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by Wolfgang Chico Töpfer

Generally it could be confirmed that grammatical structures and formal languages reflect fundamental requirements for effective, automated music composition. Certain structures and properties of music could be adequately described by grammatical structures and formal models. Composition could be formalized as an algorithmic, data-based model which, as experiments have shown, proved to generate satisfactory results. A subset of certain aspects of (tonal) music evolved throughout the initial phases and laid the foundation of this work.

One important aspect is that only certain sequences of musical functions are musically sensible. Musical criteria to recognize similarity between musical segments and a musical reduction of the theme to its essential elements are other striking aspects that were considered necessary to formalize.

Focusing similarity on the theme melody was found to be an adequate, efficient and sufficient similarity refinement for the respective set of themes (ie. basically Mozarts piano variations). A special similarity definition with an emphasis on musical structure and diminution proved to be very useful and is thought to be successfully appliable on other types of tonal material as well.

Theme reduction is perceived as a prerequisite for the task of variation because otherwise the relevant theme elements do not seem to be distinguishable from the irrelevant.

Furthermore, a reductional theory has surfaced on top of Lerdahl and Jackendoffs time-span reductions (GTTM, 1983) and Viecenz' ground lines (Kernlinien, 1924), postulating a so-called theme groundline (Themakernlinie ) that reflects the essential elements of a musical theme. As a result, this theme groundline consists of two components so that a different reduction degree of bass and melody can be adequately represented. The identical structural design of each component allows a flexible interchange that makes relations between variations possible.

Abstract descriptions of theme and variation structures that explicitly represent musical information turned out to be elements of major importance. The complex segments, a music piece notation derived from the SALIERI sequences (and independently of the new GUIDO notation [Hoo97]) proved to be of great use for the description of theme phrase structures.

A scheme description language SLIM (Scheme Language for the Interpretation of Music) was developed in order to describe variation structures. It is generally able to represent musical information extracted from (particulary tonal) music given in conventional score notation.

A musically sensible concept is the application of multiple perspectives on single, musical objects. Thus, the theme ground line and base phrases possess different perspectives which allow to view music from isolated main parameters such as the pitch. An example for a dynamic, multi-perspective object is AVAs note agent, a representation of a tone as an intelligent identity that is able to switch the tonal view from purely diatonic to chromatic.

A category of its own is built by the aspects which are involved in the generation of structurally sensible variations. The placement of schemes according to functional and phrase-structural descriptions have proven to be sensible. The scheme search methods which are responsible for the scheme placement have shown themselves to be a fundamental, structurally directed means for the automated generation of (tonal) music. Switching off the functional dependency has produced a number of acceptable variations, also thanks to the approach of always choosing the most similar function (see experiments ).

Finally, a series of experiments was conducted with half of the generated variations satisfying a relatively high structural quality.

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