Neo-Riemannian Perspectives on the Harmonieschritte, with a Translation of Riemann's Systematik der Harmonieschritte

This article examines Riemann's discussion of the Harmonieschritte within the Skizze, locating that discussion within a nineteenth-century combinatorial tradition shaped by Riemann's conception of key. In this article, Riemann's Harmonieschritte is examined from three neo-Riemann standpoints. The first section offers a short introduction to the Harmonieschritte and examines neo-Riemann theory's embrace of these relationships, emphasizing the conflation of functional relations and root-interval transformations that this embrace has entailed. The second section discusses the development of Riemann's system of Harmonieschritte despite of neo-Riemannian theorists's acknowledgement of the system's susceptibility to interpretation as a group of transformations on the consonant triads. The third section focuses on tonal coherence, with particular interest on Riemann's recognition that Harmonieschritte might portend the sort of harmonic practice embraced by neo-Riemannians if left unchecked. The article concludes with a translation of Riemann's Systematik der Harmonieschritte, the summary of the complete “chromatic” family of triadic relations from the Skizze.

Modal Types and Ut, Re, Mi Tonalities: Tonal Coherence in Sacred Vocal Polyphony from about 1500

An evaluation of Pietro Aron's understanding of "mode in polyphony" (Trattato della Natura et Cognitione di tutti gli tuoni [1525]) coupled with an analytical examination of Josquin's motet oeuvre leads to a new theory of tonal coherence in sacred vocal polyphony from about 1500. This theory provides a designation for, and identifies the markers of, the tonalities represented in the motets of Josquin; it is based on a nomenclature derived from the technical vocabulary of modal theory and the exigencies of a musical tradition rooted in plainchant, hexachordal manipulation of the gamut, and counterpoint. Three main tonal categories are defined and identified by hexachordal function of final as Ut, Re, and Mi tonalities. Comments by Glarean (Dodecachordon [1547]) support the essentially practical basis of these tonal designations. Each of these tonalities consists of, and is defined by, a distinct collection of "modal types," melodic-contrapuntal paradigms of tonal coherence that are identifiable in a variety of structural guises, from simple contrapuntal contexts to more abstract frameworks. Analytical examples from Josquin's motets illustrate procedural similarities in works belonging to different modal categories and structural distinctions within the same category, as well as demonstrating why diverse analytical approaches have seemed successful with certain works but inappropriate to others.