  We report experimental realization of a quantum time quasicrystal, and its
transformation to a quantum time crystal. We study Bose-Einstein condensation
of magnons, associated with coherent spin precession, created in a flexible
trap in superfluid $^3$He-B. Under a periodic drive with an oscillating
magnetic field, the coherent spin precession is stabilized at a frequency
smaller than that of the drive, demonstrating spontaneous breaking of discrete
time translation symmetry. The induced precession frequency is incommensurate
with the drive, and hence the obtained state is a time quasicrystal. When the
drive is turned off, the self-sustained coherent precession lives a
macroscopically-long time, now representing a time crystal with broken symmetry
with respect to continuous time translations. Additionally, the magnon
condensate manifests spin superfluidity, justifying calling the obtained state
a time supersolid or a time super-crystal.
