🤯 Partials ≠harmonics! See from 9'00" here:
How Distortion and Filtering Impact Wave Shape and Frequency | Music Production | Berklee Online
The exact way that partials don't line up with mathematical harmonics is what gives a piano its sound 🤯
[See also the temperment problem]
Why It's Impossible to Tune a Piano
A piano string is actually vibrating with its fundamental freq. and superpostion of higher harmonics, see last drawn image here:
Every real-world instrument playing a note also has various amounts of higher overtones. The instrument cannot make "lower" harmonics – only higher frequencies are layered on top.
What we hear is a sum of all the frequencies produced. Our ear picks out the lowest freq. peak as the main "pitch", and this peak (surely) has the highest amplitude too.
The difference between a clarinet playing an "A", a piano playing an "A" and a violin playing the same "A" is the relative abundance of the various higher overtones/partials/harmonics.
Example: a tuning fork has very low-amplitude overtones (hence why it has such a "pure" sound).
****For now, I'm still confused about the difference between perfect partials (mathematical exact integers) and the real-world harmonics instruments produce. (I read about equal temperament every few years, and it still confuses me.)
From Loudon Sterns' video: