Hypermetrical Schemas, Metrical Orientation, and Cognitive-Linguistic Paradigms

Abstract

This article extends existing approaches to hypermeter by introducing schemas that make measure-by-measure correlations between grouping units and hypermeasures. These schemas offer an account of how listeners track hypermeter through irregularities and discontinuities. In order to ground these schemas in a cognitive, listener-oriented framework, the article also introduces the concept of metrical orientation. Metrical orientation involves heard measures, measures that are organizationally similar to notated measures but that may differ from the notated measures of the score with respect to both period and phase. The downbeats of these heard measures are the hyperbeats that relate to one another by means of the hypermetrical schemas. Metrical orientation is top-down and schema driven; it thus complements low-level, bottom-up cognitive accounts of meter. The hypermetrical schemas can give analyses considerable flexibility, but this flexibility presents challenges to rule systems and in particular to Lerdahl and Jackendoff’s Metrical Well-Formedness Rules. Two paradigms from cognitive linguistics are used to address this: radial structuring as a way of organizing prototype categories, and approaches to well-formedness that have also been used in examining the interpenetration of syntax and semantics. These concepts function together to provide an alternative to rule systems that is both rigorous and flexible.

Features of interdisciplinarity of modern pedagogy

“…Enlightenment recognizes a priori that education in recent years has become radically different and qualitatively different from previous traditional views on it. Education views education broadly, just as (Ito, 2013):…”

Historical Hypermetrical Hearing: Uncertainty, Floors and Trapdoors

“…It is similar to William Caplin's concept of the ‘real’ (as opposed to the ‘notated’) bar, which relates to phrase construction (, p. 35). A closer affinity is with Ito's ‘metrical orientation’: a ‘mental construct akin to the notated measure’ against which hypermetre is understood (, p. 48). Ito argues that hypermetre is the ‘metrical organization specifically of the downbeats [… downbeats] as heard, not necessarily as notated’ (pp.…”

Phrase Rhythm and Loss in the Music of Maurice Ravel

“…88Yust locates the former strategy in a tradition of Schenker‐influenced analysis which often takes as a starting point the alignment of hypermeasures with tonal middlegrounds and allows for temporal plasticity atop that base, citing among others Schachter (1976, 1980 and 1987), Yeston (1976), and Rothstein (1989; 2018, p. 123); Ito (2013), which extends the approach of Rothstein (1989) into ‘hypermetric schema’, follows in this tradition. The second strand of theory is sceptical of that sort of irregularity in hypermetre and focuses instead on the separability of metric structure from phrase structure, generally considering hypermetre as a metre‐like regular frame against which groupings can shift; Yust traces the foundational distinction between metre and grouping to Lerdahl and Jackendoff (1983), and cites Kramer (1988), Temperley (2003), and Ng (2012) in this category; Stefan Caris Love's concept of the ‘hypermetric floor’ as the highest, most persistently regular rhythmic level in a piece also belongs in this category (2016, pp.…”