Examine this schematic, where gain is set by 3 effects.
In (1), gain is set --- almost exactly --- by ratio of Rc/Re.
In (2), we summarize the changes in Vbase, Vemitter and Vcollector, showing gain is 1.000.
In (3), we install a huge capacitor, so the Vemitter becomes nearly zero (less than 1 microvolt, or 0.000,0001 volts) at 1KHz within the audio band. The gain increases, set by Rc/reac where 'reac' is the slope of the diode equation for Vdiode/Idiode of the emitter diode.
I chose 0.018 volts because e^0.018/0.026 is 2.000X larger.
simulate this circuit – Schematic created using CircuitLab