I think many people tried to help you and to extract what you actually want to do. There is nothing people can do if you don’t answer the questions.
No one seems to know (myself included) what YOU mean with operating frequency. Nobody else is using that term, hence nobody knows what you mean.
It might be futile, since the answers were given before, so I might repeat what others said before, apologies if I don’t reference each one’s input.
Pitch and frequency are connected values.
A higher pitch means a higher frequency.
The third important parameter is speed, how fast the samples are produced. If you produce the samples faster, the frequency AND the pitch will be higher. To achieve that people use a resampler, means to change the samplerate effectively changing the speed the individual samples are produced.
This changes the duration of the signal. In an instrument that can be acceptable depending on use case, in a realtime effect this is impossible, because your effect needs to produce exactly the same number of samples it consumed. Changing the duration while keeping the pitch or changing the pitch while keeping the duration is called elastic audio (there are a few names for different strategies to achieve this).
That’s the reason why everybody is stumped with your reiterated question, how you want to change the frequency and the pitch independently, when they are the same thing.
Can you follow and maybe clear that up?
Feel free to ask further questions (except the question you asked that no one can answer )