We have discovered rotary resonances between rf field strength, omega (1), and magic-angle spinning (MAS) frequency, omega (R), which dramatically enhance the sensitivity of triple quantum preparation and mixing in the multiple-quantum MAS experiment, particularly for quadrupolar nuclei having low gyromagnetic ratios or experiencing strong quadrupole couplings. Triple quantum excitation efficiency minima occur when 2 omega (1) = n omega (R), where n is an integer, with significant maxima occurring between these minima. For triple quantum mixing we observe maxima when omega (1) = n omega (R). In both preparation and mixing the pulse lengths required to reach maxima exceed one rotor period. We have combined these rotary resonance conditions into a new experiment called FASTER MQ-MAS, and have experimentally demonstrated a factor of 3 enhancement in sensitivity in comparison to conventional MQ-MAS. (C) 2001 American Institute of Physics.