I. Lineage

The seven geometries are inheritance, not invention. The Vesica Piscis opens Euclid's Elements in the third century BCE, where the overlap of two circles is used to construct the equilateral triangle — its name "fish bladder," from the Latin, came later through Christian iconographic adoption. The Seed of Life and Flower of Life appear across millennia and cultures: among gold artefacts at Mycenae, in northern Iran, in Assyrian relief, in the Forbidden City, and in contested form at the Osireion in Abydos. The Torus was studied by Pappus of Alexandria in the third century CE for its surface-area properties, and formalised in modern topology by Euler, Gauss, and Riemann. The Vector Equilibrium is the cuboctahedron — a name R. Buckminster Fuller gave it in 1940, recognising it as the only polyhedron whose edge length equals its radial distance from centre. He systematised the work in Synergetics (1975) and Synergetics 2 (1979). The Merkabah in Hebrew means chariot; its origin is Ezekiel's vision (sixth century BCE) and the Merkavah mystical tradition that emerged from it (c. 100 BCE–1000 CE). Metatron's Cube carries its name from the angelic figure of the Babylonian Talmud and medieval Kabbalistic literature. The depiction of Metatron's Cube and Merkabah as discrete geometric solids — and their grouping with the broader vocabulary of sacred geometry — is largely contemporary, traceable through Drunvalo Melchizedek's The Ancient Secret of the Flower of Life (1990, 2000) and the wider Western esoteric tradition.

The rendering technique sits in the lineage of pointillism. Georges Seurat and Paul Signac began the practice in Paris in the 1880s, building on Michel-Eugène Chevreul's earlier work on simultaneous contrast. Their wager — that the eye assembles colour optically from discrete marks more vividly than from blended pigment — is the wager our engine makes at computational scale. The rendering primitives are built on the p5.js community work.

We name these sources because the geometries and the technique are not ours, and the brand does not claim them as discoveries. We have built the engine that maps voice to geometry; the rest is inheritance.

II. The Rendering Engine

Every piece is constructed from individual stipple marks — single points of colour placed with floating-point precision on an 800×800 canvas. No gradients, no fills, no blend tricks. Every hue you perceive is the optical result of thousands of discrete ink marks overlapping at subpixel resolution.

The engine draws two primitive types: ink circles (100 concentric rings of stipples spiralling outward from a centre point) and ink rings (a single stipple ring at a given radius). Every geometry in the collection is composed entirely from these two primitives.

Rendering is chunked — each circle or ring cluster is processed as an independent task, yielding to the browser between tasks so the interface remains responsive. A typical piece takes 12–45 render tasks depending on the geometry, with each task placing tens of thousands of stipples before yielding.

Macro detail. Golden Metatron. Each dot is one stipple mark.

The MULTIPLY blend mode means colours mix subtractively, as pigments do on paper. Where a blue stipple circle overlaps a yellow one, you see green — not through computation, but through the same optical physics that governs watercolour and lithographic printing. This is pointillism in the tradition of Seurat and Signac, executed at computational scale.

III. The Seven Geometries

Your vocal frequency — captured as a 5-second weighted average during the hum — determines which sacred geometry manifests. The frequency spectrum is divided into seven zones, each mapped to a geometry — from the foundational Seed of Life at the lowest register to the counter-rotating Merkabah at the highest. The voice does not reach for a form. It arrives at one.

The Hz ranges above are rounded to whole numbers. The engine operates on the continuous logarithmic curve — boundaries are computed as floating-point thresholds, not integer values.

Every geometry is built exclusively from circles and rings — the fundamental language of geometry. There are no straight lines, no angular fills, no polygon rendering. The forms emerge from the overlapping relationships between curved elements, just as they do in classical geometric construction with compass and straightedge.

Equilibrium is derived from the cuboctahedron — a form Buckminster Fuller called the "Vector Equilibrium" because it is the only polyhedron in which every edge length equals the radial distance from centre to vertex. Fuller considered it the zero-phase geometry from which all other forms emerge. Our rendering projects its 12 vertices as concentric ink circle clusters arranged in an inner ring of 4 and an outer ring of 8, connected by a fine bridge spray of stipples that preserves the relationship between the two orbits without collapsing their colour fields. Spectrum-tier Equilibrium pieces render with two or three of the assigned palette colours rather than the full set, so the colour-DNA dot count on the archive label varies by geometry within Spectrum tier.

The Merkabah is the star tetrahedron — two interlocking tetrahedra, one pointing upward, one downward, rotating in opposite directions. In three dimensions it is a solid of counter-rotation; in the two-dimensional rendering, each tetrahedron is projected as three spiralling ring paths, giving six paths in total. The spiral motion preserves the sense of rotation that defines the form — static geometry made kinetic through the stipple field.

See where each geometry belongs → Placement

IV. The Colour System

The colour field emerges independently of the voice frequency — a separate dimension of the capture. Where your voice determines the geometry, the palette arrives at the moment of materialisation. No two captures receive the same palette in the same order, even within the same geometry. Colour and form arrive together, seeded by the mathematics of the moment.

Perceptual Colour Space

All colour generation operates in the OKLCH perceptual colour space (Oklab Lightness-Chroma-Hue), defined in the CSS Color Level 4 specification. Unlike HSL or RGB, OKLCH ensures that equal numerical steps in hue produce equal perceptual steps in colour. This means our harmonic schemes produce genuinely balanced palettes, not the lopsided results that plague HSL-based generation.

The conversion pipeline runs: sRGB → Linear RGB → CIE XYZ → OKLab → OKLCH, with the reverse pipeline for rendering. All intermediate calculations use floating-point precision.

Palette Character — Full Reference

Twelve palette types across four families. Each carries a different tonal quality — from monochromatic restraint to full-spectrum colour. The three Alchemical palettes and the two Fortune palettes are fixed and assigned at the moment of capture. Heritage draws from the Mediterranean. The six Spectrum schemes are generated mathematically from the OKLCH colour space, each with its own harmonic logic.

Every palette is shuffled after generation. Because colour assignment to geometric elements is position-dependent, the same set of colours in a different order produces a visually distinct piece. This shuffle multiplier is a significant driver of collection diversity.

V. Combinatorial Uniqueness

More possible captures than will ever be made.

Across seven geometries and the colour-system distributions, 16,974 distinct palettes generate 118,818 possible compositions. The collection is capped at 7,777 sealed editions. Roughly 15 possible compositions for every edition that will ever exist — though only one composition arrives for each captured voice.

Layer 1: Discrete Palette Combinations

Layer 2: Geometry × Palette

Each of the 16,974 palettes can manifest across any of the 7 geometries.

With 7,777 pieces drawn from 118,818 possible combinations, the probability of any two pieces sharing the same geometry and exact palette (including colour order) is vanishingly small.

Layer 3: The Moment of Capture

Even if two pieces shared the same geometry and identical palette, they would still be different at the level of the field. Every stipple is placed using floating-point coordinates fixed at the instant of capture — a configuration that exists nowhere before the hum and is committed permanently when the geometry materialises. With up to 2.98 million stipples per piece, the field of any one capture is a singular event in the engine's history.

No two captures occupy the same moment. No two moments produce the same field. The mathematics that places the stipples is deterministic — given the captured frequency, the assigned palette, and the moment's seed, the field can be reproduced exactly in print. But the moment itself is unrepeatable. Once committed, a capture is fixed: in the registry, in the render, and in the geometry of its specific stipple field.

VI. Voice Mechanism

The voice capture system records 5 seconds of audio via the Web Audio API, computing a real-time FFT (Fast Fourier Transform) to extract the dominant frequency. The system uses a weighted averaging algorithm that prioritises the sustained fundamental over transient harmonics, producing a stable Hz value that represents the speaker's natural vocal resonance in that moment.

The weighting follows a sinusoidal bell curve across the 5-second window — samples at the midpoint carry maximum weight, while the first and last moments are suppressed. This discounts breath onset, initial pitch instability, and trailing off, isolating the sustained core of the hum.

The voice does not merely select a shape. It initiates a cascade. The geometry determines the stipple architecture — how many circles, how many rings, how many hundred thousand marks. The palette, bestowed at the moment of capture, determines how those marks blend optically. The entropy of the rendering determines where each mark falls. Every layer is distinct. Every layer is unreproducible. The voice is the first domino.

For those who prefer not to use their voice, the Entropy path generates geometry through computational entropy, using the system's floating-point randomness as a frequency proxy. Every piece produced through this path carries an entropy hash in place of a Hz value.

VII. The Perfect Fourth

Divide the human vocal range into seven equal logarithmic zones and the step ratio between them lands close to the Pythagorean perfect fourth. Divide it into five and the ratio approaches the perfect fifth; into nine, the major third; into eleven, the minor third. Consonances from the harmonic series appear at every natural division of the range.

