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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
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...
Journal Article
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...
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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...
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...
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Published: 01 April 2023
Example 4. One subset of each set of equivalence classes for the eight equivalence relations in the IRK scope. More
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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
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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
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Published: 01 April 2021
Image 9. An English country dance set. Squares represent men and circles women. More
Journal Article
Journal of Music Theory (2002) 46 (1-2): 153–205.
Published: 01 October 2002
...Robert Peck COMPOSITE INTERVAL CYCLE SETS, THEIR RELATIONS, AND APPLICATIONS Robert Peck Introduction In the past forty years, a significant body of the music-theoretic lit- erature has been devoted...
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 (2004) 48 (2): 147–218.
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...
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Published: 01 October 2021
Example 4. Interpreting chromatic semitones in settings with three or more voices. More
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Published: 01 April 2023
Figure 7.3. Improvising by alternating a hexachord's intrinsic 024 6 sets. More
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Published: 01 April 2023
Figure A3. Categorizing small sets using the first three Fourier components. More
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Published: 01 April 2023
Figure 7.5. Improvising using hexachordal 013 6 ( top ) and 012 6 ( bottom ) sets. More
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Published: 01 April 2023
Figure 5.4. In a seven-tone scale, the M2 transform sends clusters to tertian, tertian sets to quartal, and quartal to cluster. The equipollent set-classes (open note heads = trichord, closed note heads = tetrachord) are preserved under the transform. More
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Published: 01 April 2023
Figure 7.4. The quartal hexachordal voicing chains together hexachordal 023 6 and 013 6 sets. More
Journal Article
Journal of Music Theory (2010) 54 (2): 143–177.
Published: 01 October 2010
... of a 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...