The frequency and amplitude of edge localized instabilities in DIII-D tokamak H mode discharges are shown to depend on the discharge shape squareness. An abrupt increase in instability frequency and decreases in instability amplitude and edge pressure gradient are observed when the squareness is changed to a sufficiently large or a sufficiently small value. The observed changes in the instability frequency and amplitude correlate with a predicted loss, at high and low values of discharge shape squareness, of access in the H mode edge region to the ideal infinite toroidal mode number ballooning mode second regime of stability. When no edge region second stability regime access is predicted, the measured pressure gradient is in agreement with the predicted ballooning mode first stability regime threshold. When the second stability regime is predicted to be locally accessible, the edge region pressure gradient increases to values well above the first stability regimelimit.