  We use inelastic neutron scattering to study the low energy spin excitations
in moderately doped non-superconducting Fe$_{1.01}$Te$_{0.72}$Se$_{0.28}$. The
spin excitations in this system contain components near (0.5,0,0) and
(0.5,0.5,0) in a-b plane reciprocal lattice units using tetragonal unit cell
notation (a=b=3.772 \AA and c=6.061 \AA). At low energies the scattering is
centered around (0.5,0,0). With increasing energy, the spectral weight of low
energy spin excitations centered around (0.5,0,0) abruptly shifts around 3 meV
to the incommensurate spin excitations centered around (0.5,0.5,0). However
both types of spin fluctuations exhibit the identical temperature dependence.
These results indicate that the (0.5,0,0) type spin excitations and the
incommensurate excitations around the (0.5,0.5,0) position have a common origin
and both must be taken into account to understand the nature of magnetism and
superconducting pairing in the iron chalcogenides.
