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Integrating Spaces: Exploring Granular Synthesis through Tetrahedral Geometry in Spherical Loudspeakers Arrays

Abstract. This composition pioneers a speculative approach to sound synthesis by employing tetrahedral geometry within spherical loudspeakers arrays, alongside a distinctive tuning process performed by the interpreter. This process involves identifying frequencies within a defined range that enhance spatial auditory qualities, through modalities like zeroth and first order Ambisonics propagation, thereby tailoring the performance to the unique acoustics of the space. Utilizing a custom-developed granular synthesis technique, realized through a dedicated C++ software, the work invites a recalibration of standard sound synthesis paradigms by intertwining the precise geometry of loudspeakers with the acoustic characteristics of performance spaces. Crucially, the inclusion of a pre-performance, that is a listening-based tuning by the interpreter to align the piece’s frequencies with the room’s acoustical properties, presents a ‘what if’ scenario that reimagines the role of instrumentalists in acousmatic music as active listeners and responders to the environment. Instead of delivering a fixed-media piece, this approach allows for a live, adaptive interplay between the composition, technology, and the unique spatial qualities of each performance environment. The resulting work not only challenges traditional auditory experiences but also opens new avenues for artistic exploration in the integration of sound synthesis, spatial audio, and live performance within music technology.
Keywords: Sound Synthesis, Spatial Audio, Outer-Radiating Spherical Loudspeakers Array, Ambisonics, Tuning Process, Low-order Modes of Propagation, Acousmatic Music, Space Perception
1 Introduction
In an era where technological advancements incessantly reshape the creative landscapes of sound synthesis and music technology, a deepened exploration into speculative applications becomes not only pertinent but essential. This project, embodied in the acousmatic composition Campi Instabili, presents a pioneering inquiry into the interplay between complex computational technologies and the acoustic environment, mediated through a novel application of tetrahedral geometry within spherical loudspeakers arrays.

Campi Instabili deviates from conventional methodologies by integrating a custom-developed granular synthesis technique with an outer-radiating spherical loudspeaker array, named S.T.One, structured on the principles of tetrahedral geometry. This configuration facilitates a unique auditory experience that transcends traditional sound propagation, utilizing both zeroth and first order Ambisonics to sculpt a 3D soundscape that is inherently tied to and influenced by the physical dimensions and characteristics of the performance space.

Central to this composition is the role of the interpreter, who, through a meticulous pre-performance tuning procedure, adjusts the frequencies to leverage the acoustical properties of the space, enhancing the spatial auditory qualities of the performance. This not only reimagines the role of instrumentalists in acousmatic music but also challenges the very paradigms through which standard sound synthesis is often approached.

The integration of computational processes and aesthetic inquiry in Campi Instabili serves as a speculative exploration into how generative potential of sound technologies can be made aesthetically palpable and creatively productive. This project seeks to make visible (or rather, audible) the computational underpinnings of sound synthesis, illuminating the oscillation between control and contingency inherent in artistic practice. Here, sound synthesis is not merely a technical function but a compositional tool that echoes the speculative ethos of combining experience with imagination to foster new knowledge and provoke alternative aesthetic experiences.

The subsequent chapters will delve deeper into the conceptual backgrounds and theoretical underpinnings of the project, elucidate the design and development process, and evaluate the aesthetic considerations integral to this approach. Furthermore, an analysis and discussion will reflect on the implementation and reception of the work, followed by insights into future perspectives and a concluding reflexion on the broader implications of this research within the fields of sound synthesis and music technology.

Through Campi Instabili, we venture into a realm where technology, space, and artistic creativity converge, creating a vibrant tableau that asks us to listen more closely to the architectures of sound and the spaces they inhabit. This project is not just an exploration of sound through technology but an invitation to reconsider the relationships between composer, interpreter, audience, and environment in the digital age.

