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 the integration of spectral analysis in orchestration technique can expand the boundaries of the composer's imagination and intuitive flair.

The article is organized as follows. After reviewing related research, we introduce the structure and mathematics of our tool and its potential to analyze and compare different orchestrations. Then, the tool's main asset, its capability to produce orchestral propositions, is illustrated with an example from the works of the first author: L'identité voilée. Finally, we sketch unresolved issues and the directions we intend to follow with our approach.

Related Research

Carpentier and colleagues (Carpentier et al. 2006, 2007; Carpentier, Tardieu, and Rodet 2007) introduced a tool that generates orchestral mixtures that imitate a target sound. The tool uses a short-hand instrument database, reduced from a larger sound-sample database. A sound is analyzed and defined in the instrument database in terms of acoustical features: pitch, fundamental frequency, spectral centroid, and harmonic spectrum, each of which affects the timbre. Based on pitch criteria, the orchestration engine selects sounds from the instrument database that could potentially be part of the proposed orchestral mixtures. Then, using a hybrid genetic/local-search algorithm, combinations are created. These are then evaluated using a multi-objective approach, searching for the sound mixture that has the best value for each of these acoustical features.

Hummel (2005) proposes a method that synthesizes the spectral envelope of a phoneme using the spectral envelopes of different sounds of musical instruments. A database of spectral envelopes is created by measuring, for each sound, its absolute amplitude in dBA, then calculating and normalizing its spectral envelope. The program then computes the target's spectral envelope and iteratively accesses the database to find the best approximation. First, the spectral envelope of an instrument that best matches the target's spectral envelope is identified. Subtracting this envelope from the target's creates a new envelope. The tool then searches for the best match to this new envelope. The process is repeated until the target's spectral envelope is simulated sufficiently well.

Psenicka (2003) presents a similar method in his Lisp-based program called SPORCH (SPectral ORCHestration), but his iterative matching algorithm works on spectral peaks rather than spectral envelopes. In this case, each instrument is defined in the reduced database in terms of its most prominent peak values taken from an analysis of...