Zenodo · Apr 16, 2026
Spectral Differentiation: A Log-Frequency Coordinate System for Human EEG Bands
By Lacy M
EEG frequency bands have been defined by clinical convention rather than principled theory. We present the first formal model comparison of EEG frequency scaling using 5.2 million oscillatory peaks from 10 datasets (N = 3,323, ages 5-88). The study makes two contributions. The first is a coordinate system. Log-frequency organization is decisively superior to linear (ΔBIC > 50). Five genuine density troughs are recovered in 100% of subject-level bootstrap iterations, with a global geometric mean ratio of 1.617 (95% CI [1.609, 1.623]). Among named mathematical constants proposed in the frequency-scaling literature, only φ ≈ 1.618 falls within the bootstrap confidence interval, though a free-ratio model fits better. A φ-lattice coordinate system (bands at f₀ × φⁿ) produces the simplest within-band enrichment profiles (R² = 0.968), with all four boundaries within 2% of locally optimal positions. No fine-structure exists at φ-specific positions within bands. The second is a biomarker. Using this coordinate system, we introduce spectral differentiation --- the concentration of oscillatory peaks within bands --- as a novel individual-differences measure. Beta-low spectral differentiation predicts reasoning (ρ = -0.27, FDR-corrected, age-partialed, replicated under IRASA at ρ = -0.29). The lifespan trajectory shows developmental rise through adolescence, plateau from ~15 to ~40 years, and mid-life decline, substantially coupled to alpha peak frequency maturation (ρ = +0.76 to +0.78). Five-year test-retest reliability reaches ICC = 0.75. Spectral differentiation is uninformative about personality (0/11,970 FDR), medical variables (0 FDR), and psychiatric diagnosis after age control (0 FDR), suggesting domain specificity. A 10th confirmatory dataset (TDBRAIN, N = 1,226, 26 channels, clinical psychiatric referrals) replicates all population-level findings and extends the lifespan trajectory to age 88, revealing late-life α/β boundary degradation. All findings are organized into four evidential tiers from robust structural (multi-dataset, method-independent) through mechanistic hypotheses (untested). The complete extraction and analysis pipeline is replicated under IRASA (Irregular Resampling Auto-Spectral Analysis); we report which findings survive this method-independence check and which do not. Keywords: EEG, frequency bands, logarithmic scaling, golden ratio, spectral parameterization, oscillatory architecture, biomarker, cognitive development, spectral differentiation, FOOOF, IRASA Related identifiers: Supersedes: https://doi.org/10.5281/zenodo.18765773 (EEGMMIDB preprint) Supersedes: https://doi.org/10.5281/zenodo.18856274 (LEMON preprint) Data: https://doi.org/10.5061/dryad.1vhhmgr8t Code: https://github.com/neurokinetikz/research License: CC BY 4.0