High-brightness sources of coherent and few-cycle-duration light waveforms with spectral coverage from the ultraviolet to the terahertz would offer unprecedented versatility and opportunities for a wide range of applications from bio-chemical sensing(1) to time-resolved and nonlinear spectroscopy, and to attosecond light-wave electronics(2,3). Combinations of various sources with frequency conversion(4,5) and supercontinuum generation(6-9) can provide relatively large spectral coverage, but many applications require a much broader spectral range(10) and low-jitter synchronization for time-domain measurements(11). Here, we present a carrier-envelope-phase (CEP)-stable light source, seeded by a mid-infrared frequency comb(12,13), with simultaneous spectral coverage across seven optical octaves, from the ultraviolet (340 nm) into the terahertz (40,000 nm). Combining soliton self-compression and dispersive wave generation in an anti-resonant-reflection photonic-crystal fibre with intra-pulse difference frequency generation in BaGa2GeSe6, the spectral brightness is two to five orders of magnitude above that of synchrotron sources. This will enable high-dynamic-range spectroscopies and provide numerous opportunities in attosecond physics and material sciences(14,15). Using a gas-filled anti-resonant-reflection photonic-crystal fibre, a high-brightness table-top source of coherent carrier-envelope-phase-stable waveforms is demonstrated across seven octaves (340 nm to 40,000 nm) with ultraviolet peak powers up to 2.5 MW and terahertz peak powers of 1.8 MW, without the need for changing nonlinear crystals.