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As I understand it, the formant is the difference between the interval from the harmonic series, and the interval using whatever temperment you're in. Piano-notes are in equal temperment. String players, and some wind instruments allow you to play the "in-between" notes selectively (like a true major third, unlike the horrid thing a equal temperment produces) giving you a powerful emotional tool

I wouldn’t go as far as to say the major third from equal temperament is a horrid thing, but it sure doesn’t hit as well as a true major third

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