In this paper, the basic conceptual foundations of my piano concert No. 1 are discussed. The actual compositional process happens at a subconscious ‘intuitive’ level which is difficult (or impossible) to describe in detail. Thus, instead of describing the ‘emotional core’, we focus on the purely constructional part of the composition. The basic concept relies on the theory of transformations of local and global compositions in suitably defined musical spaces, as outlined in Mazzola (1990) and implemented in the composition software PRESTO. The mathematical concepts used here are, in particular: algebraic modules, symmetries, manifolds and hierarchies.

1.  General background, basic principles

1.1.  Introduction, background

In this paper, we discuss the basic principles used in the composition of my piano concert No. 1 (CD SToA 1002.92, 1992). The concert was composed in 1988 and revised in 1992. A multimedia performance took place in the Art Museum Zurich in 1988. The performance at the KlangArt 1999 combined life piano improvisation with prerecorded music.

Since the actual compositional process happens at a subconscious ‘intuitive’ level, which is difficult (or impossible) to describe in detail, we refrain from describing the ‘emotional core’. Instead, we focus on the purely constructional part which may be of interest beyond this specific composition.

1.2.  The basic structure

The basic structure of the composition can be described as follows:

1. Basic theme (A): The entire concert is based on the melodic line given in in bars 65–66 of Beethoven’s Sonata op. 106 (Hammerklavier-Sonata).
2. Step 1: Consider A as a ‘point cloud’ in the four dimensional space M = T ×P ×D ×L, where T = Onset time, P = Pitch, D = Duration, L = Loudness. Apply a transformation f on A such that
   1. _T×P(f(A)) = _T×P(A) where _T×P is the projection on the subspace T ×P.
   2. f(A) is in general position in the sense that B = f(A) is not in any 3-dimensional hyperplane.