Seven was chosen for the geometric collection. The ratio that emerged — 1.3335, against the Pythagorean 1.3333 — is a property of geometric means over a 2.9-octave range. It is true. It is not unique. We surface both.

VIII. The Logarithmic Scale

Frequency-to-geometry mapping uses a logarithmic scale, not linear. Musical intervals are logarithmic by nature — a jump from 100 Hz to 200 Hz (one octave) is perceptually equal to 200 Hz to 400 Hz (one octave). A linear mapping would cluster most human voices into just 2–3 geometries, leaving the higher forms practically unreachable. The logarithmic mapping divides the vocal range (80–600 Hz) into 7 perceptually equal zones, ensuring all seven geometries are achievable across the natural range of human vocal production.

Neither boundary was chosen for mathematical convenience. 80 Hz is the floor of reliable vocal capture — below it, ambient noise dominates the signal. 600 Hz is the ceiling of sustainable hummed pitch across the human population. Both are determined by the body, not by the system.

The same person humming at different pitches on different days will produce different geometries. All seven are achievable. The system does not simulate or approximate — it measures and maps.

IX. High-Resolution Export

Sealed pieces are rendered at 6144×6144 pixels via a dedicated high-resolution buffer that re-executes the entire geometry pipeline at print scale. The high-resolution render uses identical parameters to the screen version — same stipple counts, same colour values, same geometric positions — scaled proportionally to ensure the print is a faithful enlargement, not a reinterpretation.

At 6144 pixels across, the print is rendered at more than seven times the resolution of the screen version. On Hahnemühle German Etching at 70×70cm, the stipple field reads as continuous tone at viewing distance and reveals its mark-by-mark construction only when the viewer steps in.

The high-resolution render is not an upscale of the screen image. The same stipples are placed at the same relative positions, recomputed at print-scale coordinates — every circle reconstructed at scale, every mark repositioned to its new floating-point location on the 6144×6144 canvas. The geometry is not enlarged; it is re-executed. This is why the print exhibits no upscaling artefacts: there was no image to upscale.

The same JavaScript runtime that draws the screen version produces the print version. There is no separate print engine, no Photoshop step, no human intervention between capture and output. The mathematics that placed the first stipple is the same mathematics that places the millionth.

X. The Archive Label

Every sealed print carries an archive label rendered directly into the artwork — not a sticker, not a separate certificate, but part of the image itself. The label sits in the lower border of the print and contains:

The label is baked into the high-resolution render at print time. It cannot be removed, altered, or forged without destroying the stipple field around it. No certificate of authenticity is needed. The art authenticates itself.

This is what we call moment engraving. We borrow the term from horology — where the maisons of Geneva, Glashütte and the Vallée de Joux engrave the movement's serial number directly into the metal of the calibre during finishing, in the same operation as the Côtes de Genève striping. The serial is the witness of the production moment. It cannot be separated from the watch without destroying the watch.

Vox et Forma extends the principle into the digital print. The Archive Label is engraved into the stipple field by the same engine that draws the field, in the same render pass, at the moment of capture. The seed that places every mark also places the label. Without the seed, neither can be reproduced.

We do not know of a precedent in printed-edition practice that integrates the certificate into the artwork at the moment of conception in this way. Sol LeWitt's Wall Drawings (1968–) treat the certificate as the artwork — but the certificate carries instructions for production, not identifying metadata about a specific produced instance. Manfred Mohr (P-021, 1969–) and Vera Molnár (Interruptions, 1968–69) signed their plotter drawings by hand, in graphite, after the plotter finished. Tyler Hobbs's Fidenza prints (2021–) are signed in graphite and accompanied by a separate certificate. If a precedent exists that combines what we have combined, we will cite it. Until then, this is the discipline we have chosen and the lineage we cite for it.

XI. The Rarity Policy

Rarity is assigned by uniform random draw at the moment of capture. The probability of each palette tier — Alchemical, Fortune, Heritage, Spectrum — is fixed in code and is the same for every voice that crosses the threshold.

We do not bias the assignment by traffic source, referrer, geography, browser, device, dwell time, collector history, time of day, or any other signal. Rarity is not weighted by behaviour or by route. The roll is the same for the first edition and the last.

The probability percentages are documented in Section IV. The Colour System. The voice-to-geometry mechanism is documented in Section VI. Voice Mechanism. Both are inspectable. The policy on this page is the brand's commitment to leave that probability undistorted.