E8 Root-Space Laboratory · Visual + Auditory

01Root receiver

Visible root set Projection Structural colour

Draw root-graph edges Mark ETQ-101 selected roots Show projection axes and rings

Edge visibility 15% Root size 1.00×

02Eight-dimensional view

Rotation speed 0.24× Exponent-7 depth 72% Depth-plane phase 0° Triality phase q → q

Drag the canvas to rotate. Scroll to zoom. Double-click to reset. Coxeter-plane mode preserves the exact two-dimensional projection; added depth is a declared display receiver.

03ETQ auditory receiver

Event traversal Receiver tempo 120 BPM Event subdivision External receiver A4 432.0 Hz

Map family, degree and ring to timbre

Canonical: symbolic MIDI notes 13–113. Acoustic tuning and sound are external receiver choices.

04Local capture

Load settings

WAV rendering is deterministic 48 kHz stereo PCM and remains entirely inside this browser.

ACTIVE PROJECTION RECEIVER

Complete E8 · 240 roots

Eight exact Coxeter rings, each containing 30 roots, with the exponent-7 invariant plane supplying optional display depth.

COXETER + DEPTH

E8 root polytope receiver

240 roots 6,720 edges audio idle

drag rotate · wheel zoom · click inspect · double-click reset

q = 0 q = 1 q = 2 triality fixed Colours change with the structural palette.

ROOT INSPECTOR

Select a root

Doubled coordinates will appear here.

ETQ symbolic note — Receiver frequency: —

EVENT RECEIPT

ETQ-101 basis traversal

101 events · 33 low / 33 mid / 33 high + 2 singlets

E8 roots 240 112 integer + 128 half-integer

Root graph 6,720 56 neighbours per root

D4 triality 12 + 76×3 fixed roots + three-cycles

ETQ selector 2 + 33×3 101 root-indexed states

SONIFICATION PROFILE

Canonical identity first, receiver sound second.

ETQ-101 supplies the reversible symbolic code: M(m,q) = 14 + 33q + m, with fixed singlets at MIDI notes 13 and 113. This lab then declares a separate e8-geometry-auditory-display-v1 receiver: root family shapes partials, selected-graph degree shapes brightness, Coxeter ring shapes spectral colour, qutrit label shapes pan, and the SCL value shapes phase modulation. Tempo, A4, gain, timbre, PCM, and WAV are recorded receiver settings—not E8-derived constants.

q = 0 MIDI 14–46 · low lane · SCL +1 q = 1 MIDI 47–79 · mid lane · SCL −2 q = 2 MIDI 80–112 · high lane · SCL +1

INTERPRETATION BOUNDARY

Exact E8 mathematics; authored projection and auditory display.

The 240 roots, inner products, 6,720 graph edges, Coxeter element, 8×30 ring structure, embedded order-three D4 triality, and ETQ-101 selector are reproducible mathematical constructions. The exponent-7 depth axis, screen perspective, traversal order, low/mid/high display polarity, receiver tuning, waveform, loudness, timbre and WAV realization are declared design choices. They do not establish a preferred physical frequency, a 101-dimensional E8 representation, or an acoustic law of E8.