Interdisciplinary Pedagogy of the Meter Visualising Mathematical Music Theory Through the Ski-hill Graph (Keynote)

Abstract

This paper aims to convey how and why teaching the fundamentals of the meter through interdisciplinary Ski-hill graph pedagogy of the meter brings benefits to school-age students. Arguably, the lack of a comprehensive theory of the meter has contributed to problems in fields as diverse as music education, mathematics, acoustics (psychoacoustics) and physics. However, the Ski-hill graph and modern theory of the meter (Cohn, 2020) provide solutions for inclusive meter theory in diverse music education. This paper presents a music educator's response to modern meter theory's emphasis on the meter's subjective psychoacoustic - mind and body processes (acoustics as music) and the importance of its accurate representation. The paper explores the flexible three-step approach (Calilhanna, 2018; 2020) of Ski-hill graph pedagogy to enable school-age students to accurately visualise, conceptualise, and apply to performance, the details of their quantification of all the pulses and all the meters and their relations from listening to music. The Ski-hill graph augments theories of the meter as time signatures and groups of beats in a measure through mathematical music theory to visualise each pair of adjacent pulses in a relation of ratio 2:1 (duple meter) and or 3:1 (triple meter). Represented in the mathematics of cyclic hierarchies, the detailed visualizations of the meters through the Ski-hill graph provide a visceral and dynamic map of the metric space - the listener's temporal information of patterns often overlooked, over-simplified, or forgotten in analyses. The paper situates Cohn's Ski-hill graph and theorem as a bridge between the arts and sciences. Keywords: Ski-hill graph, meter, mathematics, psychoacoustic, inclusion.