3D Lattice & Laue Harmonic Ring
Reciprocal diffraction vectors locked to Circle of Fifths
Consonant Bragg Lock
Impurity / Crack Vector
Proton NMR Chemical Shift ($\delta\text{ ppm}$) & Harmonic Pitch Map
Top: Chromatic-Musical Spectrogram • Bottom: Cochlear Beating & $1/f^\alpha$ PSD
Click any spectral peak to audition its isolated pitch
Active Chord: C4 – E4 – G4 – C5 (Resolved)
1. Stage 1 Bayesian Coupling
$$\mu(S, \Delta\nu) = e^{-D_{KL}(P \parallel Q)}$$
Measures phase-lock between observed spectral peaks ($P$) and ideal harmonic lattice eigenstates ($Q$).
2. Octave-Scaled Mapping
$$f_{\text{audio}} = f_{\text{spec}} \cdot 2^{-n}$$
Maps THz/MHz spectroscopy peaks down $n$ octaves into the human cochlear band ($200\text{–}1000\text{ Hz}$).
3. Spectral Slope & Noise
$$P(f) \propto \frac{1}{f^\alpha}$$
Healthy crystals exhibit $\alpha \approx 1.00$ pink equilibrium; pre-fracture stress steepens $\alpha \to 2.08$.
4. Stage 2 Prigogine Work
$$W(S) = \mu\eta\dot{E}_0 S^m - \gamma S^k$$
Quantifies structural lattice integrity before defect frustration triggers macroscopic fracture.