  Magnon frequency comb provides opportunities for exploring magnon nonlinear
effects and measuring the transmission magnon frequency in magnets, whose
controllability becomes vital for modulating the operating frequency and
improving the measurement accuracy. Nevertheless, such controllable frequency
comb remains to be explored. In this work, we investigate theoretically and
numerically the skyrmion-induced magnon frequency comb effect generated by
interaction between the magnon excitation mode and skyrmion breathing mode in
synthetic ferrimagnets. It is revealed that both the skyrmion breathing mode
and the magnon frequency gap closely depend on the net angular momentum
{\delta}s, emphasizing the pivotal role of {\delta}s as an effective control
parameter in governing the comb teeth. With the increase of {\delta}s, the
skyrmion size decreases, which results in the enlargement of the breathing
frequency and the distance between the comb teeth. Moreover, the dependences of
the magnon frequency gap on {\delta}s and the inter-layer coupling allow one to
modulate the comb lowest coherent frequency via structural control.
Consequently, the coherent modes generated by the comb may range from gigahertz
to terahertz frequencies, serving as a bridge between microwave and terahertz
waves. Thus, this work represents a substantial advance in understanding the
magnon frequency comb effect in ferrimagnets.
