Distribution and Instrumental Partition in the Variations op. 30 by Webern

This paper releases part of a research in progress, whose two goals are: (1) to build a method for the analysis of orchestration, which would be able to attend the concept of sonority as a structural element of musical form; (2) to point out, in Webern’s Variations op. 30, the interaction between what we define as “primary level” of composition (i.e. the organization of motivic-serial material) and the “secundary level”, which is the level where the orchestral resources the composer chose are organized. In this paper, we address only instrumental partitions and textures, and suggest some of their relations with the primary level.

For this task, we make use of an expanded version of the classical Theory of Partitions applied to music analysis, following and adapting an experimental developpment by Pauxy Gentil-Nunes. This way, this theory helps to evaluate the relative complexity of a texture by its index of dispersion – the most dispersed, the most complex. We borrow from Wallace Berry his textures’ categories to qualify that dispersions.

The size of this paper only allows short few notes about the way textures relate with orchestration and motivic-serial material in that work. Sections in which Webern appears to want the listener to easily grasp a “theme” or a serial-motivic contour, show more stable orchestral sonorities (i.e, less mutating, less dynamical) and less complex textures, than transitional or “climax” ones. On another hand, in most cases, the frequence of change of orchestration is faster than that of the serial sub-sets, although almost no instrumental setup is repeated along the piece – an interesting application of the principle of non-repetition. And, as a third and last insight, we observe that, in this piece, the density of orchestration (that is, the number of instrumental resources used at a given momentum) is not systematically correlated to simpler qualities of textures, as it may be expected, and as it is usual in previous orchestral music (e.g. Beethoven’s Symphonies), in which the denser the orchestration, the more agglomerated the voices.

In our conclusion, we suggest orchestration, as analyzed through partitions and texture’s qualities, is a key element to define each structural section of the piece, and its own funcionality in the whole form. We also suggest the hypothesis that the art of sound-organization (through the combination of available instrumental resoucres) could well be the locus of Webern’s aesthetics.