  This work investigates the suppression of individual harmonics,
simultaneously affecting specific even and odd orders in the high-harmonic
spectra generated by strongly tailored, two-colour, multi-cycle laser pulses in
neon. The resulting spectra are systematically studied as a function of the
electric-field shape in a symmetry-broken ($\omega$-$2\omega$) and
symmetry-preserved ($\omega$-$3\omega$) configuration. The peak suppression is
reproduced by macroscopic strong-field approximation calculations and is found
to be unique to symmetry-broken fields ($\omega$-$2\omega$). Additionally,
semi-classical calculations further corroborate the observation and reveal
their underlying mechanism, where a nontrivial spectral interference between
subsequent asymmetric half-cycles is found to be responsible for the
suppression.
