There are reasons why analog synths are largely obsolete today, and the main one is that making a good VCO that stays in tune over a wide range of voltages and temperatures is super difficult. I suggest an alternative, hybrid approach.
Use a simple microcontroller, either with the built in DAC or external audio DAC, as your "oscillator". The input to the MCU could be an analog voltage to the internal ADC, MIDI data, or some other digital data. The output would be a sine wave of the correct frequency. The output then goes to your analog circuitry of choice.
Be sure to run the MCU off of a real XTAL or quartz oscilator and not from the internal oscillator. The internal oscillator is not accurate enough to keep things in tune.
The cool thing about this approach is that you can easily output things other than sine waves. Square, triangle, sawtooth, or something "custom" is just as easy as a sine wave. This gives your analog filters more harmonics to play with and create more interesting and useful sounds. Oh, and it is fairly low power when compared to the typical ways to do VCOs.
The first "digital" synths in the 1980's used this hybrid approach and is really the main technological advancement that made synths have a wider market appeal-- at least until we have the processing power to do it entirely in the digital domain.
There is a calculator on this website here. Here are the results for the two scenarios of: -
- input voltage = -10V, o/p = 0V
- input voltage = +10V, o/p = +5V
I've arbitrarily chosen R1 to be 1K and I knew from experience that V2 needs to be half the range of the output requirements so I set that to 2.5V. By simple examination of range of input voltages to range of output, the gain has to be 0.25.
As you can see, both scenarios produce the same result of R2 = 250ohms, R3 = 1kohm and R4 = 250ohms.
Best Answer
R3 connects to the half rail supply but consider that it could be on its own half rail supply - instead of using one 8k2 for R3, use two 16k4 (or nearest preferred value); one down to ground and one up to 9V.
Ditto R11 - it can become two 16k2 resistors in the same way. The two half-rail generators are now independant.
About noise and interference
The proposal I've made will neither improve nor reduce the effects of noise and fluctuations on the 9V power supply. However this type of design could benefit from 100uF decoupling caps on the 9V near these chips.