The Calculus of Finite (Metric) Dissonances

“Metric dissonance” is a term borrowed from the realm of pitch relationships, but many studies of metric dissonance draw primarily from a conception of dissonance based on the relative complexities of frequency ratios while downplaying the important syntactical aspect that dissonance plays in tonal music. This article develops existing models of metric dissonance, most notably that of Harald Krebs, by formalizing them through the calculus of finite differences, thereby introducing a methodology for quantifying metric dissonance. Such a formalization not only establishes a heuristic for comparing musical passages but also suggests an experiential model for hearing metrically dissonant music.

Formal Functions of Metric Dissonance in Rock Music

This article explores the interactions of metric dissonance with phrase structure and form in rock music, offers categorization schemes for common formal functions of metric dissonance, and presents several corpus studies of metric dissonance in the works of single artists and bands as well as in a cross-section of rock songs. These data allow for comparative analyses of the metric profile of a given artist or band, suggest genre correlations with particular metric patterns, and demonstrate a trend of increasing metric dissonance throughout the history of rock.

Tonal and Rhythmic-Metric Process in Brahms's Early C-Minor Scherzos

The scherzos Brahms composed for his Piano Quintet in F Minor, Op. 34 (1862; rev. 1864) and for the Dietrich-Schumann-Brahms F-A-E violin sonata (1853) are dramatic, C-minor pieces that allude to works of Beethoven's middle period. Both scherzos open with tonal and rhythmic-metric dissonance and end with tonal and rhythmic-metric consonance, yet there are significant refinements in Brahms's handling of these global progressions in the piano quintet scherzo. The piano quintet scherzo engages a smaller network of interrelated dissonances, intensifies these dissonances throughout the movement, and resolves them convincingly near the end of the scherzo.

Variant Timekeeping Patterns and Their Effects in Jazz Drumming

In accompanying improvising soloists, jazz drummers must both maintain a steady pulse in conjunction with the bassist and generate intensity and excitement by means of irregular, improvised accompaniment patterns known as “comping.” Timekeeping and comping practices are generally conceived in opposition, with the former understood as “solid” and the latter as “liquid.” This essay shows how one modern jazz drummer employs variants of common timekeeping patterns in a more “liquid” way to generate motional energy through the strategic production of metric dissonance at key moments within a performance. In this way, timekeeping patterns may be understood not as extraneous to rhythmic intensification, but as integral to it.