Mus2 serial serial#

This partition appears at the top of Boulez's precompositional table for this piece. Band der Structures von Pierre Boulez, Liner Notes, Wergo 60 011, Baden-Baden, this row is derived from Messiaen's Mode de Valeurs et d'Intensités. Klangfelder und Formflächen: Kompositorische Grundprinzipien im II.

Mus2 serial serial#

It is based on the sons simples that result from the more standard serial procedures Boulez employed in earlier works.Īccording to 4 Häusler, J. It is important to note that bars 105–120 and 170–185 feature a different generative technique, which I will not discuss in this context. Band der Structures von Pierre Boulez, Liner Notes, Wergo 60 011, Baden-Baden. Figure 1c presents a mathematical formula for the operation.Īn early and insightful discussion of this piece appears in 4 Häusler, J. All doubled pitch-classes are eliminated as these notes are combined in the final product. However none of these sources demonstrates the importance of these relationships to the structure of the music beyond the foreground.īuilding i5 and i3 (the ordered pitch-class intervals above the bass in e) over. In Pierre Boulez: Eine Festschrift zum 60. Renverser la vapeur…: Zu Musikdenken und Kompositionen von Boulez in den fünfziger Jahren. Bennett (Transl.) (original work published by Gonthier, Paris, 1963)ĭecroupet, P. Penser la Musique Aujourd'hui, Cambridge: Harvard University Press. The existence of isomorphic relationships in these works is mentioned in the literature (see for example 15–17 Boulez, P. It refers perhaps to Boulez's use of the terms sons complexes for sonorities generated by multiplication techniques as opposed to sons simples for sonorities generated by more standard serial procedures. Heinemann's term ‘complex multiplication’ is unrelated to the term as it is normally used in a mathematical context.

Pitch-class set multiplication in theory and practice. Simplifying complex multiplication, To be published clarifies the transpositional scheme behind the operation that Heinemann 6 Heinemann, S. paper presented at the Annual Meeting of the Society for Music Theory.

Musikalisches Hören serieller Musik, Saarbrücken: PFAU-Verlag. Simplifying complex multiplication, To be published 12 Mosch, U. Pitch-Class Set Multiplication in Boulez's Le Marteau sans Maıˆtre, University of Washington. Band der Structures von Pierre Boulez, Liner Notes, Wergo 60 011, Baden-Baden In Pierre Boulez: Techniques d’ Écriture et Enjeux Esthétiques, Edited by: Decroupet, P.

“ ‘ Penser sensiblement’ la musique: production et description du matériau harmonique dans le troisième mouvement du Marteau sans Maıˆtre”. In Pierre Boulez: Techniques d’Écriture et Enjeux Esthétiques, Edited by: Decroupet, P.

Some of these transpositional schemes have been individually described. Reproduced by permission of European American Music Distributors LLC, sole US and Canadian agent for Universal Edition Notes © 1967 by Universal Edition (London) Ltd., London Used by Permission of European American Music Distributors LLC, sole U.S. Transcriptions of Boulez's sketches are reproduced by permission of the Paul Sacher Foundation, Basel, Switzerland Research leading up to this article was funded by a University Research Council Grant from the University of Cincinnati.Ĭopyright clearance was secured from the following sources. I would like to thank Pascal Decroupet, Stephen Heinemann, Philip Lambert, Maria Losada, Guerino Mazzola, Andrew Mead, Brian Moseley, Robert Piencikowski, Joseph Straus, and the anonymous reviewers and editors of Journal of Mathematics and Music for their comments on earlier versions of this article.