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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 the evolving landscape of music technology, where technological advancements incessantly reshape creative practices, “Campi Instabili” pioneers a novel exploration that incorporates tetrahedral geometry within spherical loudspeaker arrays to challenge and enhance spatial auditory experiences. This project not only pushes the boundaries of conventional sound synthesis but integrates granular synthesis technique and spatial audio design to optimize acoustic interactions within varied performance spaces.

The introduction of a custom-developed C++ software bridges technological ingenuity with artistic inquiry, enabling a bespoke synthesization process that tailors soundscapes dynamically to the acoustical properties of each performance location. This shifts the conventional role of performers in acousmatic music to active participants who respond and adjust to their sonic environment, facilitating an immersive and adaptive auditory experience.

2 Conceptual Background and Theoretical Underpinnings

The core idea of “Campi Instabili” draws upon the speculative essence of sound synthesis, uniting computational technologies with philosophical insights on potentiality and aesthetic experience. This initiative goes beyond the limited traditional views by intertwining sound technology with live spatial tuning, exploring the possibilities within acoustic and architectural dynamics.

### 2.1 Speculative Sound Synthesis

The speculative approach in “Campi Instabili” explicitly challenges pre-existing compositional frameworks, proposing instead a dynamic and interactive methodology where sound synthesis becomes an explorative artistic tool rather than just a technical process.

### 2.2 Interdisciplinary Integration

Drawing on principles from acoustics, psychoacoustics, and computational musicology, this project views sound as a complex interplay between physical space and human perception. Utilizing an innovative spherical loudspeaker array, it challenges traditional inward-focused listening experiences by designing outward-radiating soundscapes that redefine spatial dynamics.

### 2.3 Reimagining Musical Composition

Here, musical composition is treated synonymously with sound synthesis, illustrating a shift from traditional composition pathways to a model where integration with the designed hardware is intrinsic to the creative output. This method seamlessly incorporates technology with artistic expression, enhancing both the control over and contingency within the resulting soundscapes.
2.4 Contemporary Music Influences
Drawing from an array of venerable composers and their distinctive approaches to music composition and performance, “Campi Instabili” is deeply informed by a rich tapestry of contemporary musical thought. The piece conceptualizes loudspeakers not merely as mediums of sound projection but as integral performers—akin to traditional instrumentalists—exploring the spatial qualities of their environment. This innovative perspective is inspired by Giorgio Netti’s profound inquiry into what constitutes an instrument, treating it as a “tool to investigate the space.” This notion is vividly integrated into the composition, paralleling the practices of a string instrument performance where interaction with space is intrinsic to the sonic outcome.

Gerard Grisey’s technique, particularly evident during a rehearsal at Villa Medici, where he adjusted the performance tempo of “Les espaces acoustiques” to accommodate the room’s reverberance, profoundly influenced the adaptive approach in “Campi Instabili.” This concept of pre-performance tuning is directly borrowed to allow the piece to resonate harmoniously with the unique acoustics of any given space, questioning traditional rigidity in acousmatic compositions.

Further enriching the piece’s conceptual underpinnings is Agostino Di Scipio’s “Audible Ecosystemics”, which explores the dynamism of live electronics in evolving, self-organizing auditory setups. Likewise, John Cage’s philosophies from “Silence” emphasize the uniqueness of all listening points and the potential of non-conventional performance spaces, which encourages embracing the inherent variability and richness of sonic experiences outside traditional venues.

Iannis Xenakis’s experiments with granular synthesis and Michelangelo Lupone’s work, particularly “Canto di Madre” and “Forma del Respiro”, also serve as significant inspirations. Under Lupone’s mentorship during the advanced master in Electronic Music Composition at Santa Cecilia in Rome, a crucial bottom-up approach in music composition was adopted, emphasizing a granular and foundational buildup in structuring sound—a technique pivotal to the realization of “Campi Instabili.”

3 Design and Development

The design and development of “Campi Instabili” focus on combining advanced sound synthesis techniques with a unique outer-radiating spherical loudspeaker array, known as S.T.One, based on tetrahedral geometry. This geometry is crucial for exploring the complex interplay between zeroth and first order Ambisonics which are vital in achieving the piece’s aesthetic and conceptual goals.

