Spectral Elasticity: Development of Computational Frameworks for Spectral and Microtonal Composition
Motivation & Context
Traditional Western music theory and the majority of acoustic instruments are predicated on the natural harmonic series and the fundamental frequency ratio of the octave (2:1). While French Spectralism (e.g., Grisey, Murail) shifted the compositional focus toward the interior of sound, many contemporary digital tools remain constrained by traditional harmonic grids or the fixed physical realities of acoustic instruments.
My research is driven by the compositional desire to transcend this physical „nature.“ I aim to construct an „Artificial Acoustics,“ in which spectral logic is preserved but rendered elastic. If we alter the fundamental axiom of the octave – changing the ratio from 2:1 to, for instance, 2.005:1 (stretched) or 1.995:1 (compressed) – the entire overtone structure (and consequently the harmonic resonance) must adapt logarithmically to maintain sensory consonance within this new system.
The objective is not purely technical but artistic: to explore the creation of new harmonic colors through new tonal systems that are perceived as logical and „correct“ to the human ear, despite their non-existence in physical nature. This requires the development of adaptive tools that allow composers to transform Timbre (Spectrum) and Tuning (Scale) in real-time, and therefore expanding the toolkit for composers like me being able to control the tonal system itself as a variable for their musical expression.
Objectives
The primary objective of this pre-doctoral project is the development and evaluation of a software library (framework) that makes „Spectral Stretching“ accessible through various synthesis methods for compositional application.
Specific Sub-Goals:
- Technical Implementation: Development of algorithms in SuperCollider, PureData, and Csound that allow for the parametric control of partial spreading (inharmonicity coefficients) and the resulting interval structures.
- Comparative Analysis of Synthesis Methods: Investigation of the advantages and limitations of different synthesis techniques in various contexts (Live vs. Offline) and applications (Abstract Synthesis vs. Concrete Sound Processing):
- Additive Synthesis (Discrete control of partials)
- Spectral Processing (Fourier / Inverse-Fourier Transform)
- Frequency Modulation (FM) (Algorithmic spectra)
- Physical Modeling (Modal Synthesis, Modified Karplus-Strong, Digital Waveguides / Kelly-Lochbaum Models)
- Artistic Validation: Composition of etudes and miniature studies to investigate how melodic and harmonic functions must adapt within stretched spectra to generate „consonance“ within inharmonic systems.
Research Plan & Methodology
My approach follows the „Research through Practice“ methodology. I am currently in the phase of technical foundation (Creative Coding) to build the instrumental basis for the artistic PhD.
- Phase 1: Additive Synthesis (Current Focus) Additive synthesis offers the most precise control. I am developing engines that generate overtones not as integer multiples but based on variable spreading coefficients.
- Phase 2: Spectral Transformation (FFT/IFFT) The research will expand to the manipulation of existing audio material. Using Fast Fourier Transform (FFT), spectral bins will be algorithmically shifted (stretched/compressed) and resynthesized via Inverse FFT.
- Phase 3: Extended Synthesis Techniques I aim to evaluate further digital synthesis methods regarding their suitability for spectral elasticity, specifically focusing on the trade-offs between computational efficiency and spectral precision (e.g., in FM or Modal Synthesis).
- Phase 4: Compositional Application Creation of an „Artistic Proof of Concept.“ This phase will investigate whether traditional compositional strategies (counterpoint, chord voicing) function within stretched spectra or if entirely new strategies must be developed – such as dynamic timbral matching, where the tuning scale automatically adapts to the timbre in real-time.