Emitter resistor - why?
This transistor is used as a converter from voltage to current, changing the frequency of the oscillator with the input voltage. Notice how the capacitor C1 is very quick charged through the diode D2 and discharged only by the collector current of T1.

So, the frequency of the oscillator is proportional to the collector current of T1. But in so designed schematic, the collector current is not proportional to the input voltage. BJT, without negative feedback is highly non-linear device. 

Adding emitter resistor will improve the linearity of the conversion. In this case, the base resistor should be omitted.

But the best approach is to use IC2A together with the T1 as a highly linear voltage to current converter with negative feedback:







simulate this circuit &ndash; Schematic created using CircuitLab

This converter is only as an idea. It can be implemented as inverted as well.