#### 3.1 Hardware Integration

A significant aspect of the project revolves around utilizing the tetrahedral loudspeaker configuration. The S.T.One, with its geometric precision and symmetry, offers an optimal setup for experimenting with different sound placements and transitions essential for exploring the spatial dynamics of sound. The positioning and distance between the speakers are meticulously calculated to optimize auditory effects and control crosstalk, which directly affects the perception of the compositional content.

#### 3.2 Custom Granular Synthesis Development

At the heart of “Campi Instabili” is a custom-built granular synthesis engine specifically crafted for integration with the S.T.One hardware setup. This granulator uses synthetic sine waves manipulated at various phases to match the spatial characteristics dictated by the tetrahedral array. Each grain of sound is enveloped within unique curves tailored to utilize phase relationships effectively between the loudspeakers, enabling the creation of complex auditory phenomena.

#### 3.3 Software Architecture

The granular synthesis software is based on an object-oriented programming paradigm, efficiently encapsulating various audio processing functionalities. This architecture offers flexible manipulation of sound particles, where parameters like grain size, dispersion, and envelope shapes can be dynamically adjusted. Specific classes manage tasks such as audio output and waveform generation, working cohesively to ensure a direct and intuitive link between compositional decisions and their auditory outcomes.

#### 3.4 Integrating the Listening Environment

Adjusting to the acoustic interplay between the loudspeaker array and the surroundings is critical. Tuning sessions adjust frequencies and timbres based on the room’s response to sound propagation, aligning the synthesis with the specific concert space and mirroring traditional practices of tuning instruments to their environment. 

#### 3.5 Rendering and Performance Preparations

The final sound output involves rendering the piece into an A-Format audio file, compatible with the S.T.One system. This conversion process is streamlined to maintain the spatial and timbral nuances designed during the development phase, ensuring high fidelity during live performances.


4 Aesthetic Consideration
The aesthetic framework of “Campi Instabili” centers on exploring new modalities of listening and comprehension within a space influenced by sound technology. This involves a critical engagement with sonic material, spatial characteristics of the environment, and the perceptual faculties of the audience.

#### 4.1 Redefining Spatial Perception

The spatial arrangement in “Campi Instabili” invites the audience to experience sound as a fluid, immersive environment rather than emanating from a localized source. This outer-radiating setup enhances the uncertainty between source and reflection, prompting listeners to navigate the space through auditory cues.

#### 4.2 Sound Materiality and Synthesis

Using purely synthetic sine waves, the sound design focuses on the clarity and purity of tones, highlighting micro-variations that inform the spatial character of the sound. This approach emphasizes textural possibilities and the gestalt phenomena arising from microscopic sonic changes.

#### 4.3 Interactive Composition and Performance

The integration of room acoustics into performance redefines the roles of composer and performer, advocating for a participatory role for performers akin to that of instrumentalists. This transforms the performance into a dynamic interaction between human and computational processes, where both are integral in shaping the auditory experience.

#### 4.4 Audience as Part of the Performance Ecology

Each listener’s unique position within the space suggests a non-dominant acoustic field view, emphasizing an egalitarian approach to auditory experiences. This dynamic engagement encourages continuous renegotiation of auditory perspectives, actively constructing individual auditory experiences through movement and attention.

#### 4.5 Challenging Conventional Aesthetic Experience

By merging sound art with technology, “Campi Instabili” questions traditional musical performance boundaries, engaging critically with the influence of technology on cultural perceptions of sound and space.

5 Analysis and Discussion


“Campi Instabili” manifests an innovative integration of computational sound design and real-time acoustic adaptation, demonstrating how advanced technology can be harmoniously embedded in artistic practices. This project serves as a case study in utilizing speculative art to push the envelope in digital music performance, emphasizing the fluid roles of composer, performer, and technology in creating immersive auditory experiences.

### 5.1 Technology and Space: A Symbiotic Relationship

The project exemplifies how spatial characteristics can actively shape and be shaped by computational sound technologies, illustrating a symbiotic relationship that enhances and personalizes the listener’s experience.

### 5.2 Rethinking Compositional Practice

Reflecting on the speculative nature of the composition, this intervention in traditional music making reveals new pathways for artistic expression where variability and adaptability become central elements.

