Ligeti’s influential use of tone-clusters and fluctuating densities is well known. Yet, another facet of Ligeti’s compositional technique has, until now, been neglected, perhaps because it couldn’t be appropriately described or modeled beyond triviality. It’s been “hidden in plain sight.” This other well-known texture of Ligeti’s is a cascade of pitches promoting a sense of infinite descent or ascent (showcased in Devil’s Staircase, Infinite Column, and throughout many works from his 1968 Second Quartet and 1971 Melodien (likely inspired by Shepard/Risset/Tenney’s 1960s computer generated glissando illusion) onward. Through his career Ligeti forged his discretized directed textural motion into a flexible, malleable form-building device, one that accommodates gradual change and ambiguity within a web of complexity, and that, paradoxically, granted license to and inspired later 20th-21st century composers to baldly infuse their music with scalar and arpegiated passages while avoiding any association to scales or arpeggios in traditional tonal music. No other Euro-American avant garde post-war composer did this.
Although adjacent facets of Ligeti’s style have been studied (mechanico-patterns by Clendenning, the lament trope by Bauer), statistical form by Iverson, texture by Levy, and register by Bernard) none have made this distinctive facet of Ligeti’s style a point of focus, and none gave it any precise definition.
I model it by defining it as a quantifiable property, which therefore can flow and fluctuate over the course of a work or passage (or be algorithmically simulated). I call it the Textural Incline of Pitch (TIP) and define it as the proportion of (or difference between) the number of note-to-note ascents vs. descents, disregarding the distance of ascent or descent (therefore independent of pitch range). From one span (a beat, measure, etc) to another, the property can shift gradually (or abruptly).
This paper explains Textural Incline of Pitch (TIP) as a useful flexible concept apt for late 20th and early 21st century compositions by Saariaho, Haas, Ferneyhough, Berio, and others. As a textural phenomenon that emerges from the interaction of pitch and contour, TIP reveals and enables topical intertextually-based listening possibilities that are distinct from those brought into focus by other music-theoretic tools.