To find a star's period we fold the data: take every observation, compute its phase at a trial period, and stack. The right period stacks the signal into a clean shape; a wrong one smears it into noise. That works beautifully — except for two families of wrong periods that stack just as cleanly as the right one.
Ground-based surveys observe at night. If you get roughly one observation per
night, then a signal at frequency f and one at
f + 1 cycle/day complete a whole extra turn between visits — and
land on exactly the same phase every time. The samples cannot tell
them apart.
A periodogram scores every trial frequency at once. The tall peak is the signal; the forest around it is the window function — the fingerprint of when you observed, not of the star. Switch the cadence and watch the forest change while the star stays the same.
A periodogram returns its tallest peak and no error bar. But when several periods
fit the data within the noise, the honest answer is not one number — it is a set of
modes with weights. On real ATLAS data the mode positions are predictable in
advance from the survey's own measured lattice
f = a·fsidereal + (b/4)·fsolar, and contact
binaries turn out to be genuinely ambiguous between P and
P/2 in 7 of 7 cases while detached eclipsing binaries are in
only 2 of 8 — the posterior is ambiguous exactly where the physics is.
The alias explorer has the real data.