The ideal laser source for nonlinear terahertz spectroscopy offers large versatility delivering both ultra-intense broadband single-cycle pulses and user-selectable multi-cycle pulses at narrow linewidths. Here we show a highly versatile terahertz laser platform providing single-cycle transients with tens of MV/cm peak field as well as spectrally narrow pulses, tunable in bandwidth and central frequency across 5 octaves at several MV/em field strengths. The compact scheme is based on optical rectification in organic crystals of a temporally modulated laser beam. It allows up to 50 cycles and central frequency tunable from 0.5 to 7 terahertz, with a minimum width of 30 GHz, corresponding to the photon-energy width of Delta E=0.13 meV and the spectroscopic-wavenumber width of Delta(lambda(-1))=1.1 cm(-1). The experimental results are excellently predicted by theoretical modelling. Our table-top source shows similar performances to that of large-scale terahertz facilities but offering in addition more versatility, multi-colour femtosecond pump-probe opportunities and ultralow timing jitter. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement