Understanding the organizing principles of brain activity can advance neurotechnology and medical diagnosis. Traditionally, brain activity has been viewed as consisting electrical field potentials oscillating at different frequency bands. However, emerging evidence suggests these oscillations can manifest as transient bursts rather than sustained rhythms. Here, we examine the hypothesis that rhythmicity (sustained vs. bursty) adds an additional dimension to brain organization. We segment neurophysiological spectra from 859 participants encompassing a dozen datasets across multiple species, recording techniques, ages 18-88, sexes, brain regions, and cognitive states in health and disease using a novel rhythmicity measure. Combined with simulations and brain stimulation, our results reveal a universal spectral architecture with two categories: high-rhythmicity bands exhibiting sustained oscillations and novel low-rhythmicity bands dominated by brief bursts. This universal architecture reflects stable modes of brain operation: sustained bands suitable for maintaining ongoing activity, and transient bands which can signal responses to change. Rhythmicity thus provides a powerful, replicable, and accessible feature-set for neurotechnology and diagnosis.