...Jason Yust The discrete Fourier transform on pitch-class sets, proposed by David Lewin and advanced by Ian Quinn, may provide a new lease on life for Allen Forte's idea of a general theory of harmony for the twentieth century based on the intervallic content of pitch-class collections. This article...

...Michael Buchler 2001 © Yale University, New Haven, Connecticut 06520 2001 Buchler, Michael. 1997 . “ Broken and Unbroken Interval Cycles and Their Use in Determining Pitch-Class Set Resemblance .” Ph.D. diss., University of Rochester. ____. 2000 . “Relative Saturation of Subsets and...

.... Buchler, Michael. 1998 . “Relative Saturation of Subsets and Interval Cycles as a Means for Determining Set-Class Similarity.” Ph.D. diss., University of Rochester. Callender, Clifton. 1998 . “Voice-Leading Parsimony in the Music of Alexander Scriabin.” Journal of Music Theory 42 : 219 –34...

...Justin Hoffman Recent music-theoretical research has proposed two ways of mapping the pitch-class set universe. Fourier spaces, constructed by Quinn, relate sets to one another based upon their composition from members of interval cycles, reflecting what might be called “harmonic quality.” Voice...

... quantify similarity of interval content. The first section of the article shows how to find the minimal voice leading between chord types or set-classes. The second uses voice leading to approximate the results of Quinn's Fourier-based method. The third section explains how this is possible, while the...

... Hejiden, gen. eds. New York: Chapman & Hall/CRC Press. Buchler, Michael. 1997 . “ Relative Saturation of Subsets and Interval Cycles as a Means for Determining Set-Class Simlarity .” Ph.D. dissertation, University of Rochester. Cambouropoulos, Emilios. 1997 . “The Role of Similarity in...

...Robert Peck 2002 © Yale University, New Haven, Connecticut 06520 2002 Ayres, Frank, Jr. 1965 . Schaum's Outline of Theories and Problems of Modern Abstract Algebra. New York: McGraw-Hill, Inc. Babbitt, Milton. 1961 . “Set Structure as a Compositional Determinant.” Journal of Music...

...David Lewin 2001 © Yale University, New Haven, Connecticut 06520 2001 SPECIAL CASES OF THE INTERVAL FUNCTION BETWEEN PITCH-CLASS SETS X AND Y David Lewin 1. Pcset pairs <X,Y> for which IFUNC(X,Y) is constant 1.1.1 Example...

... numbers, and outlines a partitional approach to pitch-class inversion. Part II explores analytical implications of the partitional model and outlines a methodology for the analysis of note-against-note and free inversional settings. The analyses use the set-class inventories for even and odd index numbers...

... direct product of orbit restrictions is a wreath product of the commuting group of one orbit restriction (as above) by the symmetric group on the set of orbits. Third, the commuting group for any group with any type of action is a direct product of such wreath products for each union of orbit...

...Joseph N. Straus Pitch sets and pitch-class sets whose integers share the same sum are connected by pure contrary voice leading and share a center of balance. This article studies progressions of chords that may belong to different T/I set-classes but that belong to the same sum class. sum sum...

...Joseph N. Straus This article creates transformational spaces for interpreting progressions of sets belonging to the same T/I equivalence class. Within these spaces, sets are placed in proximity based upon contextual inversion , specifically those contextual inversions that (like the familiar neo...

... rise to the instrument's rhythmic complexity. Drawing upon these permutational relationships, this study analyzes excerpts from bluegrass banjo repertoire in terms of the connections among rhythmic patterns rendered as beat-class sets. Last, it examines the interaction between these sets and metric...

... of affinity spaces is probed in Bartók's “Divided Arpeggios,” an intriguing posttonal piece appearing late in the Mikrokosmos set. José Oliveira Martins received his Ph.D. in music history and theory from the University of Chicago and currently is principal investigator in music and the...

...Jason Yust This article introduces a type of harmonic geometry, Fourier phase space, and uses it to advance the understanding of Schubert’s tonal language and comment upon current topics in Schubert analysis. The space derives from the discrete Fourier transform on pitch-class sets developed by...

... period of repertoire discussed, and major composers or theorists they were devoted to. Among the major findings, one can trace in a precise manner the centripetal process toward focus on Schenkerian and set theories (and the more recent opposite process), the almost total separation of discussions of...

... Fanny Mendelssohn Hensel's setting of Bach's “Das alte Jahr” in the concluding “Nachspiel” of her piano song cycle, Das Jahr , as suggesting interactions of public and private sonic worlds. I follow potential tonal-harmonic alternatives (after Schoenberg and Berg on the chorale) and implications of...

... the D/F# complex with the central poetic subject: the Christmas rose. The article introduces Wolf's setting, reevaluates Bailey's idea, and offers an in-depth hermeneutic analysis of the two songs. 2007 2007 Matt BaileyShea is an assistant professor of music theory in the College Music...

...Clifton Callender This article generalizes Ian Quinn's recent harmonic characterization of pitch-class sets in equal tempered spaces to chords drawn from continuous pitch and pitch-class spaces. Using the Fourier transform, chords of any real-valued pitches or pitch classes are represented by their...

...Mark Anson-Cartwright Among the many qualities that set Bach apart from his contemporaries is his manner of transforming his thematic material—most notably his fugue subjects. Bach himself believed that all good fugue writers should know how and when to change (or mutate) their subjects. The...