1-20 of 310

Search Results for set

Save search
Follow your search
Access your saved searches in your account
Would you like to receive an alert when new items match your search?
Close Modal
Sort by
Journal Article

Approximate Set Theory: Chord Categories, Voicings, and Interval Cycles

Available to Purchase
Dmitri Tymoczko
Journal of Music Theory (2023) 67 (1): 1–70.
DOI: https://doi.org/10.1215/00222909-10232057
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 | View all 53
First thumbnail for: Approximate <span class="search-highlight">Set</sp...
Second thumbnail for: Approximate <span class="search-highlight">Set</sp...
Third thumbnail for: Approximate <span class="search-highlight">Set</sp...
View articletitled, Approximate <span class="search-highlight">Set</span> Theory: Chord Categories, Voicings, and Interval Cycles View PDF for article titled, Approximate <span class="search-highlight">Set</span> Theory: Chord Categories, Voicings, and Interval Cycles
Journal Article

Relative Saturation of Interval and Set Classes: A New Model for Understanding Pcset Complementation and Resemblance

Available to Purchase
Michael Buchler
Journal of Music Theory (2001) 45 (2): 263–343.
DOI: https://doi.org/10.2307/3653442
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 View PDF 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

Available to Purchase
Joseph N. Straus
Journal of Music Theory (2005) 49 (1): 45–108.
DOI: https://doi.org/10.1215/00222909-2007-002
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...
View articletitled, Voice Leading in <span class="search-highlight">Set</span>-Class Space View PDF for article titled, Voice Leading in <span class="search-highlight">Set</span>-Class Space
Journal Article

On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces

Available to Purchase
Justin Hoffman
Journal of Music Theory (2008) 52 (2): 219–249.
DOI: https://doi.org/10.1215/00222909-2009-016
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 View PDF 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

Available to Purchase
Dmitri Tymoczko
Journal of Music Theory (2008) 52 (2): 251–272.
DOI: https://doi.org/10.1215/00222909-2009-017
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 View PDF 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

Available to Purchase
Jason Yust
Journal of Music Theory (2016) 60 (2): 213–262.
DOI: https://doi.org/10.1215/00222909-3651886
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...
View articletitled, Special Collections: Renewing <span class="search-highlight">Set</span> Theory View PDF for article titled, Special Collections: Renewing <span class="search-highlight">Set</span> Theory
Image
Example 4. One subset of each set of equivalence classes for the eight equivalence relations in the IRK scope.

One subset of each set of equivalence classes for the eight equivalence rel...

Available to Purchase
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. More
Image
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-step voice leadings among equiheptatonic set-classes.

A . Three-note set-class space, with regions corresponding to clustered (tr...

Available to Purchase
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 More
Image
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 (oval) set-classes. Small italic labels show equal-tempered chromatic sets; large bold labels show equiheptatonic set-classes.

The single-semitone layer of chromatic tetrachordal set-class space, superi...

Available to Purchase
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 More
Image
Image 9. An English country dance set. Squares represent men and circles women.

An English country dance set. Squares represent men and circles women.

Available to Purchase
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. More
Image
Set of five adjacency graphs for Bhatkhande's ten-thaat system. In each panel, edges connect thaats separated by a fixed geodesic distance , ranging from 1 to 5.

Set of five adjacency graphs for Bhatkhande's ten- thaat system. In each p...

Available to Purchase
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. More
Image
Set of five adjacency graphs for the thaat cycle based on purvi. Bhairav appears naturally in these graphs.

Set of five adjacency graphs for the thaat cycle based on purvi . Bhair...

Available to Purchase
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. More
Image
A pair of very similar brightness graphs. Each has a lopsided U-shape, with a vertical chain of six interconnected modes on the left and a single outlier mode on the right, which is only connected to the mode at the very bottom. The outlier mode is positioned slightly higher in the first diagram than in the second. Otherwise the two graphs are nearly identical, except for the specific pitch differences between the scales. (Mode one of the first scale includes pitch class integers 0, 1, 2, 3, 4, 5, and 7; mode one of the second scale includes pitch class integers 0, 1, 2, 3, 4, 5, and 8.)

Isomorphic brightness graphs for the modes of two set classes (7–2 and 7–3)...

Available to Purchase
in Modal Color Theory > Journal of Music Theory
Published: 01 April 2025
Figure 3c. Isomorphic brightness graphs for the modes of two set classes (7–2 and 7–3). More
Image
Independent transposition of two different components of a harmonic superimposition.

(left) Atonal set theorists have used dual transpositions to transform subs...

Available to Purchase
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 More
Journal Article

Special Cases of the Interval Function between Pitch-Class Sets X and Y

Available to Purchase
David Lewin
Journal of Music Theory (2001) 45 (1): 1–29.
DOI: https://doi.org/10.2307/3090647
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...
View articletitled, Special Cases of the Interval Function between Pitch-Class <span class="search-highlight">Sets</span> X and Y View PDF for article titled, Special Cases of the Interval Function between Pitch-Class <span class="search-highlight">Sets</span> X and Y
Journal Article

Associative Sets, Categories, and Music Analysis

Available to Purchase
Dora A. Hanninen
Journal of Music Theory (2004) 48 (2): 147–218.
DOI: https://doi.org/10.1215/00222909-48-2-147
Published: 01 October 2004
..., gen. eds. New York: Chapman &amp; 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...
View articletitled, Associative <span class="search-highlight">Sets</span>, Categories, and Music Analysis View PDF for article titled, Associative <span class="search-highlight">Sets</span>, Categories, and Music Analysis
Journal Article

Composite Interval Cycle Sets, Their Relations, and Applications

Available to Purchase
Robert Peck
Journal of Music Theory (2002) 46 (1-2): 153–205.
DOI: https://doi.org/10.1215/00222909-46-1-2-153
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...
View articletitled, Composite Interval Cycle <span class="search-highlight">Sets</span>, Their Relations, and Applications View PDF for article titled, Composite Interval Cycle <span class="search-highlight">Sets</span>, Their Relations, and Applications
Image
Example 4. Interpreting chromatic semitones in settings with three or more voices.

Interpreting chromatic semitones in settings with three or more voices.

Available to Purchase
in An Intervallic Approach to Sixteenth-Century Chromaticism > Journal of Music Theory
Published: 01 October 2021
Example 4. Interpreting chromatic semitones in settings with three or more voices. More
Image
Figure 7.3. Improvising by alternating a hexachord's intrinsic 0246 sets.

Improvising by alternating a hexachord's intrinsic 024 6 sets.

Available to Purchase
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. More
Image
Figure A3. Categorizing small sets using the first three Fourier components.

Categorizing small sets using the first three Fourier components.

Available to Purchase
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. More