  We measure and compare the pattern speeds of vertical breathing, vertical
bending, and spiral density waves in two isolated N-body+SPH simulations, using
windowed Fourier transforms over 1 Gyr time intervals. We show that the pattern
speeds of the breathing waves match those of the spirals but are different from
those of the bending waves. We also observe matching pattern speeds between the
bar and breathing waves. Our results not only strengthen the case that,
throughout the disc, breathing motions are driven by spirals but indeed that
the breathing motions are part and parcel of the spirals.
