The Cosmic Score | Lab 21: Chordal Alloy & Metamaterial Synthesizer

Harmonic Orbital & Chromatic Wheel

Click any of the 12 nodes to assign Element A, B, or C

12-Step Circle

Outer: 400–700 nm + 5ths Inner: Valence Orbitals (s,p,d,f)

Aerospace Ti-6Al-4V Hume-Rothery Structural Lattice

3:2 Perfect Fifth valence coupling between Titanium (3d) and Aluminum (3p) locks into a low-strain HCP/BCC crystal.

Geometry: 109.5° / HCP-BCC Hybrid

Host A Sites Alloy B Sites Dopant C / Cooper Wave

Drag to Rotate 3D Unit Cell • Scroll to Zoom

Standing-Wave Hybridization & Phonon Dispersion

Superposition Ψ_A(x) + Ψ_B(x) + Ψ_C(x) & acoustic phonon transport

3:2 Phase-Locked

Cyan: Host Ψ_A • Gold: Alloy Ψ_B White/Crimson: Hybridized Lattice Envelope

Electronic Bandgap & Chromatic Emission Spectrum

Valence-to-Conduction energy interval ΔE_g (eV) & optical photon peak

Metallic / 510 nm

400 nm (Violet / 3.1 eV) 700 nm (Red / 1.77 eV)

Emergent Solid-State / Metamaterial Class Consonant Hume-Rothery

CONSONANT STRUCTURAL ALLOY (3:2 PERFECT FIFTH)

Outer valence orbitals phase-lock at a low-integer 3:2 harmonic interval. Destructive wave scattering is minimized, yielding high tensile toughness, fatigue resistance, and smooth 1/f phonon damping.

Bayesian Orbital Phase-Locking (μ) 94.2%

Lattice & Boundary Controls

STAGES 1–3

Harmonic Detuning / Lattice Strain (Δν) 0.04 (Tuned)

0.00 (Exact Rational Lock) 0.25 (Strained) 0.50 (Incommensurate)

Dopant Frustration / Calcification (1 − δ) 0.15

Elastic Lattice (δ → 1) Optimal Doping Calcified / Brittle (δ → 0)

Thermal / Acoustic Excitation (Ė₀) 300 K (0.85)

Cryogenic (90 K Supercond.) Room Temp (300 K) High-Temp Drive

Chordal Telemetry Matrix

Harmonic Interval Ratio

3:2 (1.500)

Perfect Fifth Triad

KL Divergence D_KL(P||Q)

0.060 bits

Orbital Mismatch

Stage 1 Coupling μ = e^−D_KL

0.942

Hume-Rothery Stability

Bandgap / Photon Peak

0.00 eV (512 nm)

Metallic Conduction

Stage 2 Coherent Work W(S) & Lattice Q-Factor

W = μηĖ₀S^m − γS^k

+1.84 eV/cell (Q = 480)

Scale-Invariant Unification Law: Whether hybridizing 10⁻¹⁰ m atomic orbitals ($s, p, d, f$) or engineering 10⁻² m 3D-printed metamaterial struts, standing-wave consonance ($1:1, 3:2, 4:3$) maximizes structural stability ($\mu \to 1$), whereas controlled tritone frustration ($\sqrt{2}:1$) nucleates topological bandgaps and Cooper-pair toroidal transport.