### 5.3 Broader Implications

Ultimately, “Campi Instabili” not only challenges conventional auditory experiences but also encourages a broader discourse on the role of computational technologies in the future of sound art and music performances, suggesting possibilities for further interdisciplinary studies.
### 5.4 Case Study: Performance in Rome

On September 24, 2023, “Campi Instabili” was performed at the Teatro Studio Borgna within the Auditorium Parco della Musica in Rome, marking the final presentation of a year-long advanced master in Electronic Music Composition. Giuseppe Silvi, the creator of the S.T.One loudspeaker, showcased the composition, which utilized the unique S.T.OneL model. This model employs a truncated tetrahedral design optimized to enhance sound dispersion and promote aural delocalization, critical in achieving the composition’s spatial effects.

During the technical setup, it became apparent that the acoustical dynamics of the live environment differed significantly from the studio conditions. Particularly, the omnidirectional subwoofer signal, initially part of the composition, was found to disrupt the spatial delocalization effect and was subsequently deactivated. This decision highlighted the critical nature of live environmental testing and adjustments.

Throughout the rehearsal and live performance, meticulous attention was paid to refining the sound’s clarity and dispersion, especially in sections featuring granular synthesis. The fine tuning allowed the piece to interact dynamically with the venue’s acoustics, placing the finale’s harmonics effectively at the back of the room, thus enhancing the audience’s spatial experience.

The performance was well-received, prompting discussions around the techniques employed, especially the aspect of sound delocalization. Noteworthy was the conversation with Michele Dall’Ongaro, director of Santa Cecilia, who praised the delocalization technique’s effectiveness. Michelangelo Lupone, a luminary in adaptive electronic composition, also gave positive feedback, drawing parallels with his own experiential sound installations.

Further, the trial use of a tetrahedral Ambisonics microphone provided visual feedback on sound directivity, aligning well with auditory perceptions, and suggesting its utility in future performances and research.

The live setup involved a dedicated computer system running a DAW, connected to a sound card and a power amplifier with built-in speaker equalization filters, exclusively handling the S.T.OneL, thus eliminating the need for a mixer. This setup underscores the composition’s requirement for a precise acoustic design catered to each performance’s unique environmental characteristics.

Reflecting on the performance, the interplay between the audience’s engagement, the acoustic properties of the venue, and the technological setup, provided invaluable insights. These are anticipated to guide future adjustments in the composition and performance practice, particularly in enhancing the clarity and intelligibility of sound in various acoustic conditions, thus pushing the boundaries of spatial audio and performance interaction. This singular live experience, juxtaposed with studio settings, continues to shape the evolving narrative and dramaturgy of listening in “Campi Instabili,” emphasizing its speculative and adaptive essence in the realm of contemporary sound art.

### Future Directions: An Interdisciplinary Approach to Expanding the “Campi Instabili” Concept into Spatial Sound and Architecture

#### Introduction to Framework

Building on the groundbreaking work of “Campi Instabili,” which successfully integrated tetrahedral geometry and granular sound synthesis in spherical loudspeaker arrays, the next phase aims to delve deeper into the symbiosis between sound synthesis and architectural acoustics. By extending this exploration, we aim to pioneer new insights into how spatial sound compositions interact with architectural structures, thereby enriching both psychoacoustic and architectural studies.

#### Specific Research Questions

The progression of “Campi Instabili” prompts several advanced research questions:
- How do specific architectural features such as shape, materials, and internal volume influence the propagation of granular synthesis achieved through our unique tetrahedral speaker arrays?
- In what ways can unique acoustic properties of unconventional architectural spaces amplify the psychoacoustic effects of spatial sound compositions?

These inquiries seek to build on the established foundation by exploring the interaction between dynamic sound synthesis techniques and varying architectural environments.

#### Methodological Approach

In line with the methods utilized in “Campi Instabili,” we propose a continuation with a mixed-methods approach, comprising empirical acoustic measurements, in-depth psychoacoustic testing, and expansive listener feedback. However, expanding upon the foundation laid in “Campi Instabili,” our future methodological approach is structured to delve deeper into psychoacoustic testing, specifically focused on the localization and delocalization of sound sources using spherical loudspeaker arrays. The research will unfold in two key phases:

1. Localization Testing: Initial tests will assess the potential to delocalize the sound source from the loudspeakers and establish a quantitative measure of this effect. This involves determining the extent to which the source can be perceived as emanating from different points than its physical origin.

