TY - JOUR
T1 - Defining modular transformations
AU - Santa, Matthew
PY - 1999
Y1 - 1999
N2 - In a lecture at Harvard University in 1943, Bartók acknowledged his discovery and use of a transformation that maps musical entities back and forth between diatonic and chromatic modular systems. But Bartók's transformation need not be limited to these; one can find examples of mappings to and from other modular spaces in Bartók's own music. This article formalizes Bartók's transformation, as well as generalizes it to map musical entities to and from any one of five different spaces: chromatic (mod12), octatonic (mod8), diatonic (mod7), whole-tone (mod6), and pentatonic (mod5). The article then demonstrates that the generalized operation is not linked to any one compositional style in the twentieth century by showing its use in works by Debussy, Stravinsky, and Schoenberg. Finally, it defines a new equivalence class, the modular set type, which groups together those set classes that may be connected via the generalized transformation, and uses the new equivalence class and generalized transformation in analyses of Webern's op. 5, no. 3 and Stravinsky's Concerto in D.
AB - In a lecture at Harvard University in 1943, Bartók acknowledged his discovery and use of a transformation that maps musical entities back and forth between diatonic and chromatic modular systems. But Bartók's transformation need not be limited to these; one can find examples of mappings to and from other modular spaces in Bartók's own music. This article formalizes Bartók's transformation, as well as generalizes it to map musical entities to and from any one of five different spaces: chromatic (mod12), octatonic (mod8), diatonic (mod7), whole-tone (mod6), and pentatonic (mod5). The article then demonstrates that the generalized operation is not linked to any one compositional style in the twentieth century by showing its use in works by Debussy, Stravinsky, and Schoenberg. Finally, it defines a new equivalence class, the modular set type, which groups together those set classes that may be connected via the generalized transformation, and uses the new equivalence class and generalized transformation in analyses of Webern's op. 5, no. 3 and Stravinsky's Concerto in D.
UR - http://www.scopus.com/inward/record.url?scp=60949176717&partnerID=8YFLogxK
U2 - 10.2307/745862
DO - 10.2307/745862
M3 - Review article
AN - SCOPUS:60949176717
SN - 0195-6167
VL - 21
SP - 200
EP - 229
JO - Music Theory Spectrum
JF - Music Theory Spectrum
IS - 2
ER -