non-SINUSoidal

I thought that in reality the sound of musical instruments is never static in height. Let it be in a microscale, but it always shifts. The piano string also "stirs" with overtones. If the sound moves in height, then it accelerates and slows down in this movement. There is no static frequency and there is no static linear acceleration. If the wave is graphically displayed by a sinusoid, then when the altitude acceleration vector changes, it must lose its sinusoidal form:

How is this manifested in the synthesis?
And even if it's almost invisible, but suddenly, it's just as important as the presence of iodine, for example, in the body, which in us is 0.00004% ...