Evidence of discrete acoustic Rayleigh wave turbulence (DARWT) is reported on the free surface of complex viscoelastic materials under monochromatic excitation. These surface elastic non-linear Rayleigh waves exhibit dispersionless dynamics governed by bulk shear rigidity at coexistence with dispersive capillary waves supported by surface tension. Using Laser Doppler Vibrometry (LDV), the discrete Kolmogorov-Zakharov (KZ) spectrum is measured, characterized by a power-law envelope in an inertial cascade of discrete harmonics. When shear rigidity dominates, KZ-spectrum characterized by an ω