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discrete Fourier transform

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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 (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
... conform to the interval cycles that occur in equal temperaments. Because of the association of Quinn’s spaces with the discrete Fourier transform, these spaces are called Fourier spaces and the harmonic qualities that they model Fourier...
Journal Article
Journal of Music Theory (2007) 51 (2): 277–332.
Published: 01 October 2007
... Angle: A Similarity Measure for Pitch-Class Sets.” Perspectives of New Music 36/2 : 107 -42. Smith, Julius O., III. 2008. Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications, 2nd ed. http://ccrma.stanford.edu/~jos/mdft/ . Soderberg, Stephen. 1995 . “Z-Related Sets...
Journal Article
Journal of Music Theory (2023) 67 (1): 1–70.
Published: 01 April 2023
... of the result; the discrete Fourier transform will then have three nontrivial components corresponding to the terms clustered , quartal , and tertian . Another possibility is to remain in twelve-tone equal temperament but ignore Fourier components beyond the third. Collections with a strong first component...
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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
... 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 . 1982 . '' Analysis and Performance: Webern's...
Includes: Supplementary data
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...