🤯 Partials ≠ harmonics! See from 9'00" here:
The exact way that partials don't line up with mathematical harmonics is what gives a piano its sound 🤯
[See also the temperment problem]
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:
In reality, an electronic synth will produce overtones at exactly 2*440 = 880 HZ, 3*440=1320 Hz, but a piano will produce harmonics at approx ~880 Hz, approx ~1320 Hz. That delta (being not exactly at 880/1320 Hz) is the other part of what gives a piano its distinct sound.
So there are two things going on – I thinkkkkk...
1. The relative abundance of higher harmonics is the difference between a piano and a violin playing the same note.
2. How different the actual harmonics are from the mathematical exact multiples (880 Hz, 1320 Hz, etc.) are what gives an instrument its particular character (one piano vs. another piano vs. a synthetic piano).