  Moir\'e patterns are omnipresent. They are important for any overlapping
periodic phenomenon, from vibrational and electromagnetic, to condensed matter.
Here we show, both theoretically and via experimental simulations by ultracold
atoms, that for one-dimensional finite-size periodic systems, moir\'e patterns
give rise to anomalous features in both classical and quantum systems. In
contrast to the standard moir\'e phenomenon, in which the pattern periodicity
is a result of a beat-note between its constituents, we demonstrate moir\'e
patterns formed from constituents with the same periodicity. Surprisingly, we
observe, in addition, rigidity and singularities. We furthermore uncover
universal properties in the frequency domain, which might serve as a novel
probe of emitters. These one-dimensional effects could be relevant to a wide
range of periodic phenomena.
