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Abstract Studies of laser-driven strong field processes subjected to a (quasi-)static field have been mainly confined to theory. Here we provide an experimental realization by introducing a bichromatic approach for high harmonic generation (HHG) in a dielectric that combines an intense 70 femtosecond duration mid-infrared driving field with a weak 2 picosecond period terahertz (THz) dressing field. We address the physics underlying the THz field induced static symmetry breaking and its consequences on the efficient production/suppression of even-/odd-order harmonics, and demonstrate the ability to probe the HHG dynamics via the modulation of the harmonic distribution. Moreover, we report a delay-dependent even-order harmonic frequency shift that is proportional to the time derivative of the THz field. This suggests a limitation of the static symmetry breaking interpretation and implies that the resultant attosecond bursts are aperiodic, thus providing a frequency domain probe of attosecond transients while opening opportunities in precise attosecond pulse shaping.