...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...

... (1973) pitch-class set theory to a diatonic context. This application is what he likens to examining a score lacking clef and key signature: a musical staff alone provides informa- tion solely about mod-7 steps. One can still discern transpositional and inver- sional operations in such a context...

... . 1959 . “ Re: Intervallic Relations between Two Collections of Notes .” Journal of Music Theory 3/2 : 298 – 301 . ———. 2001 . “ Special Cases of the Interval Function between Pitch-Class Sets X and Y .” Journal of Music Theory 45/1 : 1 – 29 . ———. 2007 . Generalized Musical Intervals...

... five features of tonality concern pitch, which Tymoczko models as the continuous set of real numbers, consistent with “atonal” pitch-class set theory 2  The two primary sources I would point to are Tymoczko (218 n. 26) in Edward Aldwell and Carl Schachter’s Har- 2006 and Callender...

... of contact with other analyti- cal approaches, in particular those using pitch-class set theory. David Head­ lam’s review in Music Theory Online (2012) notes that Hall’s bibliography does not include references to his own work (Headlam 1996) or the important...

... .'' Paper presented at the national meeting of the Society for Music Theory , Montreal . Hoffman Justin . 2008 . '' On Pitch-Class Set Cartography: Relations between Voice-Leading Spaces and Fourier Spaces. '' Journal of Music Theory 52 : 219 – 50 . Hook Julian . 2002...

... the overtone series.3 And while the standard ap- proach to post-tonal music—pitch-class set theory—is in many respects indebted to Schoenberg,4 its conception of intervals and harmonies bears no trace of Schoenberg’s contention that “all musical phenomena can be referred to the overtone series, so that all...

.... Rochester: University of Rochester Press. Morris, Robert D. 1982 . “Set Groups, Complementation, and Mappings among Pitch-Class Sets.” Journal of Music Theory 26/1 : 101 -44. O'Donnell, Shaugn. 1998 . “Klumpenhouwer Networks, Isography, and the Molecular Metaphor.” Intégral 12 : 53 -79...

...: Approaches to Textual Analysis in Popular Music . New York: Oxford University Press. Morris, Robert D. 1982 . “Set Groups, Complementation, and Mappings among Pitch-Classes,” Journal of Music Theory 26 : 101 -44. Rockwell, Joti. 2007 . “ Drive, Lonesomeness, and the Genre of Bluegrass Music...

... in which the inversion operates, not the index of inversion as in familiar pitch-class set theory. (Thus the familiar I4(3) would be represented here as I12(3, 4 In the context of this article it will be employed simply as an alterna- tive way...

... Adam . 2011 . “ Non-coinciding Sequences .” Music Theory Spectrum 33 , no. 2 : 124 – 45 . Rings Steven . 2011 . Tonality and Transformation . New York : Oxford University Press . Rogers John E . 1971 . “ Pitch-Class Sets in Fourteen Measures of Mozart’s Jupiter Symphony...

...—­ circumstances that certainly aided in its placement in the journal. Continuing in the Babbitt-inspired vein, there are also Forte’s own endeavors. As is well known, during the 1960s he began to develop his ideas of pitch-class set theory. In the prior decade, Salzer had inspired Schenker...

... of these subgroups, including an attractive representation as a wreath product of familiar small groups. The UTT theory admits natural extensions in any of several directions, a few of which are sketched in Part 5. For example, the standard inver- sion operator I of pitch-class set theory is not a UTT, but I...

... and Transformations. New Haven: Yale University Press. Morgan, Robert P. 1976 . “Dissonant Prolongation: Theoretical and Compositional Precedents.” Journal of Music Theory 20 : 47 -91. Morris, Robert D. 1982 . “Set Groups, Complementation, and Mappings among Pitch-Class Sets.” Journal of Music Theory...

....” Journal of Music Theory 35 : 93 -173. Lewin, David. 1959 . “Re: Intervallic Relations between Two Collections of Notes.” Journal of Music Theory 3 : 298 -301. ———. 2001 . “Special Cases of the Interval Function between Pitch-Class Sets X and Y.” Journal of Music Theory 45 : 1 -29...

... in Determining Pitch-Class Set Resemblance.” Perspectives of New Music 38/2 : 52 -87. Bullough, R. K. 1961 . “On Homometric Sets. I. Some General Theorems.” Acta Crystallographica 14 : 257 -68. Callender, Clifton. 2004 . “Continuous Transformations.” Music Theory Online 10/3 . Callender...

...-Class Sets.” Music Perception 11 : 289 –305. Hutchinson, W., and L. Knopoff. 1978 . “The Acoustic Component of Western Consonance.” Interface 7 : 1 –29. Isaacson, Eric J. 1990 . “Similarity of Interval-Class Content between Pitch-Class Sets: The IcVSIM Relation.” Journal of Music Theory...

... Function between Pitch-Class Sets X and Y.” Journal of Music Theory 45 : 1 -29. Quinn, Ian. 2001 . “Listening to Similarity Relations.” Perspectives of New Music 39 /2: 108 -58. ———. 2006 . “General Equal-Tempered Harmony (Introduction and Part I).” Perspectives of New Music 44 /2: 114...

.... and trans. 1987 . The Berg-Schoenberg Correspondence . New York : Norton . Buchler Michael . 2000 . “Broken and Unbroken Interval Cycles and Their Use in Determining Pitch-Class Set Resemblance.” Perspectives of New Music 38 / 2 : 52 – 87 . Callender Clifton Quinn Ian...

... Music.” Music Analysis 10/3 : 345 -55. Rahn, John. 1980 . Basic Atonal Theory . New York: Longman. Roeder, John. 1987 . “A Geometric Representation of Pitch-Class Series.” Perspectives of New Music 25/1-2 : 362 -409. Roig-Francoli Miguel A. 2001 . “A Theory of Pitch-Class-Set...