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New, massively redundant low‐frequency arrays allow for a novel investigation of closure relations in interferometry. We employ commissioning data from the Hydrogen Epoch of Reionization Array to investigate closure quantities in this densely packed grid array of 14‐m antennas operating at 100 to 200 MHz. We investigate techniques that utilize closure phase spectra for redundant triads to estimate departures from redundancy for redundant baseline visibilities. We find a median absolute deviation from redundancy in closure phase across the observed frequency range of about 4.5°. This value translates into a nonredundancy per visibility phase of about 2.6°, using prototype electronics. The median absolute deviations from redundancy decrease with longer baselines. We show that closure phase spectra can be used to identify ill‐behaved antennas in the array, independent of calibration. We investigate the temporal behavior of closure spectra. The Allan variance increases after a 1‐min stride time, due to passage of the sky through the primary beam of the transit telescope. However, the closure spectra repeat to well within the noise per measurement at corresponding local sidereal times from day to day. In future papers in this series we will develop the technique of using closure phase spectra in the search for the H  I  21‐cm signal from cosmic reionization.

H I 21‐cm Cosmology and the Bispectrum: Closure Diagnostics in Massively Redundant Interferometric Arrays