On the Horizontal and Vertical Presentation of Musical Ideas and on Musical Space (II)

Abstract

The difficulties connected with the idea of synthesis do not originate with the fact that as soon as he starts to elucidate the laws that have been formulated in general terms, Schoenberg postulates a musical space that only has two dimensions, the horizontal and the vertical. The scientific origin of these concepts could tempt one to think of this space (strictly geometrically) as a plane surface, and then to imagine it as comprising the paper on which music is notated, the dimensions then comprising the directions of the notation itself or of reading. But this is not yet musical space, and only if one tries to imagine a synthesis on this plane surface does one tend towards the concept of a diagonal. The inadequacy of the ‘diagonal’ seems to have been sensed by those authors who directed attention to the temporal aspect of music and who (perhaps by a popularizing analogy with the idea of time as the fourth dimension) attempted to locate the synthesis within the domain of ‘time’—say, the rhythmic domain. Schoenberg—and Webern followed him in this—distinguishes with terminological exactitude: wherever vertical and horizontal appear as concepts on their own, the explanation is always added: ‘The elements of a musical idea are partly incorporated in the horizontal plane as successive sounds and partly in the vertical plane as simultaneous sounds’; or: ‘In accordance with this [law], harmony and melody, vertical and horizontal, form a musical unit, a space, in both of whose dimensions the musical substance is deposited’, and similarly in the draft for the Princeton lecture. The conception of the dimensions of musical space is therefore connected with ‘harmony and melody’—without ‘vertical’ and ‘harmony’, or ‘horizontal’ and ‘melody’, thereby being identical. But how do matters stand on this plane with the ‘unit(y)’ that primarily interested Schoenberg and with the ‘synthesis’ upon which Webern apparently directed his attention?

The Americanization of Arnold Schoenberg?. Theory, Analysis, and Reception

“…82 Ibid., 143. 83 See also Ringer 1990, 73-76, for a discussion of Swedenborg's ideas in the context of Schoenberg's unfinished oratorio Die Jakobsleiter. For a discussion of Schoenberg's conception of the unity of musical time and space and its relationship to Webern's music and thought, see Busch 1985;Busch 1986a;Busch 1986b. For a consideration of the impact of these ideas on Berg's music, see Covach 1998. the United States).…”