Review of Paolo Susanni and Elliott Antokoletz, Music and Twentieth-Century Tonality: Harmonic Progression Based on Modality and the Interval Cycles (Routledge, 2012)

[1] For the first installment in Routledge's "Studies in Music Theory" series, Paolo Susanni and Elliott Antokoletz have contributed a book on analyzing twentieth-century music. As its title suggests, the book adopts a fairly specific framework: it focuses on non-serial, post-tonal music, mainly from the standpoint of scalar collections and interval cycles. The collections include the usual suspects-diatonic, pentatonic, whole-tone, and octatonic-along with some non-diatonic "hybrid" modes, such as Lydian with . The cycles are also the familiar ones: those generated either from moving by a single interval repeatedly or by alternating between two different intervals. Together with these primary topics, the book mixes in a few secondary ones, the chief one being the technique of inversion about an axis.Example 1. Ravel: Ma mere l'oye, "Laideronnette," measures 38-41[2] The book is unified by an overarching concern with how these various concepts interact and relate to one another. For a brief sample of its approach, consider the excerpt from Ravel's Mother Goose Suite quoted in Example 1. (Chapter 6 discusses the opening of the movement up to and including this point [109-11].) The first two measures convey the Fmajor hexachord, i.e., F-G-A-B-C-D, rendered in scalar order. This collection could be understood, at least on an abstract level, as part of a 5- or 7-cycle: B-F-C-G-D-A. Yet this hexachord also comprises portions of both whole-tone collections-F-G-Afrom WT0 and B-C-Dfrom WT1-in other words, a pair of incomplete 2-cycles. This whole-tone potential is then realized in the next two measures, where the music expresses the WT0 collection, i.e., a complete 2-cycle. The trichord F-G-A, prominent throughout in both hands of the piano part, thus serves as a link from the diatonic (or 5- or 7-cycle-based) first half to the whole-tone (or 2-cycle-based) second half.[3] To its credit, the book features many examples of this sort, drawn from a range of composers spanning from the best known (Debussy, Bartok, Stravinsky) to ones less often discussed (Riegger, Symanowski, Muczynski). Yet a number of problems beset the book. The first concerns its intended purpose: it's not clear whether this book is meant to be a work of scholarship or a work of pedagogy. Several factors point to the former: the book's methodological focus; its lack of the usual textbook apparatus (such as exercises, self-tests, and an accompanying anthology); its sheer quantity of detailed analytical discussions, which would make it heavy going for a less experienced student; and of course its inclusion in Routledge's "Studies in Music Theory," which is presumably meant for research monographs.[4] Yet the book breaks little ground in the way of original research. Instead, it advocates an analytical approach based primarily on Antokoletz's prior work.(1) Beyond this, the book exists mostly in a scholarly vacuum. For example, even though the book is centrally concerned with interval cycles, it does not substantively engage with, build upon-or in most cases, even cite-more recent work relating to them.(2) For a more specific but telling example, Chapter 2 shows how to take an augmented triad and move one or two of its pitches by a semitone in order to obtain various major and minor triads. This discussion impinges on fundamental principles of Neo-Riemannian theory, yet the book does not make the connection.[5] Indeed, such is their lack of engagement with contemporary post-tonal music theory that the authors hardly invoke its most basic elements, including not just pitch-class sets and set classes, but even pitch-class numbers.(3) Their stance toward pitch-class set theory emerges most strongly in the Preface, where they dismiss it as a form of "mathematical reductionism" (xiii). In the same paragraph, they concede that pitch-class set analysis "is perhaps applicable to atonal music such as that of Schoenberg," but then assert that "[t]he complicated numerical formulae that arise from these kinds of analyses are so far removed from any form of simple musical terminology that they tend to further alienate prospective students and teachers. …