In this paper, we devise a novel array beampattern synthesis algorithm, namely, without lobe level mask (WLLM), to avoid specifying a possibly improper or infeasible pattern mask by minimizing the ratio of the maximal sidelobe level to the minimal mainlobe level. To solve the resultant nonconvex and nonlinear fractional programming, we introduce auxiliary exponent variables to separate the numerator and denominator, and simplify each of the corresponding subproblems as a special single-variable optimization problem with a piecewise objective function and the constraints are removed via introducing unitstep functions. We also analyze the convexity or concavity of each piecewise function to compute the corresponding local minimum from which the global minimum can be obtained. Furthermore, our developed method is extended for solving the phase-only and constant modulus pattern synthesis problems. Numerical examples show that the WLLM beampattern synthesis methods can attain sufficiently low sidelobe level relative to the mainlobe level, and is suitable for arbitrary array configurations.