  The ground states of the frustrated pyrochlore oxide
Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ have been studied by inelastic neutron scattering
experiments. Three single-crystal samples are investigated; one shows no phase
transition ($x=-0.007<x_{\text{c}}\sim -0.0025$), being a putative quantum
spin-liquid (QSL), and the other two ($x=0.000, 0.003$) show electric
quadrupole ordering (QO) below $T_{\text{c}} \sim 0.5$ K. The QSL sample shows
continuum excitation spectra with an energy scale 0.1 meV as well as
energy-resolution limited (nominally) elastic scattering. As $x$ is increased,
pseudospin wave of the QO state emerges from this continuum excitation, which
agrees with that of powder samples and consequently verifies good $x$ control
for the present single crystal samples.
