I’m so glad to see harmonics well discussed in the comments, and was so disappointed to see it not mentioned once in the article. Putting aside percussive differences between instruments or playing style (which also have harmonic effects but aren’t always perceived that way), the difference between a “frequency” that sounds different but measures the same is generally because there are many less prominent frequencies behind the dominant one. That’s why some sounds twang and other sounds thunder. That’s why some coated strings sound dull. That’s why loose drum heads sound loose. That’s why a sawtooth or sine wave sounds synthetic: it is, nothing in real life sounds like that.
I can’t speak to the ocarina but a violin??? It’s an instrument infamous for screechy off sounds. Those are caused by unexpected friction on the strings amplifying or even making harmonics dominant. The most prominent sound wave may mimic a sawtooth because of the mechanics of a bow (I don’t know, just trusting you on this), but every bit of loose fiber on the bow and every inconsistency in rosin and every physical variation on the surface of the string can produce harmonics before any sound hits the curves of the body, which produces yet more.
