I see that nobody wants to take a stab at my three questions.
I'll answer by asking you to perform a couple of experiments which, hopefully, your hypothesis will be able to explain.
(1). Raise the damper on E3 using the sustain pedal. Play E4. What do you hear? Why?
(2). Raise the damper on E4. Play E3. What do you hear? Why?
(3). Raise the damper on E3. Play E5. What do you hear? Now play E4. What do you hear now? Explain your observations.
Play a 200Hz sine tone into a loudspeaker. Describe the motion of the cone.
Play a 400Hz sine tone into a speaker. Describe the motion.
Now play both the 200Hz and 400Hz sines at the same time. What do you hear? How is the cone moving?
Using Audacity, generate an anti-aliased square wave at 0.5 amplitude and 200Hz. Now add another track and generate a 601Hz sine wave at amplitude 0.5. Play both tracks back simultaneously. What do you hear? Why?
Pluck a guitar string at different points along its length. Explain why the timbre changes.
Why do piano manufacturers set the hammer strike point where they do. How does this affect the tone? Why?
Please explain all of your observations above using your hypothesis.
As for the pitch of a note - do you mean measured or perceived? You can experiment with this with inharmonic tones using audacity with various relative amplitudes, including setting the fundamental to zero, or with an additive synthesizer.