2. Accuracy of Delocalization: Following successful delocalization, we aim to evaluate how accurately listeners perceive the projected sound source location. This phase tests the precision with which the delocalized source is perceived to be coming from the intended points around the listener.

Additionally, to support these psychoacoustic tests, we propose a significant enhancement in our use of Ambisonics technology. Building on the preliminary use during the performance in Rome, an Ambisonics microphone could be employed in a more analytical capacity, providing a visual and measurable reference of sound source localization which can be directly compared with listener feedback. This not only adds a robust research component but also aligns with the scientific rigor required to validate psychoacoustic phenomena.


#### Integration with “Campi Instabili” Outcomes

Reflecting on the outcomes from “Campi Instabili,” we aim to explore additional spherical loudspeaker arrays that can be assessed for their potential in achieving sound delocalization. This exploration will include both psychoacoustic tests and technological assessments using Ambisonics microphones to measure and compare the efficacy of different arrays. This comparative study will help in identifying the optimal configurations that maximize the perceptual impact of sound delocalization, thereby enhancing the listener’s spatial audio experience.

#### Anticipated Impact and Relevance

The expansion of the “Campi Instabili” project into architectural realms is expected to have substantive multidisciplinary impacts. Academically, it will enrich discourse in environmental acoustics and computational musicology. Practically, the findings could influence architectural design practices by integrating advanced acoustic considerations from the onset. By harnessing the capabilities of advanced sound delocalization, we can transform ordinary architectural spaces into immersive sound environments. This broadens the public’s access to innovative sound art experiences and invites reevaluation of both non-traditional and traditional acoustic spaces, enhancing the relationship between sound spaces and listeners. This shift not only challenges but also expands the boundaries of conventional concert acoustics and everyday auditory experiences, pointing towards a future where every space can be reimagined as an immersive sonic environment.

#### Collaborative and Resource Opportunities

Just as “Campi Instabili” benefitted from interdisciplinary collaboration, this future direction will also thrive on partnership across disciplines. Engagements with architects, urban designers, sound engineers, and technology providers will be crucial. These collaborations, complemented by academic partnerships and potential funding from technological and cultural foundations, will facilitate research and the real-world implementation of our findings.

#### Challenges, Limitations, and Mitigation Strategies

Technical challenges in integrating bespoke sound systems within architectural designs demand meticulous planning and consideration of environmental variability. The primary challenge lies not in isolating background noise but in controlled manipulation of systematic sound sources to harmonize with ambient noise conditions. This involves adapting to non-standard acoustic effects such as uneven reverberation and invasive resonances, which might occur outside the controlled settings of traditional concert halls.

### Risk Management in Mitigation Strategies:
Systematic noise sources and uneven reverberation represent significant challenges when exiting traditional concert spaces. These elements require careful analysis and integration within both the compositional framework and sound design. We plan to develop an array of tools designed for:
1. Analyzing and integrating systematic noise sources rhythmically and spectrally within compositions.
2. Adjusting to spatial and temporal reverberation discrepancies that could lead to excessive sound localization or resonance within certain frequencies or areas.

Furthermore, limited access to specific acoustic spaces necessitates the development of advanced analytical tools. These tools should enable both quantitative and qualitative pre-assessment of spaces, thereby allowing for tailored sound interventions that mitigate adverse acoustical effects. By equipping composers and sound designers with these tools, we aim to establish a robust framework for adapting to and enhancing the acoustic qualities of diverse environments.


#### Proposed Timeline and Phases

Echoing the structured approach of “Campi Instabili,” the proposed timeline over three years will encompass:
- Year 1: Extensive pilot studies and development of initial architectural collaboration frameworks.
- Year 2: Implementation of sound interventions in various architectural settings and comprehensive data gathering.
- Year 3: In-depth analysis and evaluation, leading to public dissemination through exhibitions and symposia.

#### Conclusion: An Invitation for Expanded Collaboration

“Campi Instabili” has opened a fascinating conduit between sound synthesis and spatial dynamics. We extend an invitation to the academic, artistic, and architectural communities to collaborate in this promising interdisciplinary venture. Together, we aim to further dissolve the boundaries between sound, space, and perception, paving the way for future innovations at the nexus of technology, art, and architecture.
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