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Fourier transform

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Journal Article
Journal of Music Theory (2008) 52 (2): 251–272.
Published: 01 October 2008
...Dmitri Tymoczko In this article, I consider two ways to model distance (or inverse similarity) between chord types, one based on voice leading and the other on shared interval content. My goal is to provide a contrapuntal reinterpretation of Ian Quinn's work, which uses the Fourier transform...
Includes: Supplementary data
Journal Article
Journal of Music Theory (2015) 59 (1): 121–181.
Published: 01 April 2015
...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...
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 (2021) 65 (2): 325–374.
Published: 01 October 2021
...Jason Yust Abstract This article demonstrates how to obtain a periodicity-based description of cyclic rhythms using the discrete Fourier transform and applies this to understanding Steve Reich's use of rhythmic canons in a series of works from the early 1970s through the 1990s. The primary...
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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 (2008) 52 (2): 219–249.
Published: 01 October 2008
... prototypical set. In order to locate sets in this space, Quinn employs the discrete­ Fourier transform, a I thank Joe Dubiel, Scott Gleason, Jerry Ianni, Tom Robinson, Joe Straus, Dmitri Tymoczko, and JMT’s two anonymous readers for their insightful suggestions and helpful feedback...
Journal Article
Journal of Music Theory (2001) 45 (1): 1–29.
Published: 01 April 2001
... be impossible here to give a crash course on the relevant mathematics for readers knowing little of the pertinent mathematical background. That background includes the behavior of complex num- bers, and the theory of Fourier transformations for certain complex- valued functions defined on certain...
Journal Article
Journal of Music Theory (2012) 56 (1): 1–52.
Published: 01 April 2012
... 27/1 : 1 – 49 . ———. 2008c . “ Set-Class Similarity, Voice Leading, and the Fourier Transform .” Journal of Music Theory 52/2 : 251 – 72 . ———. 2009b . “ Three Conceptions of Musical Distance .” In Mathematics and Computation in Music , ed. Chew Elaine Childs Adrian Chuan...
Journal Article
Journal of Music Theory (2011) 55 (1): 43–88.
Published: 01 April 2011
...., Oxford University. Tymoczko, Dmitri. 2006. “The Geometry of Musical Chords.” Science 313: 72–74. 2008. “Set-Class Similarity, Voice Leading, and the Fourier Transform.” Journal of Music Theory 52: 251–72. Wintle, Christopher...
Includes: Supplementary data
Journal Article
Journal of Music Theory (2003) 47 (1): 103–123.
Published: 01 April 2003
... for two sets Y and Z to form identical progression vectors as successors to a given set X. These conditions are framed in terms of various “fourier properties” and “fourier relations,” which are so named because the underlying mathematics involves Fourier transformations. Some of the progressions...
Journal Article
Journal of Music Theory (2005) 49 (1): 45–108.
Published: 01 April 2005
...). The correlation between offset and similarity as measures of chromaticness is similarly high for set-classes of larger cardinality, and always higher for set-classes of the same size. 24. Generic prototypicality may be interpreted as maximal imbalance on the associated Fourier Balance...
Journal Article
Journal of Music Theory 9930876.
Published: 08 September 2022
.... Of course, a great numb­ er of the sci­ent­ ists whom Napoleon brought along were equally untested: even Joseph Fourier, who was a well estab­ lished fig­ure prior to his depart­ ure for Egypt, published his Théorie analytique de la chaleur (1822) only after the exped­ it­ ion. Most of those involved, howe­...