Cross-type transformations and the path consistency condition

Music Theory Spectrum

Volumn 29, Issue 1, 2007, Pages 1-40

  Hook, Julian ^a  

^a NONE

Author keywords

Cross type transformations; Generalized Interval Systems; Interscalar mappings; Path consistency; Transformational theory

Indexed keywords

EID: 51249156018     PISSN: 01956167     EISSN: None     Source Type: Journal    
DOI: 10.1525/mts.2007.29.1.1     Document Type: Article

References (32)

1. Alpern, Wayne. 1998. "Bartók's Compositional Process: 'Extension in Range' as a Progressive Contour Transformation." Presented at the annual meeting of Music Theory Midwest, Louisville
2. Callender, Clifton. 1998. "Voice-Leading Parsimony in the Music of Alexander Scriabin." Journal of Music Theory 42.2: 219-33
3. Capuzzo, Guy. 2004. "Neo-Riemannian Theory and the Analysis of Pop-Rock Music." Music Theory Spectrum 26.2: 177-99
4. Childs, Adrian P. 1998. "Moving Beyond Neo-Riemannian Triads: Exploring a Transformational Model for Seventh Chords." Journal of Music Theory 42.2: 181-93
5. Clough, John and Gerald Myerson. 1985. "Variety and Multiplicity in Diatonic Systems." Journal of Music Theory 29.2: 249-70
6. Cohn, Richard. 1997. "Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations." Journal of Music Theory 41.1: 1-66
7. Cook, Robert. Forthcoming. "Parsimony and Extravagance." Journal of Music Theory
8. Douthett, Jack and Peter Steinbach. 1998. "Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition." Journal of Music Theory 42.2: 241-63
9. Dummit, David S. and Richard M. Foote. 2004. Abstract Algebra, 3rd ed. Hoboken, NJ: John Wiley & Sons
10. Gollin, Edward. 1998. "Some Aspects of Three-Dimensional Tonnetze." Journal of Music Theory 42.2: 195-206
11. Harary, Frank. 1969. Graph Theory. Reading, Mass.: Addison-Wesley
12. Hook, Julian. 2002a. "Uniform Triadic Transformations." Ph.D. dissertation, Indiana University
13. -. 2002b. "Uniform Triadic Transformations." Journal of Music Theory 46.1-2: 57-126
14. Kolman, Oren. 2004. "Transfer Principles for Generalized Interval Systems." Perspectives of New Music 42.1: 150-190
15. Lewin, David. 1987. Generalized Musical Intervals and Transformations. New Haven: Yale University Press
16. -. 1992. "Some Notes on Analyzing Wagner: The Ring and Parsifal." 19th-century Music 16.1: 49-58
17. -. 1993. Musical Form and Transformation: Four Analytic Essays. New Haven: Yale University Press
18. -. 2006. Studies in Music with Text. Oxford: Oxford University Press
19. Mead, Andrew. 1994. An Introduction to the Music of Milton Babbitt. Princeton: Princeton University Press
20. Mendelson, Elliott. 1997. Introduction to Mathematical Logic, 4th ed. London: Chapman and Hall
21. Parks, Richard. 1980. "Pitch Organization in Debussy: Unordered Sets in 'Brouillards.'" Music Theory Spectrum 2: 119-34
22. Rahn, John. 2004. "The Swerve and the Flow: Music's Relationship to Mathematics." Perspectives of New Music 42.1: 130-48
23. Rimsky-Korsakov, Nikolai. [1886] 1930. Practical Manual of Harmony. Trans. Joseph Achron. New York: Carl Fisher
24. -. [1909] 1935. My Musical Life. Trans. Judith A. Joffe. New York: Tudor
25. -. [1913] 1964. Principles of Orchestration. Trans. Edward Agate. New York: Dover
26. Santa, Matthew. 1999. "Defining Modular Transformations." Music Theory Spectrum 21.2: 200-29
27. Schillinger, Joseph. [1941] 1978. The Schillinger System of Musical Composition. New York: Da Capo Press
28. Slonimsky Nicolas. 1979. 51 Minitudes for piano: 1972-76. New York: Schirmer
29. Soderberg, Stephen. 1998. "White Note Fantasy." Music Theory Online 4.3
30. Straus, Joseph. 2003. "Uniformity, Balance, and Smoothness in Atonal Voice Leading." Music Theory Spectrum 25.2: 305-52
31. Tymoczko, Dmitri. 2005. "Voice Leadings as Generalized Key Signatures." Music Theory Online 11.4
32. Zbikowski, Lawrence. 2002. Conceptualizing Music: Cognitive Structure, Theory, and Analysis. Oxford: Oxford University Press