We present ac susceptibility measurements with the frequency spanning three orders of magnitude on single grain, icosahedral R–Mg–Zn (R = rare earth) quasicrystals. The freezing temperature in Gd-based, Heisenberg spin glasses in this family increases by ∼2% with a frequency increase from 10 Hz to 10 kHz, whereas the freezing temperature in the non-Heisenberg members of the family is significantly more responsive to the frequency change (by 16–22%), suggesting that an additional magnetic anisotropy distribution in the non-Heisenberg spin glasses causes changes in the low frequency magnetic dynamics.