I would really like to do this completely electrically with no computers/micro-controllers involved.
Who are you as a newbie, who admittedly "don't know much about electronics," to come here and tell the experts on this forum how to solve your problem? What does it mean to "do this completely electrically?" This whole forum is about how to do things electrically using appropriate technology, and that sometimes means computers/micro-controllers are required.
We are not about hand-waving here, where you make a non-nonsensical statement such as " I assume this can be done with a variable resistor." Why would you assume anything when you have no idea what a solution would be? Why would you even assume a solution exists when you can not state your requirements clearly and unambiguously? Let us start with a quote from your original post:
How can I build a circuit that receives a sound signal(not a pure frequency) and outputs a modified signal so that the properties of the sound are kept but the main frequency is changed and all it's overtones are changed respectively?
What, precisely, does this mean? If the properties of the sound are kept, but the main frequency and all it's overtones are changed, what exactly are those properties that are NOT changed? What is a modified signal, and how could it possibly keep the properties of the original sound if the sound is modified? What, exactly, is modified in the original sound? Why does this modification not change the properties of the sound? How do you determine or specify what the main frequency is? Is this the frequency with the loudest amplitude? The frequency that occurs most often?
Let me pose a hypothetical: suppose you are listening to someone singing but you would like them to sing in another key, higher or lower. Most professional singers can easily shift to a different key, thereby changing their "main frequency and all its overtones". But no one can sing in any arbitrary key. That is why there are basses, tenors, sopranos, and the like. Everyone who sings has a particular range of notes which they can sing comfortably. But along comes
@peleg68 with his "magic box" and it allows anyone to sing in any key! Just hold up your pitch-pipe and play a note to set the key and then start singing. The "magic box" will do all the work for you, converting your singing to whatever key you have selected... all done purely electrically without the use of computers/micro-controllers. You see, it's all magic! Never once did his hands leave his arms or his body! Pay the man!
The circuit also needs to be able to "convert" to different frequencies, I assume this can be done with a variable resistor.
Well of course you would assume that. After all it is a "magic box". Either dial in the variable resistor or use the pitch-pipe option (extra cost for that model) to "convert" to different frequencies. No problemo.
I'm a newbie, I don't know much about electronics, I have an idea for a project and I need help. Thanks in advance!
You're welcome. We cater to newbies here, but ideas are a dime a dozen. Rather than make uninformed assumptions about how to solve a problem, you need to tell us
what you want to do, not set out limitations on
how to do it. If you knew how to do it, you wouldn't be here asking.
... But, suppose for a moment I managed to isolate the fundamental frequency and the harmonics, how can I change their frequency? ... .
The most common way is to heterodyne the spectral bandwidth of the fundamental and the harmonics with a local oscillator, shifted higher or lower in frequency with respect to the fundamental. The result will be a spectrum of frequencies that is the sum of the local oscillator frequency and the original spectrum of frequencies, as well as another spectrum of frequencies that is the difference between the local oscillator frequency and the original spectrum of frequencies. You then apply a band-pass filter to select which spectrum you want.
Note that this is NOT what you would do to shift the key someone sings in, but that is my hypothetical.