String age and harmonics

It is common knowledge that new strings, especially ones that are overwound (that is, with a helical coiled winding around a cylindrical core,  like the three  lowest -frequency ones on a steel string guitar)  don't sound right.  They are 'metallic', or 'jangly'. Over time they improve, until ultimately they start to sound 'dead'.  What is going on?

Our measurements show a large change in the harmonic structure when comparing a new and an old string: The new string produces more power in the high harmonics, and is less stiff to bending.  With age the bending stiffness increases, and the power in the high harmonics drops.

We wanted to know if, going from old to new string,  the associated measured harmonic amplitude changes were consistent with what we hear.  A simple model with one free parameter to control the high harmonic content suggests that indeed what we hear is what we measure: Too many high harmonics don't sound good.

In the examples below, the total energy in each simulated 'pluck' is held constant. Case 2, our 'standard',  has about 4% of the total energy above 1 kHz.  Case 1 has about 8%  of the energy above 1 kHz, and case 3 has about 2% of the energy above 1 kHz.