Date of Degree


Document Type


Degree Name





Joseph Straus

Committee Members

Norman Carey

Lukas Ligeti

Jeff Nichols

David Schober

Subject Categories

Algebraic Geometry | Applied Statistics | Audio Arts and Acoustics | Composition | Music Performance | Music Theory | Other Applied Mathematics


Scale, Harmony, Macroharmony, Graphical, Statistical, Analysis


In Book 3 of his piano etudes, György Ligeti charts a new path relative not only to his earlier works in the genre, but also to the rest of his oeuvre. The treatment of pitch class collection (or “scale”) in particular is a significant departure from his previous compositional processes. Despite the extent of the stylistic shifts in the four etudes of Book 3 and their importance as capstones to Ligeti’s body of work, there is a dearth of literature dedicated to their analysis.

This essay seeks to show that in Book 3, Ligeti uses processes related to scale and broader scale areas (i.e. “macroharmony”) to articulate structures and musical narratives, and that macroharmony is often the central feature of an etude that defines its dramatic shape. The primary scale type used is the diatonic, and the macroharmonic processes are largely reflective of and governed by structures inherent in the diatonic scale. This leads to juxtapositions of scale areas that are often functional in nature, an important departure from the manner in which diatonicity is treated in his earlier etudes.

Analytical techniques developed in this essay seek to shed light on our perception of varying levels of stability and instability brought about by the treatment of macroharmony and the calibration of its variables. The statistical-graphical methods used here attempt to “quantify” these levels of stability, developing a number of metrics that can be used to chart their change—and by extension approach a reflection of a listener’s experience of this feature—over the course of a work, in order to elucidate Ligeti’s particular use of macroharmony in crafting the expressive arcs of these etudes.