Time discretization from noncommutativity

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