TAI·
EN/繁中

Resonance

Hear the relationship. See the structure.

Headphones recommended
Dormant resonance field. Press Begin to enable sound and controls.

Explore the Structure

Plate drive coordinates: (0.320, 0.180)

Root moves both tones together; Partner changes their relationship. Frequency determines the modeled response. Visual speed slows its phase evolution so the structure is visible.

Frequencies
432.000 / 648.000 Hz
Ratio
1.500000000
Deviation from nearest curated ratio
0.000 cents
Frequency difference
216.000 Hz
Renderer
Relationship
Field
Sound & Performance
Model & Mapping

Wave field: two directional sinusoidal waves superposed. Spatial wave numbers are scaled from frequency for display. Visual phase runs on a separate speed control; absolute pitch sets spatial wave number, not animation speed.

Plate: a normalized isotropic thin circular plate with clamped edge (zero displacement and slope). Eight Bessel modes, damping 0.035, unit radius, fₙ = 12λₙ² Hz; a point drive weights each mode. This is a truncated simulation, not a photograph of sound.

Fusion layers waves and plate displacement with artistic reflection, persistence, mineral hue and optical bloom. Hue is a TAI presentation mapping, not a physical sound-to-light equivalence. The metal timbre and chamber are synthesized, not measured recordings.

Solfeggio roots are contemporary sound-practice presets. Their chakra associations vary between practitioners; the instrument sets the listed Hz without assigning a healing effect.

Bowl texture blends the modeled point pickup with a softly voiced, bowl-inspired spectrum. It is synthesized, not a measured quartz bowl. The root can be exactly 432 Hz; the bowl voice adds overtones and the partner remains a separate frequency. 432 Hz is a selectable pitch reference, not a healing claim.

Plate sound samples the modeled displacement at a virtual pickup, using the same modal gains and phase lags. It is a sonification of a truncated steady-state model, not recorded radiated sound. Mirrored radial symmetry, contour lighting and optional rotation form a kaleidoscope projection; Raw mathematics shows the unreflected plate.

Close frequencies can create audible beats at |f₂ − f₁|. A large frequency difference is not necessarily perceived as slow beating.

Plate modal frequencies: 122.59, 255.12, 418.52, 477.25, 612.36, 729.94, 835.99, 1014.99 Hz

A simulated plate, seen through a kaleidoscope. Frequency changes its modal response; visual speed controls motion. The modeled plate pickup can blend with a bowl-inspired timbre. Reflection and light are an artistic projection.

Sound · Mathematics · Form

Two pitches become a relationship. Exact ratios reveal repeating structure; small detunings make it drift. The golden ratio keeps the trajectory open. Here, calculation supplies the form and an optical projection gives it material and color.

Tradition presets use documented musical intervals, with an adjustable starting pitch. Sa–Pa is inspired by Indian tanpura practice; this instrument uses a synthesized, bowl-inspired voice.

Sources & assumptions

University of New Mexico — struck and bowed crystal-bowl spectra

University of Cambridge NRICH — tuning ratios

Bhattacharyya — The Changing Ecology of the Kolkata Tanpura

Oak Ridge National Laboratory — clamped circular plate model

Web Audio — audio processing independent of graphics

Reduced graphics mode uses the same ratio and phase with a simplified field. No microphone or account is required.