Harmonal density Probability changes?

I have been thinking about strings vibrating. we usually see a purely elastic string in modes of vibration as states of modes. I was thinking, what if we changed the length of the string dL such that the string in continually oscillating in length; what would the harmonics do between states? what if we took:

h = harmonics frequencies(n -> inf.)

L = length of string L -> 2PI*N

gives:

velocity:
dh/dL

acceleration:
d^2h/d2L^2

[satisfying the wave equation]

coming to the conclusion:
" If you create continuous change in the length of a string, making the string vibrate proportional to the energy stored within the string, approaching harmonics in all dimensions(L, cos(wt),isin(wt)).

We see in this case, Harmonics could be treated as: potential energies (probabilities) that give back density of states within the string action."