Modulation Index

The function $I(t)$, called the modulation index envelope, determines significantly the harmonic content of the sound.

In fact, the value of $I$ determines the maximum amount by which the instantaneous frequency deviates from the carrier frequency $f_c$.

Since $I(t)$ is actually function of time, this deviation, seen as sidebands at multiples of $f_m$ in the synthesized sound, may vary with time.

The fact that $I(t)$ is time varying, allows us to change the timbre of a sound over time, a known characteristic of musical sounds.