas, proposes that in this movement metrical dissonance is used to reinterpret an emblem of the past so as to convey a vision of the future.

Metrical Dissonance in the Works of Carl Nielsen. A Metrical Analysis of 'Sinfonia Espansiva', First Movement

Carl Nielsen’s music is known to be ambiguous in the harmonic department as well as in the metric. This article endeavors how Nielsen works with metrical irregularities, in the first movement of Sinfonia Espansiva, in order to create tension/relief- progressions, forward driven motions and finally sectional divisions. At several occasions in the music, Nielsen emancipates the notated meter and allows interaction between underlying layers to take over the metric control. The article provides a metrical map with form divisions according to the classic sonata form, and illustrates how metrical dissonances can indicate how and when sectional borders appear. The analysis is made based on theory by Dr. Harald Krebs, who has developed a useful analytic tool for this kind of musical research.

Hearing Kaleidoscopes: Embedded Grouping Dissonance in Electronic Dance Music

The rhythmic and metrical qualities of electronic dance music (EDM) are clearly among its most prominent and appreciated features. Yet scholarship on rhythm, as well as popular discourse surrounding EDM, often frames the pervasively duple metres that characterize popular dance-based styles as simplistic and limited in capacity. Given the allure of EDM’s temporal qualities, how do musicians devise creative solutions to the constraints of its duple metrical organization? This article addresses this question through a consideration of embedded grouping dissonance, one of several distinctive rhythmic phenomena found in EDM. In theorizing embedded grouping dissonance, the article both builds upon and expands recent music-theoretical formulations of ‘metrical dissonance’, which describe similar occurrences without addressing this specific phenomenon. It then situates embedded grouping dissonance in relation to EDM’s technologically mediated means of production, arguing that this rhythmic technique exemplifies recurring principles of design that shape and reflect the aesthetics of electronic dance music on a broad scale.