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NUMBERS AND NUMBER CORRESPONDENCES IN OPUS 40 BY ARNOLD SCHOENBERG: PYTHAGORAS AND THE QUADRIVIUM REVISITED
Abstract
Schoenberg's Variations on a Recitative for Organ, Opus 40, was written in 1941 at the request of William Strickland, general editor of the "Contemporary Organ Series" at the H. W. Gray Company. It is the thesis of this paper that the peculiarities of the score and Schoenberg's insistence that the printed edition conform in every detail to his manuscript were due to his use of number symbolism, to the fact that every note and every performance directive in the manuscript were created and placed to conform to an unstated numbering system of symbolic importance. These numbers, as used by Schoenberg, also express the Pythagorean theorem and the tetraktys. Further, Schoenberg used numbers to develop internal numerical correspondences between many of the various compositional components at both the micro and macro levels. The composition has many curious features. A few of the more prominent of these features would surely include: (1) the 12-note chord in m. 11 and the double pedal octaves in mm. 59-60 that are, as written, unplayable by a solo performer; (2) the registration suggestions that are not only confusing but also contrary to Schoenberg's objective of clarity and precision above all else; and (3) dynamic shadings (fp on a single note at mm. 125 and 128) that are impossible to realize because of the limitations established by the physical principles involved in organ tone production. The fact that all of the major compositional irregularities and much of Schoenberg's pronouncements concerning op. 40 can be explained by numbers, and especially numbers directly associated with Pythagoras, helps to clarify some of the mystery that has regularly surfaced following analysis by traditional means.
Subject Area
Music
Recommended Citation
ORE, CHARLES WILLIAM, "NUMBERS AND NUMBER CORRESPONDENCES IN OPUS 40 BY ARNOLD SCHOENBERG: PYTHAGORAS AND THE QUADRIVIUM REVISITED" (1986). ETD collection for University of Nebraska-Lincoln. AAI8614468.
https://digitalcommons.unl.edu/dissertations/AAI8614468