  We show that a particular noncommutative geometry, sometimes called angular
or $\rho$-Minkowski, requires that the spectrum of time be discrete. In this
noncommutative space the time variable is not commuting with the angular
variable in cylindrical coordinates. The possible values that the variable can
take go from minus infinity to plus infinity, equally spaced by the scale of
noncommmutativity. Possible self-adjoint extensions of the "time operator" are
discussed. They give that a measurement of time can be any real value, but time
intervals are still quantized.