2 Conceptual Background and Theoretical Underpinnings
2.1 Speculative Sound Synthesis and Philosophical Foundation

The concept of Campi Instabili stems from a speculative approach to sound synthesis, drawing on the philosophical inquiry of how computational technologies enable new aesthetic experiences. At the heart of speculative philosophy is the notion of potentiality—an exploration of what might be rather than what is. This project intertwines sound synthesis with speculative thought to question and expand the boundaries of traditional music composition and sound technology.

Campi Instabili ventures beyond the conventional paradigms of music production, where standardization often limits the acoustic and aesthetic possibilities. By employing a tetrahedral loudspeaker array, the project shifts focus from the listener as a passive recipient to an active interpreter who interacts with the space and the sound emanating equipment. This mode of interaction invites a reconsideration of the composer’s and listener’s roles, elevating both to co-participants in a sculptural compositional reality shaped by the performance space’s acoustic characteristics.

2.2 Interdisciplinary Approaches to Sound and Space

The project draws heavily from interdisciplinary theories, notably from acoustics, psychoacoustics, and computational musicology. By understanding sound as both a physical and perceptual phenomenon, Campi Instabili engages with concepts like spatial acoustics and human auditory perception to exploit the room’s acoustic properties actively. The use of a uniquely designed spherical loudspeaker array facilitates a direct engagement with these theories, using the physical space as an integral element of the sound synthesis process.

Moreover, the piece’s methodology resonates with the principles of Ambisonics, though it subverts the traditional inward-focused listening mode by radiating sound outward, redefining the spatial dynamics between the sound source and the listener. This approach challenges the listener’s auditory perception, encouraging a unique interaction with the diffused sound, thus aligning with speculative practice by oscillating between the known and the unknown, the experienced and the imagined.

2.3 Musical Composition as Sound Synthesis

Traditional distinctions between musical composition and sound synthesis are blurred in Campi Instabili. Here, composition is approached as a form of sound synthesis, integrating granular synthesis techniques directly with hardware design. This synthesis is not merely a tool for sound creation but a fundamental compositional element that shapes the music’s structural and aesthetic qualities. 

The granular synthesis approach in Campi Instabili, using sinusoidal waves and customized envelope curves, is a key aspect here. It allows for micro-level manipulation of sound, enabling the creation of complex acoustic phenomena such as standing waves and focal sound fields. This method challenges the standard use of granular synthesis by focusing on phase relationships and spatial distribution rather than purely timbral qualities, aligning with the speculative nature of questioning and redefining established norms.
2.4 The Role of Computation in Artistic Expression

Embracing computation as a core component of artistic practice, Campi Instabili explores how software and hardware can coalesce to create new forms of musical expression. The custom C++ software developed for this project does not merely play a logistical role but is integral to the artistic output. It encapsulates the compositional logic, embeds the synthesis processes, and interacts dynamically with the spatial properties of the performance area.

This computational approach does not just serve a reproductive function but is an active participant in the music creation process. It facilitates a dialogue between the composer, the performer, the audience, and the architectural space, fostering a holistic ecosystem where each element influences and reshapes the others. This is indicative of a broader theoretical positioning that sees technology not as a mere tool, but as a co-creator of artistic reality.

2.5 Conclusion

In conclusion, the theoretical underpinnings of Campi Instabili reflect a deep engagement with speculative practices in art and technology. This project challenges and expands the traditional notions of musical composition, performance, and listener engagement through an innovative synthesis of sound, space, and computational technology. By doing so, it not only questions the existing paradigms but also proposes alternative ways of thinking about and experiencing music and sound in the digital age.

3 Design and Development

The design and development of Campi Instabili is anchored in combining advanced sound synthesis techniques with a unique outer-radiating spherical loudspeakers array, known as S.T.One, based on tetrahedral geometry. This intricate geometry facilitates exploration into both zeroth and first order Ambisonics, providing the dual capacity of localized and diffuse sound fields, paramount in achieving the piece’s aesthetic and conceptual goals.

