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Journal Article
Journal of Music Theory (2018) 62 (2): 279–338.
Published: 01 October 2018
...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...
Journal Article
Journal of Music Theory (2020) 64 (2): 241–281.
Published: 01 October 2020
...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...
Journal Article
Journal of Music Theory (2001) 45 (1): 1–29.
Published: 01 April 2001
...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...
Journal Article
Journal of Music Theory (2005) 49 (1): 45–108.
Published: 01 April 2005
.... 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...
Journal Article
Journal of Music Theory (2008) 52 (2): 219–249.
Published: 01 October 2008
...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...
Journal Article
Journal of Music Theory (2008) 52 (2): 251–272.
Published: 01 October 2008
... to 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...
Includes: Supplementary data
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Published: 01 October 2022
Figure 2. Summary of Auerbach's pitch-, pitch-class-, and duration-preserving operations.
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in Approximate Set Theory: Chord Categories, Voicings, and Interval Cycles
> Journal of Music Theory
Published: 01 April 2023
Figure 4.2. A . Three-note set-class space, with regions corresponding to clustered (triangle), tertian (quadrilateral), quartal (pentagon), and equipollent (oval) set-classes. Small italic labels show equal-tempered chromatic sets; large bold labels show equiheptatonic set-classes. B . Single
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in Approximate Set Theory: Chord Categories, Voicings, and Interval Cycles
> Journal of Music Theory
Published: 01 April 2023
Figure 5.7. The single-semitone layer of chromatic tetrachordal set-class space, superimposing the one-step layer of diatonic tetrachordal set-class space. Circles represent generated collections. Shapes represent clustered (triangle), tertian (quadrilateral), quartal (pentagon), and equipollent
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Journal Article
Journal of Music Theory (2001) 45 (2): 263–343.
Published: 01 October 2001
...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...
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Published: 01 October 2022
Example 2. Ohriner's seven groove classes and the rhythmic realizations of their prime form, beginning on the downbeat.
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Published: 01 April 2023
Figure 8. The Scambi performance space annotated with step classes relative to family 3. Each step class is illustrated with a different line style.
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in An Eightfold Taxonomy of Harmonic Progressions, and Its Application to Triads Related by Major Third and Their Significance in Recent Screen Music
> Journal of Music Theory
Published: 01 April 2023
Example 4. One subset of each set of equivalence classes for the eight equivalence relations in the IRK scope.
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Journal Article
Journal of Music Theory (2007) 51 (2): 277–332.
Published: 01 October 2007
...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...
Journal Article
Journal of Music Theory (2009) 53 (2): 227–254.
Published: 01 October 2009
..., 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...
Journal Article
Journal of Music Theory (1999) 43 (2): 193–230.
Published: 01 October 1999
...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...
Journal Article
Journal of Music Theory (2013) 57 (2): 321–371.
Published: 01 October 2013
...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...
Journal Article
Journal of Music Theory (2015) 59 (2): 273–320.
Published: 01 October 2015
..., 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...
Journal Article
Journal of Music Theory (2016) 60 (2): 213–262.
Published: 01 October 2016
...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...
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