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Enhancing Orchestration Technique via Spectrally Based Linear Algebra Methods

Spectral analysis has a rich and central place in the history and understanding of music, and modern music production relies heavily upon it. However, the advanced use of Fourier techniques as an aid to composition—as opposed to a tool for signal processing or sound synthesis—has been relatively unexplored until recently (Carpentier et al. 2006, 2007; Carpentier, Tardieu, and Rodet 2007; Hummel 2005; Psenicka 2003; Rose and Hetrick 2005, 2007). Because orchestration is the vehicle that carries a musical idea from imagination to reality, it is clear that composers’ orchestration techniques have a major impact on their musical expressions. Spectral analysis, by providing essential information about sound mixtures that are new or that are subject to constraints, can profoundly and positively influence that technique. In this article, we present our approach to such a computerized aid that extends the use of spectral analysis for orchestration. It uses a bank of Discrete Fourier Transforms (DFTs) of orchestral sounds, which are accessed in different ways designed to either perform sound analysis or propose orchestrations that imitate the energetic pattern of a reference sound. The output of the tool is a weighted set of all possible sound mixtures from the palette, a subset of the complete bank—typically instruments for which the composer is writing. Although our tool (Linear Algebra Based ORCHestration) is designed as an aid for composers, it is not our intent to propose a replacement of traditional orchestration technique with the blind use of new technology. After all, the sophisticated level reached by the empirical development of orchestration technique is proof that imagination and intuition are the composer’s most valuable and irreplaceable assets. Rather, we are proposing to combine the two, because we firmly believe that