3.1 Hardware Integration

A significant aspect of the project revolves around the utilization of the tetrahedral loudspeaker configuration. The S.T.One, with its geometric precision and symmetry, offers an optimal setting for experimenting with different sonic placements and trajectories, essential for my exploration into the spatial dynamics of sound. The positioning and distance between the speakers are carefully calculated to control crosstalk and optimize auditory effects, directly influencing the perception of the compositional content.
3.2 Custom Granular Synthesis Development

Central to Campi Instabili is a custom-built granular synthesis engine, crafted specifically for integration with the S.T.One hardware. This granulator employs synthetic sine waves, which are manipulated at various phases to coincide precisely with the spatial characteristics dictated by the tetrahedral array. Each grain of sound is enveloped within distinctive curves tailored to utilize phase relationships between the loudspeakers effectively. This facilitates the creation of complex auditory phenomena without resorting to standard Ambisonics order techniques. The synthesis engine was developed in C++, leveraging the capabilities of ‘libsndfile’ library for audio file management. This setup ensured a seamless flow from sound synthesis to spatial distribution, an integral component of the immersive experience I envisioned.

3.3 Software Architecture

The granular synthesis software is structured in an object-oriented paradigm to encapsulate various audio processing functionalities efficiently. This architecture lends itself to a flexible manipulation of sound particles, where parameters like grain size, dispersion, and envelope shapes can be dynamically adjusted. The design includes a main file where the score is programmatically described and additional class files that manage specific tasks, such as audio output and waveform generation. These classes work in a cohesive environment to facilitate a direct and intuitive link between the compositional decisions and their auditory outcomes.

3.4 Integrating the Listening Environment

Recognizing the acoustical interplay between the loudspeaker array and its environment is paramount in Campi Instabili. Before performances, a tuning phase is conducted where the frequencies and timbres are adjusted based on the room’s response to low-order sound propagations. This pre-performance tuning not only aligns the synthesis with the specific concert space but also mirrors traditional acoustic practices where instruments are tuned to the room, thus ensuring that the spatial dynamics and acoustic peculiarities of each venue are considered in the final sound output.

3.5 Rendering and Performance Preparations

Upon final adjustments during the tuning phase, the piece is rendered into an A-Format audio file, compatible directly with the S.T.One system. The rendering process, though technically intricate, is streamlined through the software to take no more than 30 seconds on a standard performance setup. This efficiency ensures that the piece can be executed with high fidelity, preserving the spatial and timbral nuances crafted during the design phase.

Through these design and development stages, Campi Instabili not only challenges conventional music composition practices but also substantially contributes to the discourse on the relationship between sound synthesis, spatial audio technology, and acoustic ecology. This project underscores the potential of computational technologies and custom sound synthesis methods to enrich the aesthetic experience, fostering a deeper engagement with both the immediate and extended auditory environments.

4 Aesthetic Consideration
The aesthetic framework of “Campi Instabili” is constructed around the pursuit of discovering new modalities of listening and comprehension within the space influenced by sound technology. This approach involves a critical engagement with the sonic material, the spatial characteristics of the environment, and the perceptual faculties of the audience. By redefining the role of traditional sound reproduction systems as active, spatially aware instruments, the project encourages a re-evaluation of auditory experiences that extends beyond conventional boundaries.

#### 1. Redefining Spatial Perception

In “Campi Instabili,” the spatial arrangement and dynamic interaction of sounds generated through the tetrahedral loudspeaker array challenge the normative distribution paradigms of traditional stereo or surround sound systems. The outer-radiating configuration invites the audience to perceive sound not as emanating from a localized source, but as a fluid, immersive environment. This setup plays on the uncertainty between source and reflection, causing the listeners to navigate the space through auditory cues, thus fostering a more active mode of listening.

#### 2. Sound Materiality and Synthesis

The choice of granular synthesis using purely synthetic sine waves creates a sonic texture that emphasizes the clarity and purity of tones. This focus highlights micro-variations in timbre and phase relationships informed by the intricate geometrical positioning of the loudspeakers. By manipulating minute details within each grain of sound, “Campi Instabili” explores the textural possibilities and gestalt sonic phenomena that arise from such microscopic changes. The aesthetic intent is to render audible the subtle nuances that inform the spatial character of the emitted sound, thereby enhancing the experiential quality of the installation.

