Here is my problem: suppose I am a composer you have contracted to create any sheet music I dream of with the unique condition it is not pure silence and that I don't stipulate the instrument section (which means, don't specify the timbre). Suppose you are the one who is in charge of the execution of the music, and you have in your disposition any kind of instrument, room, high tech equipment you ask — and suppose also that you hate me. Could you just by changes on the non-fundamental harmonics and non-fundamental frequencies aspects of the sound wave change my original composition so that it sounds something like Baby Shark melody or whatever you want?
Well, I will try to put this question on better words.
What I learned about timbre is that it is defined by the wave format and the envelope of the sound. So the same fundamental frequency can have different wave formats, a perfect sine wave or some irregular pattern, like a saw, or other things. Others definitions seems to point that timbre is about the harmonics analysis of the sound. I think these two definition are connected, because the wave format determines the harmonics of a sound (is that right?).
But if we just think about the sound wave, it could be mathematically decomposed on a sum of sine waves (I remember people saying this is the Fourier sum). So, in thesis, you could reproduce an approximation of the timbre of an instrument on a computer by this process. I guess this is what people do when they try to imitate a violin on a computer. Equivalently, I think that in theory you could control also this wave parameters so that you could create a sound corresponding to any wave format you want. I think this is what people who synthesize sounds do.
I understand also that when you play two instruments at the same time the air molecules make some kind of sum of the waves and this is why you could have the destruction phenomena of waves that cancel each other and produce silence.
Now this is my thought process to arrive at this question: I think you could, given a sound source, to change a second sound source so that the sum of the two waves produces another fundamental frequency different of the first instrument, because you can cancel the fundamental frequency by the above process and just let the harmonics of the two sounds sources audible. I think the question is if there is some way to make a destructive interference of the fundamental frequency, and resonance of the components of the sound wave, such that in the sum of the waves you could determine the fundamental frequency of each individual instrument, even if this fundamental frequencies of the instruments were determined before they were played.
But if you could do this, perhaps with a sufficient number of sound sources (you could even repeat the same note if necessary),you could change the fundamental frequency of the first instrument when you sum up all the waves of the sound sources to some other harmonics you determine.
But this is all just second hand information I received, and this is why I am here to ask you if this makes sense. The important thing to me is not to have an answer, I just to understand if what I am thinking makes sense, what are my errors, and how can I do to make a better question. Besides, I think interesting to think what kind of parameter you could relax in this experiment to have a better result. For example, if someone have all the power of the sheet music and the timbre of the music, how much could he play with this interference so that he make a music with harmonics.