  A cluster of spins $1/2$ of a finite size can be regarded as a basic building
block of a spin texture in high-temperature cuprate superconductors. If this
texture has the character of a network of weakly coupled spin clusters, then
spin excitation spectra of finite clusters are expected to capture the
principal features of the experimental spin response. We calculate spin
excitation spectra of several clusters of spins $1/2$ coupled by Heisenberg
interaction. We find that the calculated spectra exhibit a high degree of
variability representative of the actual phenomenology of curates, while, at
the same time, reproducing a number of important features of the experimentally
measured spin response. Among such features are the spin gap, the broad peak
around $\hbar \omega\simeq (40 - 70)$ meV and the sharp peak at zero frequency.
The latter feature emerges due to transitions inside the ground-state multiplet
of the so-called "uncompensated" clusters with an odd number of spins.