#### 3. Interactive Composition and Performance

The integration of room acoustics into the performance redefines the role of the composer and performer in creating music. By requiring pre-performance tuning based on the room’s acoustic response, the piece advocates a participatory role for the performer akin to that of an instrumentalist who adjusts their play to the resonant characteristics of the space. This act of listening and adjusting transforms the performance into a dynamic interaction between the human elements and the computational processes, where both are integral in shaping the auditory experience.

#### 4. Audience as Part of the Performance Ecology

The composition considers each listener’s location within the environment as unique, bringing forth the concept of an acoustic field where no single perspective dominates. This positioning challenges the normative hierarchy of performance practices and emphasizes an egalitarian approach to auditory experiences. The design of “Campi Instabili” implies that the audience, much like the performer, engages in a continual reorientation and renegotiation of their auditory perspective, actively constructing their auditory experience through movement and attention.

#### 5. Challenging Conventional Aesthetic Experience

By pushing the boundaries of what constitutes musical performance, “Campi Instabili” extends into the realms of sonic art and acoustic ecology, merging them into an integrated auditory spectacle. This approach not only serves as an exploration of technological and artistic fusion but also engages critically with the role of technology in shaping cultural perceptions of sound and space. The piece’s dependence on the architectural and acoustic peculiarities of its venue underscores a shift from a music centric to a sound ecology centric listening culture.

Through these aesthetic considerations, “Campi Instabili” not only aims to provide a unique sensory experience but also to provoke thought on the possibilities of composing and experiencing music in the context of contemporary technological landscapes. This project situates itself at the intersection of tradition and innovation, questioning and expanding the artistic potentials of sound as a medium.

5 Analysis and Discussion


#### Integration of Computational Technology with Acoustic Spaces

“Campi Instabili” represents an innovative exploration of the integration between computational processes and acoustic spaces through the use of an outer-radiating spherical loudspeakers array, S.T.One, informed by tetrahedral geometry. This setup not only challenges conventional speaker array configurations but also emphasizes alternative perspectives for sound synthesis and composition. By employing both zeroth and first order Ambisonics, the project effectively demonstrates how computational technology can be harnessed to manipulate acoustic environments in real-time, showcasing a strong interaction between sound synthesis and its propagation within a specific space.

#### Speculative Approaches to Compositional Theory and Practice

The project utilizes speculative artistic approaches by oscillating between the pre-defined and improvised, particularly in how the granular synthesis responds to the spatial characteristics detected during the pre-performance tuning phase. This methodology underscores a significant departure from standardized compositional practices, embracing instability and variability as fundamental elements of the composition process. The ability of the piece to adapt to the acoustic properties of different performance spaces exemplifies a speculative form of composition where the outcome is contingent on the interaction between the computational design and the physical environment.

#### Sound Synthesis as Compositional Technique

In “Campi Instabili,” sound synthesis does not merely serve as a tool for generating auditory textures but is elevated to the role of a compositional technique. By emphasizing phase relationships and utilizing granular synthesis tailored to a specific loudspeaker arrangement, the project highlights sound synthesis as an integral element of the compositional structure. This approach challenges traditional boundaries between composer, performer, and technology, proposing a new framework where these roles are interdependent and fluid.

#### Aesthetic Experience of Computational Sound

The aesthetic experience offered by this project notably diverges from more conventional multi-channel audio works. By positioning the spherical array as a central performer and employing a practice of custom granular synthesis, the piece intricately links technological processes with perceptual experiences. The strategic use of sinusoidal waves and their interaction with room acoustics significantly affects the listener’s spatial experience, transforming computational data into a vivid sensory and emotional landscape.

