We perform extensive band structure computation for two-dimensional (2D) periodic arrays of rigid stainless steel cylinders in air, with Bloch vector being perpendicular to the cylinders. For cylinders 2.9 cm in diameter and period of 10 cm (i.e., filling fraction f = 0.066) there is no acoustic gap for frequencies below 6.4 kHz. However, the density of states reveals prominent minima at 1.7 and 2.4 kHz. These frequencies do agree with those of the first two attenuation maxima observed in the experiment [Nature 378, 241 (1995)] and are indeed related to diffraction from the  and  planes. Thus, even with idealization, Sempere’s sculpture exhibits pseudogaps—not full gaps. We stress that, for any value of the period, there is no acoustic gap for f ⩽ 30%; magnitude of the gap, for f>30%, is inversely proportional to the period of the system. Moreover, if the filling fraction exceeds 40%, a second gap, higher in frequency, opens up. In addition, we propose the fabrication of a multiperiodic system in tandem that could create a huge hole in sound within the human audible range of frequencies. © 1997 American Institute of Physics.