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๐คฏ Partials โ 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 ๐คฏ

[See also the temperment problem]

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A piano string is actually vibrating with its fundamental freq. and superpostion of higher harmonics, see last drawn image here:

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Every real-world instrument playing a note also has various amounts of higher overtones.
The instrument cannot make "lower" harmonics โย 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.)*ย

From Loudon Sterns' video:

In reality, an electronic synth will produce overtones at

*2*440 = 880 HZ, 3*440=1320 Hz, but a piano will produce harmonics at***exactly***~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.***approx**ย

So there are two things going on โ 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*harmonics are from the mathematical***actual***multiples (880 Hz, 1320 Hz, etc.) are what gives an instrument its particular character (one piano vs. another piano vs. a synthetic piano).***exact**ย