The "chorus" effect is commonly used to enrich a sound. The effect gets its name from the way that a chorus of people singing or speaking in unison sounds different from a single person. By extension, a group of violins sounds different from a single violin (even though we don't call a violin section a "chorus"), and the same effect even takes place inside a piano because most of the hammers strike two or three strings tuned in unison rather than a single string.
If you want to make an oscillator with unstable pitch, you can modulate the pitch of the oscillator using a noise signal as an exponent with a base of 2, and applying that as a multiplier to vary the fundamental frequency. In that way, when the noise ranges from -1 to +1, it will cause a pitch variation of ±1 octave, whatever the fundamental frequency of the oscillator. Divide the amplitude of the noise by 1200 if you want to be able to represent pitch variation in cents.