Transpositional Combination of Beat-Class Sets in Steve Reich's Phase-Shifting Music

Cohn, Richard

doi:10.2307/3090631

Cited by 47 publications

(13 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under the heading 'Minimalism rescued from its devotees', Fink takes on the formalists, whom he sees as preferring a minimalist kind of criticism, limited to technical description and airy testimony about the music's sensuous effects. Tracing this criticism from its origins in the writings of composers and performers active in the scene through seminal writings in the music-theoretic literature (Epstein, 1986;Cohn, 1992;Bernard, 1995), Fink concludes that 'the critical landscape around this music has become cluttered with aging technical descriptions and restatements of compositional manifestos' (Fink, 2005, p. 18). We should welcome Fink's interest in reading minimal music in a new way, as a particularly revealing form of late-capitalist cultural practice.…”

Section: IVmentioning

confidence: 96%

Minimal Challenges: Process Music and the Uses of Formalist Analysis

Quinn¹

2006

Contemporary Music Review

View full text Add to dashboard Cite

Critiques of formalist modes of musical analysis resemble critiques of certain types of minimal music. One ironic, if not downright paradoxical aspect of this parallel is that the sharpest attacks on minimal music have come from writers sympathetic to formalism. A reconciliation of sorts has been reached by formalist admirers of minimalism, for whom the music is a staging ground for reflexive methodological critique.Since this volume focuses on theorists' responses to what we perceive as the challenges of contemporary music, I hope I will be forgiven for beginning with a personal anecdote. A dozen years ago, in my first semester of graduate study, I enrolled in Jonathan Kramer's proseminar in music theory at Columbia. The final paper for the class was meant to engage somehow with current issues in the field. At the time, the mathematical modeling of similarity among melodic contours was something of a hot topic in the corner of the field usually known as 'set theory', which I was studying at the same time in a seminar at CUNY. Seeking to apply these cutting-edge analytical tools to music that not only functioned as an appropriate testing ground, but also meant something to me, I set about looking at the slow instrumental music that opens and closes the central movement of Steve Reich's The Desert Music. This music, which is interrupted by a faster choral section that forms the keystone of Reich's arch design for the piece, consists of a series of identically structured double canons (six in two), each of which unfolds over a single harmony. Taken together, these harmonies form a progression that is also the basis of the fast music in the middle, but this was beside the point of my analytical endeavor, which was limited to the contour of the higher of the two dux melodies of each canon.What I heard in the music was easy enough to put into words: the upper melodies, despite the changes of harmony and a rhythmic process involving what John Roeder

show abstract

Section: IVmentioning

confidence: 96%

Minimal Challenges: Process Music and the Uses of Formalist Analysis

Quinn¹

2006

Contemporary Music Review

View full text Add to dashboard Cite

show abstract

“…Benjamin Boretz [2], John Rahn [3], and David Lewin [4] investigate this connection further. Later authors, including Richard Cohn [5], Robert Morris [6], and John Roeder [7], apply similar concepts to a variety of analytical situations, such as in the phase music of Steve Reich.…”

Section: Beat-class Setsmentioning

confidence: 99%

Beat-Class Set Classes and the Power Group Enumeration Theorem

Peck¹

2021

MusMat

View full text Add to dashboard Cite

The theory of beat-class sets originates in the work of Milton Babbitt, who demonstrates a correspondence between modular pitch-class spaces and metric spaces in the framework of total serialism. Later authors, particularly Richard Cohn, John Roeder, and Robert Morris, apply similar concepts to a variety of analytical situations, drawing on concepts and procedures from pitch-class set theory. In light of the correspondence between these theories, the universe of beat-class sets for a given modulus may be partitioned into equivalence classes similar to pitch-class set classes. This study investigates processes of enumerating these equivalence classes.We consider extensions to the theory of beat-class sets by including rhythms with more than one voice. Specifically, we examine equivalence classes of multiple-voiced beat-class sets using the Power Group Enumeration Theorem (PGET) of Frank Harary and Edgar M. Palmer. The PGET allows us to determine the numbers of equivalence classes of beat-class sets as determined by various groups of transformations: metric shift, retrogradation, and voice permutation, among others. Our results have implications for further applications in pitch-class set theory, serial theory, and transformational theory.

show abstract

“…Return to text 11. It is best to avoid the term "beat class," which is used in the music theory literature as a rhythmic analogy to "pitch class," which denotes a metrical position; see Babbitt 1962, Cohn 1992, and Roeder 2003. Return to text 12.…”

Section: Footnotesmentioning

confidence: 99%

Meter Metrics

Gotham

2015

MTO

View full text Add to dashboard Cite

“Consideration of a metric context is indispensable for a complete understanding of rhythm” (".fn_cite_pages($toussaint_2013, "16")."). In order to discuss the nature of a rhythm or its compositional development, it is necessary to account for the metrical context(s) in which it appears. In music that moves among a variety of metrical structures, it is also necessary to account for the relationships that exist between those meters. This article provides a detailed characterization of those relationships. What is more, the relationships introduced here may be discussed independently of any rhythmic parallel, illuminating purely metrical aspects of temporal organization, and thus offering an altogether new analytical perspective on repertoires in which metric change is an important compositional parameter. This study identifies a variety of metrical relationships, defines them (mathematically where appropriate), and assesses them for perceptual and musical significance, including the rarity of their occurrence. The focus is on “mixed” metrical structures that systematically use more than one type of duration on the same level, such as both “short” and “long” beats (which may or may not correspond to 2- and 3-unit groupings). “Simple” meters (with only one type of beat) are also discussed for the sake of completeness and because all are used together in the relevant repertoires (which include much twentieth-century Western music, some popular musics, and “world” musics including the Balkan Aksak style). The breadth of this potential application is a principal asset of the theoretical apparatus presented.

show abstract

Transpositional Combination of Beat-Class Sets in Steve Reich's Phase-Shifting Music

Cited by 47 publications

References 4 publications

Minimal Challenges: Process Music and the Uses of Formalist Analysis

Minimal Challenges: Process Music and the Uses of Formalist Analysis

Beat-Class Set Classes and the Power Group Enumeration Theorem

Meter Metrics

Contact Info

Product

Resources

About