  Contamination from instrumental effects interacting with bright astrophysical
sources is the primary impediment to measuring Epoch of Reionization and BAO 21
cm power spectra---an effect called mode-mixing. In this paper we identify four
fundamental power spectrum shapes produced by mode-mixing that will affect all
upcoming observations. We are able, for the first time, to explain the
wedge-like structure seen in advanced simulations and to forecast the shape of
an 'EoR window' that is mostly free of contamination. Understanding the origins
of these contaminations also enables us to identify calibration and foreground
subtraction errors below the imaging limit, providing a powerful new tool for
precision observations.
