The Tide Is a Chord — The Plover

Ninety days of the sea rising and falling at Seattle looks like noise — a restless wiggle, no obvious clock. But run it through a prism — the Fourier transform, which asks of any signal what pure tones is this made of? — and the noise shatters into a handful of sharp lines. Each line is a named gear in the moon–sun clockwork, and each one stands exactly where two centuries of orbital mechanics says it must. Six of these notes, added back together, redraw the month of ocean. Live from NOAA.

The top panel is a power spectrum: the horizontal axis is the period of a rhythm — how many hours one cycle takes — and a spike means the tide carries a strong pulse at that beat. A wiggle made of true noise would smear power everywhere. Instead almost all of it stacks into two clusters: a semidiurnal tower near twelve hours (the tide that comes twice a day) and a diurnal pair near a day (the once-a-day swing). The tallest spike is M2 — the principal lunar tide, the moon's pull sweeping past every 12 hours 25 minutes. Beside it sits S2, the sun's, at a clean 12 hours. K1 and O1 are the daily lines; N2 the moon's elliptical orbit beating against M2.

Two things hide in the gaps. First: M2 and S2 are only twenty-five minutes apart in period, but that tiny mismatch is the whole story of spring and neap tides — twice a lunar month the two lines fall into step and the tides run large, then drift apart and the tides go slack. The fortnightly rhythm everyone has watched at a beach is not a tide of its own; it is the beat note between two of these spikes, the same way two slightly-detuned strings throb. Second: the small spike near six hours is M4, a tone the sky never sent. It is the shallow harbour itself bending M2's smooth swell into a lopsided shape, and Fourier reads that distortion as a perfect overtone at exactly half M2's period — the sea floor harmonising with the moon.

How this was built. Ninety days of six-minute water level at NOAA station 9447130, Seattle, fetched live in your browser from the public CO-OPS API (no key) in three monthly chunks ending today, laid on a uniform six-minute grid with short gaps linearly filled. The series is linearly de-trended (removing mean sea level and any drift), Hann-windowed, zero-padded and run through a radix-2 FFT computed in the page — that is the spectrum you see. The reconstruction is a classical tidal harmonic fit: each named constituent's amplitude and phase found by projecting the record onto its astronomical frequency (M2, S2, N2, K1, O1, Q1, M4 — the set cleanly resolvable in a 90-day record; P1 and K2 fall inside K1 and S2 at this length and are folded into them), then the tones summed back, largest first. The figures are recomputed independently by the truth-check from the same samples; the FFT is verified against a second implementation and Parseval's theorem. Constituent periods are exact astronomical values; the spikes are wherever the live water decides to put them.