Why It's Impossible to Tune a Piano

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Pianos can't be perfectly tuned - it's a mathematical fact!
Thanks to http://www.audible.com/minutephysics for supporting MinutePhysics.

Equal tempered tuning: https://en.wikipedia.org/wiki/Equal_temperament

Just Tuning: https://en.wikipedia.org/wiki/Just_intonation

Harmonics: https://en.wikipedia.org/wiki/Harmonic

Pythagorean vs Just Tuning: https://www.youtube.com/watch?v=QaYOwIIvgHg
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https://www.youtube.com/watch?v=1Hqm0dYKUx4