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 1.1101 Ma cycle by simple, clean ratios — 0.74026 Ma (2/3) and 3.3335 Ma (3×) — each within a tenth of a percent of an exact fit. The 1.1101 Ma periodicity is confirmed visually by folding the full 30 Ma record at this period. The origin of these harmonic relationships, and their connection to solar system cycles of very similar period, is left for future papers.