The angular lower bound does not correspond to the Robertson lower bound in the range of coordinate variable and the correlation form between the pair of uncertainties. In addition, the pair of angular uncertainties in a singular light beam is unevaluated. Moreover, these two uncertainties are independent of n-fold symmetry of azimuthal intensity that are with the two invariable types in a light beam. Herein, we report the smaller difference between mean OAM and the product of azimuthal phase-gradient of beam cross-section and ℏ, the larger azimuthal coordinate range of one periodic helical wavefront in a set of numerous singular light beams, each of which utilises the superposition comprising two fractional OAM light beams that have a difference of δ in the azimuthal phase-gradient. This is attributed to the angular uncertain principle as an uncertainty relation between the pair of periodically angular uncertainties that is defined with the sub-n-fold periodicity of a light beam by a constant bound between 0.184ℏ and 0.204ℏ. This periodically angular lower bound corresponds to the Robertson lower bound for the infinity range of the coordinate variable and the constant correlation between the pair of uncertainties; however, it is stronger by 2.45 times of magnitude at least. Moreover, we quantitatively estimated the unevaluated OAM uncertainty in a singular light beam by using the periodically angular relation. We demonstrate that the OAM uncertainty is a monotonic function of the azimuthal phase-gradient difference δ, 0 ≤ δ ≤ n, in this singular light with identically mean OAMs of 0 and nℏ/2.