The observations of the spectrum of atmospheric motions over the range of periods from a few minutes to many hours are considered that have been made with stratosphere-troposphere/mesosphere-stratosphere (ST/MST) radars in the past five years. This range of periods includes the periods associated with buoyancy waves and the scale of atmospheric motions often referred to by meteorologists as the mesoscale. The spectra of horizontal and vertical velocities are considered. Their interpretation is examined in terms of buoyancy wave theory and turbulence theory. To help in interpreting these spectra some recently determined aircraft wave number spectra are presented.