Geomagnetic polarity reversals are widely held to occur at random, with no periodicity to their timing — a position well supported by over 50 years of statistical analysis. This paper shows that the same reversal record, examined not as a sequence of reversal timings but as the prevailing polarity condition through time, displays a clear periodicity near 1.11 million years. Using the standard 0—30 Ma geomagnetic polarity timescale sampled on a 1000-year grid, a continuous-frequency spectrum reveals twelve dominant cycles between 0.2 and 6 Ma, refined here to five significant figures. Two of the next-strongest peaks relate to the dominant 1.11019 Ma cycle by simple, clean ratios — 0.74013 Ma (2/3) and 3.33146 Ma (3×) — each within a tenth of a percent of an exact fit. Independently of this terrestrial result, two distinct mechanisms in the outer solar system yield periods of the same length: the Uranus—Neptune orbital energy exchange, established via numerical integration of the outer planets (the LONGSTOP project), gives 1.119 Myr — a drifting, near-resonant beat; and the Jupiter—Uranus perihelion anti-alignment, a stable secular frequency difference computable directly from measured planetary precession rates, gives 1.107 Myr — a fixed period. All three determinations, from three unrelated physical systems and methods, agree to within a fraction of a percent. The origin of these harmonic relationships, and of the agreement between the terrestrial and planetary figures, is left for future papers.