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Journal Article
Approximate Set Theory: Chord Categories, Voicings, and Interval Cycles
Available to Purchase
Journal of Music Theory (2023) 67 (1): 1–70.
Published: 01 April 2023
...Dmitri Tymoczko Abstract This article describes an approximate set theory modeling intuitions shared by musicians such as Cowell, Schoenberg, Messiaen, and Persichetti. The author considers five approximation strategies, showing that in each case the result resembles an exact seven-tone set theory...
FIGURES
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Journal Article
Relative Saturation of Interval and Set Classes: A New Model for Understanding Pcset Complementation and Resemblance
Available to Purchase
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...
View articletitled, Relative Saturation of Interval and <span class="search-highlight">Set</span> Classes: A New Model for Understanding Pcset Complementation and Resemblance
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for article titled, Relative Saturation of Interval and <span class="search-highlight">Set</span> Classes: A New Model for Understanding Pcset Complementation and Resemblance
Journal Article
Voice Leading in Set-Class Space
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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
On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces
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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...
View articletitled, On Pitch-Class <span class="search-highlight">Set</span> Cartography: Relations between Voice-Leading Spaces and Fourier Spaces
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for article titled, On Pitch-Class <span class="search-highlight">Set</span> Cartography: Relations between Voice-Leading Spaces and Fourier Spaces
Journal Article
Set-Class Similarity, Voice Leading, and the Fourier Transform
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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...
View articletitled, <span class="search-highlight">Set</span>-Class Similarity, Voice Leading, and the Fourier Transform
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for article titled, <span class="search-highlight">Set</span>-Class Similarity, Voice Leading, and the Fourier Transform
Includes: Supplementary data
Journal Article
Special Collections: Renewing Set Theory
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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...
Image
One subset of each set of equivalence classes for the eight equivalence rel...
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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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A . Three-note set-class space, with regions corresponding to clustered (tr...
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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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The single-semitone layer of chromatic tetrachordal set-class space, superi...
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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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in Music in the Body: The Eighteenth-Century Contredanse and Hypermetrical Hearing
> Journal of Music Theory
Published: 01 April 2021
Image 9. An English country dance set. Squares represent men and circles women.
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in Graphing Indian Classical Modes: Models of Carnatic and Hindustani Pitch-Class Systems
> Journal of Music Theory
Published: 01 April 2025
Example 2. Set of five adjacency graphs for Bhatkhande's ten- thaat system. In each panel, edges connect thaats separated by a fixed geodesic distance k , ranging from 1 to 5. (a) k = 1; (b) k = 2; (c) k = 3; (d) k = 4; (e) k =5.
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in Graphing Indian Classical Modes: Models of Carnatic and Hindustani Pitch-Class Systems
> Journal of Music Theory
Published: 01 April 2025
Example 4. Set of five adjacency graphs for the thaat cycle based on purvi . Bhairav appears naturally in these graphs.
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Isomorphic brightness graphs for the modes of two set classes (7–2 and 7–3)...
Available to PurchasePublished: 01 April 2025
Figure 3c. Isomorphic brightness graphs for the modes of two set classes (7–2 and 7–3).
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(left) Atonal set theorists have used dual transpositions to transform subs...
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in Transformations for the Twenty-First Century: Symmetries, Intervals, and the Principle of Transformational Closure
> Journal of Music Theory
Published: 01 April 2025
Figure 7.2. ( left ) Atonal set theorists have used dual transpositions to transform subsets of a composite harmony. ( right ) We can represent these transformations as combining chromatic transposition with a Schritt that moves the two subsets in contrary motion; these two transformations
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Journal Article
Special Cases of the Interval Function between Pitch-Class Sets X and Y
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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
Associative Sets, Categories, and Music Analysis
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Journal of Music Theory (2004) 48 (2): 147–218.
Published: 01 October 2004
..., 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...
Journal Article
Composite Interval Cycle Sets, Their Relations, and Applications
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Journal of Music Theory (2002) 46 (1-2): 153–205.
Published: 01 October 2002
...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...
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Published: 01 October 2021
Example 4. Interpreting chromatic semitones in settings with three or more voices.
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in Approximate Set Theory: Chord Categories, Voicings, and Interval Cycles
> Journal of Music Theory
Published: 01 April 2023
Figure 7.3. Improvising by alternating a hexachord's intrinsic 024 6 sets.
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in Approximate Set Theory: Chord Categories, Voicings, and Interval Cycles
> Journal of Music Theory
Published: 01 April 2023
Figure A3. Categorizing small sets using the first three Fourier components.
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