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And yet, musical instruments are tuned according to a precise mathematical relationship, each note having a well-defined frequency, also called pitch.
Sounds nice, neat and fine (my three suburban adjectives), but like most things that sound nice, neat and fine, it is perhaps not really true.
At the highest levels, musicians often manipulate pitch by ear in fine variations depending on the situation and their on-the-fly understanding of how it affects the audience and fits in the music. i.e., how it affects human perception. They might play a shade sharp to stand out a little, or adjust pitch to adapt to the kinds of instruments being played and how they best sound together. On a less elevated level, if you've ever tried to tune a guitar and really thought about what you were doing you may have learned the hard way that it's often a bundle of compromises up and down the fret-board. And as you may well know to some degree, pianos are tuned to kind fit in with other instruments and within their own harmonics six one and half-dozen the other, so to speak (i.e., "temperament tuning," as opposed to "just tuning") https://en.wikipedia.org/wiki/Musical_temperament. Some of this is discussed here. . . https://www.audiosciencereview.com/forum/index.php?threads/missing-fundamental.18930/
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