Extending Xenakis: From Architectural Geometry to Sonification of the Philips Pavilion

Abstract: Architecture and music have been linked through proportion and temporal structure, yet architectural geometry is rarely viewed as a source of generative music. Revisiting Xenakis' one-directional transformation from string glissandi in Metastaseis to the ruled surfaces of the Philips Pavilion, we invert this workflow and sonify the completed Pavilion as a temporal composition. We reconstruct the Pavilion as nine ruled surfaces, extract their governing ruling lines, and subdivide each surface into structural lines and spatial sampling points. Four evenly spaced ruling lines per surface generate continuous string glissandi, while 3357 sampled points develop five density-based energy blocks and a sparse brass and woodwind subsequence. Implemented in Python, the system produces MIDI rendered in Ableton Live, accompanied by a real-time 3D visualization that reveals architectural motion, stasis, and structural contrast through sound and image. In general, this work paves the way for the transfer of architectural geometry as a performable musical structure, extending Xenakis's architectural and musical thinking to sonification and interactive music practice.

• The paper presents a reproducible pipeline that reconstructs nine ruled surfaces, extracts 36 structural lines and 3,357 points, and converts them into a deterministic two-phase MIDI composition.
• The system maps line length and vertical displacement to continuous string glissandi, while point density, coordinates, and structural strata control tremolo blocks and sparse brass and woodwind events.
• The synchronized 3D visualization makes the Pavilion’s geometry perceptible over time, while uniform sampling, fixed instrumentation, and limited interactivity identify priorities for curvature-adaptive and immersive extensions.

This paper presents "Extending Xenakis," a deterministic sonification system that inverts the historical transformation through which Iannis Xenakis converted the glissandi of Metastaseis into the ruled surfaces of the Philips Pavilion. Rather than treating the Pavilion as the static terminus of a music-to-architecture process, the authors reconstruct its geometry parametrically and map that geometry back into a temporal, multi-layer MIDI composition, accompanied by a synchronized real-time 3D visualization (2607.06589).

Background and motivation

The authors situate the work against the classical distinction, drawn from Lessing, between architecture as a spatial art and music as a temporal art. They argue that even after modernist and postwar attempts to introduce temporality into architectural perception, and despite Stockhausen's spatialization of sound, architecture has remained a passive container rather than a generative musical source. Xenakis's Metastaseis-to-Philips Pavilion trajectory is identified as the foundational exception: hyperbolic-paraboloid logic governed the slope, continuity, and density of string glissandi, and the resulting musical structure informed the Pavilion's form. However, in the absence of computational tools for extracting architectural geometry as quantifiable data, this relationship could not be operated in reverse.

The paper positions itself against two prior strands of related work. Parthenios et al. applied Xenakis-style correspondences to urban facades, but without preserving the historical and structural logic of Xenakis's synthesis; Torresan et al. sonified structural vibration measurements of a footbridge, which the authors characterize as system-response sonification of engineering data rather than sonification of geometric structure itself. The claimed contribution is therefore a sonification driven directly by the Pavilion's ruled-surface geometry—lines rendered as continuity and points as discreteness.

Geometric reconstruction

The Pavilion was reconstructed in Rhino from archival drawings, with Grasshopper used to rebuild and decompose the envelope into nine ruled surfaces. Each surface $S(u,v)$ is recovered from its two governing ruling curves via the boundary evaluation $S(u,0)$ and $S(u,1)$, the inverse of the standard ruled-surface interpolation. Each surface is then subdivided into 20 interpolated structural lines between its ruling lines, from which four evenly spaced lines per surface are selected—36 line segments in total—forming the geometric backbone of the string section. Along each structural line, 20 evenly spaced spatial points are sampled, yielding 3,357 labeled points grouped by surface. These points constitute the input dataset for the energy-block and event-based layers. The authors acknowledge that uniform interpolation and equal point division, adopted for continuity, fail to capture local curvature variations and thereby simplify certain geometric features in the sonification.

Sonification mapping

The composition is organized in two phases, mirroring the dramaturgy of Metastaseis. In the string glissando phase, each of the 36 line segments drives an independent string voice (12 violins, 8 violas, 8 cellos, 8 double basses), all initialized on pitch class G with octave placement by instrument range. Glissando duration is derived from normalized 3D line length, shaped nonlinearly as $\hat{L}_i = \tilde{L}_i^{\gamma}$ with $\gamma > 1$ to bias toward shorter durations, and bounded between $T_{\min}$ and $T_{\max}$. Vertical displacement between a segment's endpoints determines the direction and range of pitch motion, realized through continuous pitch bending rather than stepped MIDI notes. All voices hold their terminal pitches, and after a one-second rest the energy block phase begins: the Pavilion is divided into five equal-width vertical strata, point counts per stratum proxy local structural density, and these counts map linearly to the durations of five synchronized tremolo blocks separated by fixed rests.

A secondary brass and woodwind layer—flute, oboe, clarinet, bassoon, horn, trumpet, trombone, tuba, and English horn, consistent with the instrumentation of Metastaseis—is generated from a deliberately reduced subset of the 3,357 points. The authors justify this thinning as a structural control: converting the full dataset would saturate the texture and obscure the line/point contrast. Each point's $z$-coordinate encodes pitch, quantized to a diatonic G major set; $x$ maps to a beat-quantized onset time within the string section's global timeline; and $y$ modulates event density and instrumental distribution. Minimum inter-onset intervals per track and probabilistic downsampling during string rests maintain perceptual clarity. The full pipeline is deterministic, implemented in Python, producing MIDI rendered in Ableton Live.

Real-time visualization

A Python/matplotlib visualization (FuncAnimation with FFMpegWriter export) shares the sonification's global time reference, so architectural activation, musical structure, and animation remain synchronized. The Pavilion is rendered as a low-opacity point cloud with the 36 ruling lines in an inactive gray state; during the glissando phase, colored traversals with a bright moving head and trailing trace make each string voice's direction legible; during the block phase, points activate as dense colored fields stratified by vertical band; and brass events appear as sparse color-coded point triggers. A slow fixed-elevation camera rotation preserves the Pavilion's three-dimensional organization without disrupting temporal continuity. Surface-group color identities are held constant across phases, maintaining architectural legibility throughout.

Limitations and open questions

The authors identify three limitations. Geometrically, uniform sampling cannot capture local curvature variation, weakening the fidelity of the sonification for structurally complex regions. Musically, the universal adoption of the Metastaseis instrumentation constrains the system's expressiveness for other architectural styles and broader musical idioms. Interactively, the system is a rendered audiovisual artifact rather than an interactive environment. The most concrete open question left by the work is whether curvature-adaptive sampling strategies can preserve geometric detail without sacrificing the continuity that the current uniform scheme provides; the authors also propose extending the system to additional buildings and to VR/AR navigation, where users hear the sonification while moving through the space.

Conclusion

The paper demonstrates a complete, reproducible pipeline—from parametric reconstruction of nine ruled surfaces, through extraction of 36 structural lines and 3,357 sampling points, to a two-phase deterministic MIDI composition with synchronized visualization—that reframes the Philips Pavilion as a generative musical source. Its principal contribution is methodological: establishing architectural geometry as a performable structure and extending Xenakis's bidirectional music-architecture vision with contemporary computational tools, while its uniform-sampling and fixed-instrumentation constraints mark the boundaries of the current implementation.