#### Implications for Contingency and Control in Artistic Practice

This project exemplifies the tension between contingency and control in artistic practice, a core theme of the symposium. The pre-performance tuning and real-time synthesis reflect a high degree of control over the sound production process, yet the ultimate sound experience remains highly contingent upon the acoustic properties of the performance space and the real-time interactions therein. This balance showcases an effective use of technology not simply as a means to an end but as an active participant in the creative process, capable of influencing both the compositional output and audience perception.

#### Interdisciplinary Contributions and New Forms of Knowledge

“Campi Instabili” contributes to the wider field of sound studies by merging music technology, computational theory, and acoustic ecology. This interdisciplinary approach not only leads to new artistic practices but also fosters new forms of knowledge about how sound operates within and reacts to different environments. It opens up discussions on the possibilities for future technologies to further blur the lines between sound creation, space, and listener engagement.

In sum, the project underscores a pivotal shift in understanding the roles of composer, technology, and environment in contemporary sound practices. It serves as a profound exploration of how speculative approaches can inform and transform traditional paradigms in music composition and performance, providing a rich ground for future explorations in the field.


Future Directions: An Interdisciplinary Approach to Spatial Sound and Architecture

### Introduction to Framework

Our project’s outcomes have made it abundantly clear that the interplay between sound and architectural space holds immense potential for deepening our understanding of both psychoacoustics and architectural acoustics. To further explore this potential, we propose a comprehensive research framework designed to pioneer novel insights at the intersection of architecture, sound technology, and auditory perception.

### Specific Research Questions

Central to this framework are several pivotal research questions:
- How do architectural variables like shape, material, and size influence the acoustic properties of granular synthesis in situ?
- Can the idiosyncratic acoustics of non-standard architectural spaces enhance the psychoacoustic experience of spatial sound compositions?

These questions aim to uncover the nuanced relationships between architectural design and sound perception, highlighting the transformative potential of their integration.

### Methodological Approach

To address these questions, we propose employing a mixed-methods approach combining empirical acoustic measurements, qualitative listener feedback, and psychoacoustic analysis. This approach will facilitate a robust examination of how sound interacts with varying architectural environments, guiding the design of sound compositions tailored to specific spaces.

### Case Studies and Precedents

Historically, projects such as Iannis Xenakis’ “Polytope de Cluny” have elegantly demonstrated the power of integrating architectural form with sonic elements. Drawing inspiration from such precedents, we plan to document a series of experimental performances in environments ranging from modernist structures to unconventional urban spaces, analyzing how these settings inform and transform the listening experience.

### Anticipated Impact and Relevance

The insights gleaned from this research are expected to have broad implications:
- Academically, providing a deeper understanding of environmental acoustics.
- Culturally, offering new forms of engaging public sound art.
- Practically, informing architectural designs with enhanced acoustic considerations.

### Collaborative and Resource Opportunities

We seek to collaborate with architects, urban planners, and sound artists, creating a dynamic research collective that can fully harness interdisciplinary knowledge. Additionally, partnerships with academic institutions and funding from arts and science grants will be critical for providing the necessary resources and platforms for our studies.

### Visualizations and Conceptual Illustrations

[Insert conceptual drawings or visualizations here]

These visual representations will aid in illustrating potential installation setups and experimental designs, making our theoretical models tangible and accessible.

### Challenges, Limitations, and Mitigation Strategies

We anticipate challenges such as varying environmental noise levels and the need for precise audio equipment setups. Strategies such as selecting appropriate times for sound measurement and employing advanced sound isolation techniques will be essential to mitigate these issues.

### Proposed Timeline and Phases

Our preliminary timeline spans three years, divided into phases:
- Year 1: Pilot studies and initial case studies.
- Year 2: Full-scale experimental implementations and data collection.
- Year 3: Analysis, dissemination of findings, and public exhibitions.

### Conclusion: An Invitation for Engagement

We invite researchers, practitioners, and technologists to join us in this endeavor. Together, we can bridge gaps between theoretical research and practical application, enriching both artistic practice and scientific study. This proposed research framework not only addresses pressing questions at the nexus of sound and architecture but also sets the stage for future explorations that could redefine how we perceive and interact with our sonic environments.
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