Set Theory Elements Applied in the Analysis of Olivier Messiaen's Modes of Limited Transposition

摘要

This paper starts from Anatol Vieru's hypothesis that the human ear perceives modes as sets. Hence the necessity to analyse Messiaen's modes with the operations known from the set theory field: inclusion, intersection, union, set difference etc. and to extract the results from such an analysis. This may prove also helpful in distinguishing the modal colours which Messiaen himself operated with when producing his opuses, more often than not inapproachable even to those with an expertise in the musical art who too superficially ascribed them an artificial character or accused them of transvestite serialism.