Mathematical Aspects in the Second Viennese School of Music
Mathematics and Music seem nowadays independent areas of knowledge. Nevertheless, strong connections exist between them since ancient times. Twentieth-century music is no exception, since in many aspects it admits an obvious mathematical formalization. In this article some twelve-tone music rules, as created by Schoenberg, are presented and translated into mathematics. The representation obtained is used as a tool in the analysis of some compositions by Schoenberg, Berg, Webern (the Second Viennese School) and also by Milton Babbitt (a contemporary composer born in 1916).
KeywordsMathematical Aspect Basic Series Chromatic Scale Inverse Series Equivalence Class Modulo
Unable to display preview. Download preview PDF.
- 1.Roland de Candé, (1983) A Música; Linguagem, Estrutura, Instrumentos, Edições 70, LisboaGoogle Scholar
- 2.Roland de Candé, (1986) Convite à Música, Edições 70, LisboaGoogle Scholar
- 3.Griffiths P., (1986) Dictionary of 20th-Century Music, Thames and Hudson, SingaporeGoogle Scholar
- 4.Holtzman S.R., (1994) Digital Mantras, The Languages of Abstract and Virtual Worlds, The MIT Press, Cambridge, Massachussets, EnglandGoogle Scholar
- 5.James J., (1993) The Music of The Spheres. Music, Science and The Natural Order of the Universe, Copernicus, Springer-Verlag, New YorkGoogle Scholar
- 6.Morgan R. P., (1991) Twentieth-Century Music,W.W. Norton und Company, New YorkGoogle Scholar
- 7.De Oliveira João P. P., (1998) Teoria Analitica da Mlsica do Século XX,Fundação Calouste GulbenkianGoogle Scholar
- 8.Carlota Simões, (1999) ‘A ordern dos nümeros na miisica do Século XX’ Coloquio Ciências, Fundaçâo Calouste Gulbenkian, N° 24, 48–59Google Scholar