2nd harmonic is double that of the fundamental, so if a piccolo’s fundamental is 4.2khz
2nd harmonic is 8.4khz,
3rd is 12.6khz
4th is 16.8khz
5th is 21khz
6th is 25.2khz
7th
8th
ect
ect
Destroy any of these, and you have destroyed it’s natural harmonic decay, your left with "gaps" in the music, which is a common Class-D complaint, as they have output filters to rid the switching noise that create phase shifts down to 3-5khz.
Like when you puck a guitar string, it vibrates faster and faster as it decays away, stop it or change it and you've killed the natural harmonic decay.
Cheers George