  The Berezin-Klauder-Toeplitz ("anti-Wick") quantization or "non-commutative
reading" of the complex plane, viewed as the phase space of a particle moving
on the line, is derived from the resolution of the unity provided by the
standard (or gaussian) coherent states. The construction properties of these
states and their attractive properties are essentially based on the energy
spectrum of the harmonic oscillator, that is on the natural numbers. This work
is an attempt for following the same path by considering sequences of
non-negative numbers which are not "too far" from the natural numbers. In
particular, we examine the consequences of such perturbations on the
non-commutative reading of the complex plane in terms of its probabilistic,
functional, and localization aspects.
