...Nathan L. Lam This article develops the notion of modal spelled pitch class by combining Julian Hook’s theory of spelled heptachords and Steven Rings’s heard scale degree. Modal spelled pitch class takes the form of an ordered triple that includes the key signature, the generic pitch classes...

...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...

...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...

...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...

..., since some musical spaces have natural boundaries. It also notes that there are spaces, including the familiar pitch-class circle, in which there are multiple paths between any two points. This leads to the suggestion that we might sometimes want to replace traditional pitch-class intervals with paths...

...Brian Alegant This paper proposes a refinement of our understanding of pitch-class inversion in atonal and twelve-tone music. Part I of the essay establishes the theoretical foundation. It reviews the index number approach formulated by Milton Babbitt, examines characteristics of even and odd index...

...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...

...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. Copyright...

..., harmonic functions, or pitch centricity. The Dasian space is a closed, nonoctave repeating scalar cycle, where each element is identified by a unique coordination of pitch class and modal quality. The dual description of each element enables both the specification of location in a given cycle and the...

... properties of these spaces derive from the properties of diatonic pitch-class sets and generic pitch spaces developed by Clough and Hook. After presenting the construction of these voice-leading spaces and defining the OPTIC relations in mod-7 space, this article presents the mod-7 OPTIC -, OPTI -, OPT...

...Seth Monahan For centuries, metaphors of agency have pervaded music-analytical writing. Today, as in generations past, critics routinely vivify their analytical narrations by ascribing sentience, emotion, and volition to musical works, their internal elements (pitch classes, contrapuntal voices...

...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...

... principle produces an ordering of pitch classes that lies behind small formal units, cycles order the presentation of twelve-tone rows and give structure to large formal spans. The present study explores four cyclic organizational principles in works from the String Quartet, op. 28 (1938), to the Second...

... in different octaves. Indeed, Stockhausen drew explicit parallels between the overtone series for pitch and categorical values for duration. In the realm of 12-tone com- positional theory and method there have been various attempts at trans- lating pitch and pitch-class relationships to the...

...〉 Normalized cp notation: 〈0, .33, 1, .67〉 〈1, .67, 0, .33〉 〈.67, 1, .33, 0〉 〈.33, 0, .67, 1〉 Figure 10.  Mapping of normalized cp notation onto translation (a) and cseg class (b) Just as a contour-space cseg can be realized in pitch space in an infinite number...

... approach.1 Essentially, for any number n from 1 to 6, and every pitch class p in a chord, the Fourier transform assigns a two-dimensional vector whose components are Vp,n 5 (cos 2ppn/12, sin 2ppn/12). (1) Adding these...

.... Hanson, Howard. 1960 . Harmonic Materials of Modern Music . New York: Appleton-Century-Crofts. Hindemith, Paul. 1942 . The Craft of Musical Composition . Translated by Arthur Mendel. New York: Associated Music Publishers. Huron, David. 1994 . “Interval-Class Content in Equally Tempered Pitch...

..., rhythmic/metric layering occurs in the presence of supermetrical disso- nance. Such supermetrical dissonances are created in a number of ways, all of which result in significantly larger pitch/pitch-class shapes that go well...

... potentially disorienting symmetrical reversals of fingering patterns for the performer. No pitch class appears twice in the same vertical row, resulting in a distinctive hand/finger coordinate for pitches of the same class...

... the abstract arrangement of musical phenomena . . . around a referential or tonic pitch class. Keys appear in two basic modal genera, major and minor, whose characteristics reflect the disposition of tones and semitones within their respective scales. And scale is a linear sequence of notes...